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The book presents high-quality papers presented at 3rd International Conference on Applications of Fluid Dynamics (ICAFD 2016) organized by Department of Applied Mathematics, ISM Dhanbad, Jharkhand, India in association with Fluid Mechanics Group, University of Botswana, Botswana. The main theme of the Conference is "Sustainable Development in Africa and Asia in context of Fluid Dynamics and Modeling Approaches". The book is divided into seven sections covering all applications of fluid dynamics and their allied areas such as fluid dynamics, nanofluid, heat and mass transfer, numerical simulations and investigations of fluid dynamics, magnetohydrodynamics flow, solute transport modeling and water jet, and miscellaneous. The book is a good reference material for scientists and professionals working in the field of fluid dynamics.



Fluid Dynamics


Unsteady MHD Nanobioconvective Stagnation Slip Flow in a Porous Medium Due to Exponentially Stretching Sheet Containing Microorganisms

This communication deals with the numerical investigation of bioconvection induced by an unsteady MHD stagnation point flow of a nanoliquid containing suspension of microorganisms over a stretching sheet. The sheet is stretched in an exponential fashion and set at the right side of porous medium saturated with nanofluid, and permeability of porous medium is considered to have a specified form. The setup deals with the velocity slip and thermal slip at the sheet surface. Here, water is considered as the carrier liquid. Similarity transformations are used to convert the governing coupled nonlinear partial differential equations into ordinary differential equations and solved numerically by employing implicit finite difference scheme known as Keller box method. The effects of nanofluid parameters and bioconvection parameters on non-dimensional velocity, temperature, nanoparticle concentration, and motile microorganism concentration are presented through graphs. The effects of related parameters on local skin friction, Nusselt number, Sherwood number, and density number of microorganisms are exhibited through tables. The substantial influence of bioconvection parameters is noticed on the profiles of velocity, temperature, nanoparticle volume fraction, and density of microorganisms.

R. Kumar, S. Sood

MHD Free Convection Flow Past an Exponentially Accelerated Inclined Plate Embedded in Porous Medium

The consequences of radiation absorption and chemical reaction in the presence of heat generation on a MHD unsteady laminar flow with mass and heat transfer of an electrically conducting, incompressible, and viscous fluid over an accelerated exponentially inclined vertical moving porous plate in a porous medium are analyzed in closed form. A perfect solution for this flow problem was obtained by resolving the resulting governing equations by the technique of Laplace transforms. The exact solutions for profiles of concentration, temperature, velocity, and the gradient of velocity are presented, and the effects of these profiles for several values of various arguments are discussed through graphs.

R. Swetha, J. Prakash, G. Viswanatha Reddy, S. Vijaya Kumar Varma

Radiation Effect on MHD Convective Flow of Nanofluids over an Exponentially Accelerated Moving Ramped Temperature Plate

The effect of thermal radiation on magnetohydrodynamic free convective flow of incompressible and viscous nanofluids, which is electrically conducting, over an exponentially accelerated moving ramped temperature plate is studied. The water-based nanofluids which contain the nanoparticles of copper, alumina, and titanium oxide are taken into consideration. The mathematical model of the problem is formulated by applying the nanoparticle volume fraction model. The governing equations for the flow, subjected to the associated conditions, have been solved analytically by Laplace transform method. Expressions of nanofluid velocity, temperature, shear stress, and Nusselt number have been obtained in compact form. Effects of controlling physical parameters on nanofluid velocity and temperature have been displayed using various graphs, whereas, for the engineering perspective, numerical values of shear stress are presented in table.

S. M. Hussain, H. J. Joshi, G. S. Seth

Free-Stream-Induced Unsteady MHD Flow with Hall Effect over Permeable Plate in a Rotating System

Analytical investigations of unsteady magnetohydrodynamic flow with Hall effect of a viscous, incompressible and electrically conducting fluid past a porous flat plate with impulsively moving free stream in a rotating frame of reference are carried out. Exact solution for the primary and secondary fluid velocities is obtained in closed form by Laplace transform technique. The expressions for skin frictions due to primary and secondary flows are also derived. The numerical values of the primary and secondary fluid velocities are displayed graphically, whereas those of skin frictions are presented in tabular form for various values of pertinent flow parameters. Asymptotic nature of the solution is also examined, for both small and large values of time T, to understand the physics of the flow.

G. S. Seth, N. Mahto, R. Tripathi, R. Kumar

Radiation Effect on MHD Williamson Fluid Flow over Stretching Cylinder Through Porous Medium with Heat Source

In this present paper, we have investigated radiation effects on MHD Williamson fluid flow past a stretching cylinder through porous medium. MHD with Hall and ion-slip currents impact is taken into consideration. The governing PDEs are transformed into BVPs by using appropriate transformations. Shooting technique with Runge–Kutta forth-order method is used to find the solution of the problem. The effect of various parameters such as curvature parameter $$\gamma$$, heat generation parameter $$\beta$$, Hall current parameter $$\beta_{e}$$, ion-slip parameter $$\beta_{i}$$ magnetic parameter M, thermal conductivity $$\varepsilon$$, Weissenberg number $$\lambda$$, Eckert number Ec, radiation parameter K and Prandtl number Pr on momentum and thermal energy profiles are discussed and displayed graphically. Local Nusselt number and skin friction coefficient are tabulated.

Shalini Jain, Amit Parmar



Particle Size and Spacing Effects on Convective Heat and Mass Transfer of a Nanofluid in Wavy Annulus

In this paper, we attempted to study the heat and mass transfer of nanofluid flowing into a horizontal annulus whose outer cylinder is sinusoidal. Graham, Jang and Choi proposed expressions were considered. Various phenomena such as magnetic parameter (M), gap of the annulus from inner cylinder to mean position of outer wavy surface (s), heat source parameter (Q H ), and Darcy parameter (1/D) are considered. The governing equations are solved by R-K sixth order and shooting methods. The enhancement of temperature is observed for reduction in gap of the annulus.

V. P. N. Srikanth Gorti, Srinivas Gosukonda

Hydrodynamics of Non-Newtonian Spriggs Fluid Flow Past an Impulsively Moving Plate

One of the fundamental problems in unsteady viscous flows is that of impulsively started motion of a body in an infinite fluid medium which is referred as Stokes’s first problem. On the basis of the fundamental understanding, we have developed a mechanistic modelling and thereby to improve existing technical applications. In this study, one of the particular non-Newtonian Spriggs fluid has considered that it is a truncated power law type of fluid. Flow of non-Newtonian Spriggs fluid caused by the unsteady impulsively moving plate is investigated using a similarity transformation. The use of similarity transformation reduces the unsteady boundary layer equations to linear and nonlinear ordinary differential equations governed by a non-dimensional material parameter. The effect of material parameter on velocity boundary layer is explained by an efficient and robust Homotopy Analysis Method. Variations of the velocity profile are presented graphically for distinct values of material constant. A physical interpretation is also provided. The flow past a plate has received much attention because of its major significance role in numerous disciplines which include the chemical engineering, manufacturing industry, heat conduction problems and geophysical flows (such as in earthquakes and fracture of ice sheets).

Atul Kumar Ray, B. Vasu

Effects of Heat-Generating Component Size and Porous Layer Thickness on MHD Mixed Convection Flow of Ag-Water Nanofluid Through an L-Shaped Channel

This paper focuses on the cooling of heat-generating components via MHD mixed convection flow of silver (Ag)-water nanofluid through an L-shaped channel with a porous inner layer. In this channel, four heat-generating components are located on the channel wall opposite to the porous layer. The governing equations with the given initial and boundary conditions are solved using the stabilized mixed finite element method based on the polynomial pressure projection technique. The effect of the thickness of the porous layer and size of the heat-generating components on fluid flow and heat transfer within the channel is investigated.

Victor Job, Sreedhara Rao Gunakala, B. Rushi Kumar, R. Sivaraj

Hall Current and Radiation Effects on Unsteady MHD Squeezing Nanofluid Flow in a Rotating Channel with Lower Stretching Permeable Wall

In analysis of present model, we have analyzed the Hall current and radiative effects on unsteady MHD squeezing nanofluid in a rotating channel. The lower wall is permeable and linearly stretching, and the upper wall is squeezing downward in the presence of MHD. By introducing similarity transformation, we get the ordinary coupled differential equation. The transformed nonlinearly coupled differential equations are solved numerically by bvp4c solver using software MATLAB. We have taken nanoparticles of copper (Cu) and alumina (Al2O3) as base fluid (water). The effect of different parameters such as magnetic field parameter M, squeezing parameter Sq, rotational parameter ω, suction parameter w0, nanofraction parameter ϕ, hall current parameter β e , radiation parameter N on velocity profile, and temperature profile is displayed through tables and graphs.

Shalini Jain, Shweta Bohra

Heat and Mass Transfer


Natural Convection of a Micropolar Fluid Between Two Vertical Walls with Newtonian Heating/Cooling and Heat Source/Sink

The aim of this paper is to investigate the natural convection of a micropolar fluid flow in two vertical walls with the Newtonian heating/cooling on one of its walls. The governing linear differential equations with their appropriate boundary conditions of the considered model are changed first into non-dimensional differential equations and boundary conditions by using the dimensionless parameters and variables. Analytic solutions of the non-dimensional differential equations have been obtained one by one for several cases of source or sink parameter. To obtain the influence of the Biot number and other physical parameters, the numerical results of the velocity, temperature, and microrotational velocity are finally shown in the graphs and table. It is found that the effect of the Newtonian heating is to increase the velocity, microrotational velocity, and rate of volume flow, while in the case of the Newtonian cooling, velocity, microrotational velocity, and rate of volume flow have decreasing tendency.

Arun Kumar Singh, A. K. Singh

Influence of Thermal Radiation and Heat Absorption of a Third-Grade Fluid in Wire Coating Analysis Through a Porous Medium

In the present study, the influence of porous matrix, thermal radiation, and internal heat absorption on wire coating using third-grade fluid like melt polymer in the presence of constant as well as temperature-dependent viscosity has been analyzed. The governing equations are solved numerically by employing fourth-order Runge-Kutta method. Models such as third-grade fluid model, Reynolds model, and Vogel’s model have been used. The results for the velocity and temperature are displayed and discussed in detail. Porous matrix has remarkable contributions in escalating the temperature whereas the effect of thermal radiation is diametrically opposite to that of porous matrix in the flow region within the die. Velocity profiles disparaged because of resistive force from medium porosity, and thereby, momentum boundary layer shrinks. Heat absorption in thermal boundary layer leads to decrease in temperature, and then, the associated thermal boundary layer thickness shrinks.

M.K. Nayak

Entropy Generation Analysis in a Vertical Porous Channel with Navier Slip and Viscous Dissipation

The intension of this paper is to investigate the effects of Navier slip and buoyancy force on the entropy in a vertical generation porous channel with suction/injection. This problem is solved analytically by perturbation technique. Closed form solutions are obtained for the fluid velocity and the temperature. The leads of slip parameter, injection/suction Reynolds number, Peclet number and Brinkmann number on the fluid velocity, temperature profiles, Bejan number, and rate of entropy generation are showed graphically and quantitatively discussed.

M. Sukumar, S. V. K. Varma, R. Swetha, R. V. M. S. S. Kiran Kumar

Effect of Newtonian Heating/Cooling on Hydromagnetic Free Convection in Alternate Conducting Vertical Concentric Annuli

This paper presents the effects of the Newtonian heating/cooling and the radial magnetic field on steady hydromagnetic free convective flow of a viscous and electrically conducting fluid between vertical concentric cylinders by neglecting compressibility effect. The derived governing equations of the model are first recast into the non-dimensional simultaneous ordinary differential equations using the suitable non-dimensional variables and parameters. By obtaining the exact solution of the simultaneous ordinary differential equations, the effects of the Hartmann number as well as the Biot number on the velocity, induced magnetic field, induced current density, Nusselt number, skin-friction and mass flux of the fluid are presented by the graphs and tables. The effect of the Biot number is to increase the velocity, induced magnetic field and induced current density in the case of the Newtonian heating and vice versa in the case of the Newtonian cooling, but the effect of Hartmann number is to decrease all above fields. Further, graphical representation shows that the velocity and induced magnetic field are rapidly decreasing, with increasing the Hartmann number, when one of the cylinders is conducting compared with when both the cylinders are non-conducting.

Dileep Kumar, A. K. Singh

Heat and Mass Transfer on Unsteady MHD Oscillatory Flow of Blood Through Porous Arteriole

We have considered the unsteady two-dimensional MHD oscillatory flow of blood in a porous arteriole under the influence of uniform transverse magnetic field in a planar channel. Heat and mass transfer during arterial blood flow through a porous medium are also studied. A mathematical model is developed for unsteady state situations using slip conditions. Analytical expressions for the velocity, temperature, and concentration profiles have been obtained and computationally discussed with respect to the non-dimensional parameters.

M. Veera Krishna, B.V. Swarnalathamma, J. Prakash

Numerical Simulation and Investigation of Fluid Dynamics


Numerical Simulation of Partially Covered Hartmann Whistle in a Sonic-Underexpanded Jet

The current study provides numerical investigation into the use of “Hartmann whistle” as an effective passive flow control device by covering the major area between the nozzle exit and cavity inlet using a cylindrical shield. The passive control is accomplished by allowing the pulsating jet to exit through two small openings in the shield so that it can be utilized for various flow control applications such as mixing enhancement, drag reduction, noise mitigation. The current study numerically investigates the effect of partially covered cylindrical shield on the shock as well as regurgitant oscillation characteristics of a Hartmann whistle when the pulsating jet exits through the two small openings of the cylindrical shield. The relevant parameters that modify the flow/shock oscillations of the Hartmann whistle are the cavity standoff distance, nozzle pressure ratio, cavity length, cavity shield, etc. The studies were performed for various standoff distances values of 10, 20, and 30 mm to demonstrate the role of standoff distance in effective flow control. The modifications in the shock as well as regurgitant oscillation features of partially covered Hartmann whistles are systematically compared using transient velocity vectors, Mach number contours, etc. for various standoff distances. The velocity vectors indicate flow diversion features near the cavity mouth as well as inflow and outflow jet regurgitant phases. The Mach contours of partially shielded Hartmann whistles indicate shock structures, zones of flow deceleration and re-acceleration. It also clearly demonstrates that the resonant oscillations are primarily driven by jet regurgitance at smaller standoff distances, but at higher standoff distances they are primarily driven by the fluid column oscillations in the shock-cells, shield as well as in the cavity zones. Thus, the current study reveals that the standoff distance is a crucial parameter that controls the strength of shock, regurgitant as well as fluid column oscillations in a partially covered Hartmann whistle in order to achieve an effectual flow control.

Arnab Samanta, S. Narayanan, Ashish Narayan, Shailesh Kumar Jha

Numerical Investigation of Hypersonic Flow Past a Spherically Blunted Nose Cone

This paper numerically investigates the flow past a spherically blunted nose cone at a hypersonic Mach number of 5.8. The present study focuses in determining the flow/shock characteristics of the nose cone such as pressure coefficient, shock detachment distance and location and shape of bow shock formed ahead of the spherically blunted nose cone etc. The shock detachment distance, pressure coefficient, location and shape of bow shock in spherically blunted cones have numerous applications in the design of high speed aerodynamic vehicles such as space shuttles, missiles, rockets etc. The design of geometric parameters in hypervelocity vehicles are very important and are highly challenging for improving its performance and hence to alleviate the aerodynamic heating. The key parameters that play a significant role in affecting the aerodynamic characteristics of nose cone are semi-cone angle, bluntness ratios etc. Therefore, the present study focuses to investigate the effect of semi-cone angles of 5° and 20° and bluntness ratios of 0.4 and 0.8, in order to understand the aerodynamic performance characteristics of the spherically blunted nose cones. The velocity vector shows the flow direction which indicate clearly the deceleration near the nose, re-acceleration through the sideways of the nose cone as well the formation of recirculation zone behind the cone base. The shape and location of the bow shock formed ahead of the nose as well as the shock detachment distance is shown with the help of the Mach number contour. It is observed that the pressure coefficient decreases rapidly up to a certain distance along the wall and thereafter it remains almost constant for both the bluntness ratios (0.4 and 0.8) and semi cone angles (5° and 20°). It is observed that there is no significant variation in the shock detachment distance observed for both the bluntness ratios (0.4 and 0.8) and semi cone angles (5° and 20°) studied. In general, it is observed that increase in temperature is more for small semi cone angles and bluntness ratios and it decreases for higher bluntness ratios and cone angles. The increase in temperature may be due to viscous dissipation which arises due to curved shocks which makes the flow rotational due to the existence of large entropy gradients. A minimum temperature is achieved for a bluntness ratio of 0.8 and 20° semi cone angle. Thus, this paper sufficiently demonstrates the effect of different bluntness ratios and semi cone angles on the aerodynamic as well as heating characteristics of a spherically blunted nose cone.

Ashish Narayan, Rakesh Kumar, S. Narayanan

Numerical Investigation of Subsonic Flow Past a Flat Plate Aerofoil

The present work numerically investigates the effect of two different trailing edge geometries such as sharp as well as blunt on the aerodynamic characteristics of a flat plate aerofoil. The modifications in the flow as well as aerodynamic characteristics of sharp and blunted trailing edge configurations of a flat plate aerofoil are systematically compared using pressure coefficient, lift coefficient, vortex shedding, etc. The study was conducted for a chord-wise Reynolds number of 4.99 × 105 at an angle of attack of 25°. The large difference in the pressure coefficient observed between the top and bottom surface in the case of blunt trailing edge as compared to sharp ones indicates that the blunted trailing edge geometry generates higher lift than the sharp trailing edge ones. It is observed from spectra that the vortex shedding for both the blunted and sharp trailing edge geometries occurs at a Strouhal number of around 0.34. The increase of energy as well as broader wake in the blunted trailing edge geometry indicates higher drag as compared to the sharp trailing edge geometry. Thus, this paper sufficiently demonstrates the effect of sharp and blunted trailing edge geometries on the aerodynamic characteristics of a flat plate aerofoil.

Shailesh Kumar Jha, S. Narayanan, L. A. Kumaraswamidhas

Compare Tornado Force Coefficients on Dome and Prism Building Using Three-Dimensional Computational Fluid Dynamics Model

Wind loads on structures have been investigated for the last five decades. For straight line (SL) wind, the forces on buildings are available from standards and wind tunnel testing. Few studies have been conducted to investigate tornado forces on cubical buildings and to distinguish between tornadic wind loads and SL wind loads. In the tornado-damaged areas, dome buildings seem to have less damage. However, few studies have been investigated to study a tornado interaction with a dome building. In this work, the forces on a dome are computed using computational fluid dynamics (CFD) for tornadic and SL wind. Then, the interaction of a tornado on a dome and a prism building are compared and analyzed. This work describes the results of the tornado wind effect on a dome building. The conclusions drawn from this study are illustrated by various visualizations. The tornado force coefficients on a dome building are larger than force due to SL wind, about 40% more in x-direction and 120% more in z-direction. The tornado maximum pressure coefficients also are higher than SL wind by 130%. The tornado force coefficients on the prism are larger than the forces on the dome, about 150% more in x-direction and about 110% more in z-direction. The tornado maximum pressure coefficients on prism also are greater, by 200%. Hence, a dome building has less tornadic load than a prism because of its aerodynamic shape.

Majdi A. A. Yousef, R. Panneer Selvam

Mathematical Study of Peristalsis in the Presence of Electrokinetic Transport in Parallel Plate Microchannel

Electrokinetic transport of fluids through microchannel by micropumping and microperistaltic pumping has much interest for many engineering, medical, and industrial applications. Motivated in part by the need of mathematical model to study the electrokinetic transport by peristaltic pumping, an analytical approach is presented. A non-integral number of wave propagation is considered for transportation of fluid bolus along the channel length. Debye-Hückel linearization is employed to find out the potential function. A non-dimensional analysis is employed to simplify the governing equations. Low Reynolds number and large wavelength approximations are taken into account. The effects of characteristic electrical double layer (EDL) thickness and maximum electroosmotic velocity on pumping characteristics are discussed by computational results.

D. Tripathi, Shashi Bhushan, Ashu Yadav, Ashish Sharma

Journal Bearing Lubrication of Power Law Fluid with Consistency Variation Including Convection

An effort is made to discuss the vital effects of temperature on hydrodynamic lubrication of journal bearing by non-Newtonian power law lubricants. Boundary surfaces are assumed to be rigid and isothermal. It is assumed that the consistency of the lubricant varies with film temperature and pressure, as considered by some researchers. The employed equations of motion and the continuity are solved numerically and analytically. For the numerical solution, Runge–Kutta–Fehlberg method is employed with adequate tolerance. The effects of temperature and pressure are analyzed through various table and graphs as functions of the consistency index of the lubricant velocity and journal velocity.

Dhaneshwar Prasad, Sudam Sekhar Panda, Venkata Subrahmanyam Sajja

Numerical Simulation of Flow Around Square Cylinder with an Inlet Shear in a Closed Channel

In this paper, two-dimensional unsteady flow of incompressible fluid past a square cylinder placed in a closed finite domain is studied in the presence of an inlet linear shear velocity profile. The flow has been investigated for Reynolds number $$Re = 100$$ and shear rate $$K = 0.0, 0.05, 0.1$$. The governing equations are solved by using the higher order compact (HOC) finite difference scheme. The purpose of the present study is to elaborate the influence of shear rate on the vortex shedding phenomenon behind the square cylinder. The results are presented in terms of streamline pattern, vorticity contours, lift–drag coefficients, and their corresponding power spectra. It is observed that the vortex shedding phenomenon strongly depends on $$Re$$ as well as $$K$$. The strength and size of vortices vary as a function of $$Re$$ and $$K$$, but not significantly for the current values of parameters.

Atendra Kumar, Rajendra K. Ray

Fluidic Logic Element Performance Calculation

The results of gas-dynamic characteristic studies of logic chips jet element are considered. The study carried out by numerical method is based on the integration of the Navier–Stokes equations. For closure of simultaneous equations in this research, the two-region hybrid turbulence model of transfer of tangential stress is used. The model of compressed viscous gas is applied. Its properties correspond to properties of air of standard atmosphere at the height of mean sea level. The main characteristics of the switching logic element output signals, depending on the influence of control signals, were found. It is shown that relative rate in the output channels depends on the relative pressure in the control channels. It is calculated the required values of pressure in control channels of logic element necessary for switching of an output signal. Because of viscous properties of working body, the Coanda effect which is used for sticking of feeding air current to channel walls for purpose of steady work logical device is realized. Zones of flow contraction are installed in channels of device

V. N. Samsonov, E. I. Kurkin, O. E. Lukyanov, V. G. Shakhov

Numerical Investigation of Extremely Viscous Short Fibers-Reinforced Multiphase Anisotropic Fluid Flow in Flat Channel

In this chapter, the parameters of molding of thermoplastics reinforced with short high-strength fibers are considered on the example of plate molding from PEEK 90HMF20 material. Modeling of thermoplastic molding was done in Moldex3D system. The setting of three-dimensional geometrical model of gating area, characteristics of system of heat supply of tool, and also molding process parameters: temperature condition, pressure, and filling time are presented. Hydrodynamic calculation of plate molding is executed. The field of distribution of casting front, temperature, and pressure is obtained. The vector field of orientation of reinforcing fibers is calculated that allows to consider anisotropy of characteristics of composite material when carrying out strength calculations. It is noted that facial layers have more ordered structure in comparison with inside layer because the fibers are turned under the influence of shear flow (so-called main effect) that confirms good agreement with carried-out calculations to theoretically known character of current. The technology of export of data about fiber orientation from Moldex3D in Digimat system is shown. This technology allows calculation of stress-strain state of structures from short-reinforced composite materials in ANSYS Mechanical using Digimat Wizard taking into account the orientation of the reinforcing fibers.

E. I. Kurkin, V. O. Sadykova

Hybrid Finite Difference-Finite Volume Schemes on Non-uniform Grid

High aspect ratio, skewness, non-orthogonality, and non-uniformity of grids have been a major issue for mesh developers for a long time. In this present work, we have taken an initial step for a numerical scheme that can handle any kind of mesh. Problems associated with non-uniformity of the grid (that can be related to aspect ratio in higher dimension) and achieving high order accuracy in those grids are discussed. A Hybrid Finite Difference-Finite Volume Method (Hybrid FD-FVM) which can retain high order accuracy on an arbitrary mesh by combining the advantage of higher order convergence property of finite difference method (FDM) and conservativeness property of FVM is presented. Though higher order version of FVM is available, they work well only on uniform meshes or slightly perturbed unstructured grid or gradually stretched grid. Smooth variation in meshes is recommended for CFD packages to obtain good accuracy—the reasons are discussed in the paper. FVM on the arbitrary mesh is at most second order accurate and are generally about first order accurate. Our method ensures higher order convergence on arbitrary non-uniform non-overlapped mesh but does not ensure complete numerical conservativeness on the non-uniform mesh for problems without shocks. The present work does not use volume averaging which is commonly used in FVM. The volume averaging works well in uniform mesh and can severely affect the result on the arbitrary varying non-uniform mesh. That also discussed here.

A. Arun Govind Neelan, Manoj T. Nair

Numerical Solution of Unsteady Free Convective Flow Past a Vertical Plate with Heat and Mass Fluxes Considering Chemical Reaction and Heat Absorption

Laminar boundary layer natural convection flow with heat and mass transfer of an optically thick heat-radiating and heat-absorbing fluid along with first-order chemical reaction has been investigated numerically. The partial differential equations (PDEs) governing the flow model are non-dimensionalized and solved using finite element technique. A grid independence analysis is carried out to ensure the convergence of solutions, and the code has been validated by comparing the results obtained via utilized method with those of earlier published results. To gain a better perspective of flow field, the solution of non-dimensional velocity, temperature, and concentration of the fluid is presented in a graphical form. Fluid temperature is observed to decrease through-out the thermal boundary layer on increasing the heat absorption. Chemical reaction has an adverse effect on species concentration.

G. S. Seth, Thirupathi Thumma, M. K. Mishra

Numerical Analysis of Unsteady MHD Mixed Convection Flow in a Lid-Driven Square Cavity with Central Heating on Left Vertical Wall

The article presents a numerical study performed on analysis of unsteady magneto-convective heat transfer in a square enclosure with partial active wall. The thermally insulated top and bottom wall while the left vertical wall is heated at Centre the rest of the left vertical wall is adiabatic and right vertical wall maintained at a lower temperature Tc. MAC (Marker-and-Cell) method is used to solve numerically set of dimensionless governing partial differential equations. The effect of local heat source on left wall is evaluated. The influence of the governing of thermophysical parameters, namely Prandtl number, Rayleigh number $$\left( {Ra} \right)$$, Hartmann number $$\left( {Ha} \right)$$, Grashof number $$\left( {Gr} \right)$$ and Reynolds number $$\left( {Re} \right)$$, is obtained. The results of streamlines and temperature are presented graphically and discussed.

K. Venkatadri, S. Gouse Mohiddin, M. Suryanarayana Reddy

Numerical Simulation of Dynamics of the Drop Formation at a Vertical Capillary Tube

The objective of this work is to study the parametric effects on the drop formation. For this, an experimentally verified computational domain that gives an accurate result is developed in the commercial software, FLUENT version 14.0. The numerical simulation of the Navier–Stokes equation has been obtained by combining the volume of fluid model with the finite volume method. To obtain the precise results in the finite volume technique, fine meshing is developed to track the movement of droplet in the air interface. The shape of drop formation obtained through the computational method is being verified with the experimental results available in the literature. The effect of parameters, i.e., viscosity and flow rate, is investigated in detail and also validated with the previous research works. The effect of viscosity on the development of satellite drop formation is also studied. This work is quite good agreement with the experimental work.

Pardeep, Mayank Srivastava, M. K. Sinha

Magneto Hydrodynamics


Squeezing of Bingham Fluid Between Two Plane Annuli

In this study, the presence of Bingham fluid between two parallel plane annuli with constant squeeze motion is theoretically analyzed. The effect of radius of separation on core thickness, pressure distribution, and squeeze force for different values of Bingham number has been investigated. By considering equilibrium of an element of the core in the fluid, thickness of the rigid plug core has been calculated numerically. The properties of the squeeze film are investigated through the non-Newtonian effects on the squeeze force of the plane for various annular spaces.

Singeetham Pavan Kumar, Kadaba Puttanna Vishwanath

Capturing the Transient Behaviour of MHD Double-Diffusive Free Convection in Vertical Channel with Adiabatic and Isothermal Walls and Mass Inflow at Adiabatic Wall

An investigation has been undertaken to capture the transient behaviour of MHD heat and mass transfer double-diffusive free convection flow of a viscous, incompressible and electrically conducting fluid in vertical channel with adiabatic and isothermal walls amid mass inflow at the adiabatic wall. Semi-analytical solutions to the governing equations representing the flow are found by first applying Laplace transformation and then inverting by INVLAP routine of MATLAB. The numerical solution for fluid temperature, species concentration, fluid velocity, Nusselt number, Sherwood number and skin friction are represented by figures for a range of pertinent flow parameters. Behavioural changes on the flow profiles occurring due to change in physical entities during transition from unsteady to steady state are captured and discussed. Formation of boundary layers near the channel walls for small values of time and their transition into main flow due to large values of time are depicted.

G. S. Seth, S. Sarkar, A. K. Singha

Effect of Newtonian Cooling/Heating on MHD Free Convective Flow Between Vertical Walls with Induced Magnetic Field

An analysis is performed for the steady MHD free convective flow between two vertical walls assuming that the fluid is viscous, incompressible, and electrically conducting. The impacts of the Newtonian cooling/heating and induced magnetic field have been considered in the mathematical formulation of the problem. The nondimensionalized simultaneous differential equations, governing the problem, have been solved analytically for the temperature, the velocity, and the induced magnetic field. The manifestations have been made for the induced current density, the skin-friction, and the mass flux. The impact of the Hartmann number, the Biot number, and the magnetic Prandtl number on the velocity, the induced magnetic field, and the induced current density diagrams have been presented by considering a temperature-dependent source/sink. It is inspected that the velocity, the induced magnetic field, and the induced current density diagrams have decreasing tendency with rise in the value of the Hartmann number. Further, it is also noticed that with enhancement in the magnetic Prandtl number the velocity diagram decreases, but the induced magnetic field and the induced current density diagrams have increasing nature. It is beheld that the impression of Newtonian cooling/heating is to reduce/raise the velocity as well as the induced magnetic field and the induced current density. The impacts of the governing parameters on the skin-friction and mass flux have also been concluded dealing with their numerical values given in the tables.

Sarveshanand, A. K. Singh

Radial Vibrations in Unbounded Micropolar Elastic Solid with Fluid Loaded Spherical Cavity

In this paper, the radial vibrations in unbounded micropolar elastic solid with fluid loaded spherical cavity have been investigated. The micropolar elastic solid is homogeneous and isotropic, while the loaded fluid is homogenous, isotropic, and inviscid. The frequency equation for radial vibrations of macro-displacements is derived and which is influenced by the loaded fluid, while the vibrations for micro-rotations are not influenced by the loaded fluid and these have been coinciding with the results of Somaiah (Comput Sci Math Biol 47–50, 2016). The dispersion relation for macro-displacements is obtained as particular case of this investigation. Further, numerical computations have been performed and have also been shown graphically to understand the behavior of phase speed and dispersion equations in the medium.

R. Srinivas, K. Somaiah

Unsteady Mixed Convective Flow in a Porous Lid-Driven Cavity with Constant Heat Flux

In this paper, we present the numerical analysis of mixed convection in a square cavity filled with porous medium. The left wall of the enclosure is kept at a constant heat flux, and the dimensionless governing equations are solved numerically with Marker and Cell (MAC) method. The numerical results are discussed graphically with the effect of Darcy number, Prandtl number, Rayleigh number, Grashof number, Reynolds number, temperature and streamlines.

B. Md. Hidayathulla Khan, V. Ramachandra Prasad, R. Bhuvana Vijaya

Chemically Reactive-Free Convective MHD Flow of Rivlin-Ericksen Fluid Past a Movable Vertical Plate Enriched in Porous Material

The chemically reactive viscous incompressible electrically conducting free convective flow of Rivlin-Ericksen fluid along a vertical semi-infinite moving permeable plate enriched in the porous material with existence of crosswise magnetic field and pressure gradient in the presence of variable suction has been considered. The study of heat transfer due to magnetic field is also done. The heat, continuity, and mass equations are solved, and their respective results are shown through graphs. In addition to that, Nusselt number, skin friction coefficient, and Sherwood number are also measured and depicted through tables. It was concluded from the actual study that highly chemically reacting Rivlin-Ericksen fluid flow becomes slow, but it can be accelerated for the values of high mass buoyancy.

Pooja Sharma, Ruchi Saboo

A Three-Dimensional CFD Simulation for the Nonlinear Parallel Flow Phenomena Through Coarse Granular Porous Media

Among many of the nonlinear equations presented throughout the decade, Forchheimer equation is the most widely experimented and investigated. In this study, a simple CFD model created using ANSYS Fluent 15.0 has been used in order to predict the flow through a parallel flow permeameter packed with crushed stone of three different sizes. The results obtained were compared with the experimental results obtained from a similar kind of experimental set under similar type of field and media conditions. Furthermore, the statistical validation of the simulation results with the experimentally obtained results suggests that this type of model can be used for analysing the flow though porous media as a substitute of the complex laboratory experiments with a reasonable precision.

Ashes Banerjee, Srinivas Pasupuleti, G. N. Pradeep Kumar, Sekhar Chandra Dutta

Solute Transport Modeling and Water Jet


Dust Ion Acoustic Solitary Waves in Quantum Dusty Plasmas: A New Approach to Obtain Sagdeev Potential

Quantum hydrodynamic model is used to study the existence and propagation of dust ion acoustic solitary waves (DIASWs). Here, Sagdeev’s nonperturbative method is used, and the Sagdeev potential is obtained numerically by using fourth-order Runge–Kutta method. A critical Mach number is observed for the existence of DIASWs. The numerical simulation results indicate that the dust grains may influence not only the amplitude and width but also the existence domain of the soliton. The quantum effects on the solitary waves are also mentioned.

Gadadhar Banerjee, Sarit Maitra

Influence of Abrasive Water Jet Turning Parameters on Variation of Diameter of Hybrid Metal Matrix Composite

Abrasive water jet turning is one of the recently developed manufacturing technologies. It has gained its importance due to its capability to machine difficult-to-cut material with advantages such as absence of thermal effects, high machining flexibility and little cutting force. In this study, the influence of water jet turning parameters such as abrasive type and abrasive mass flow rate has been analysed on the variation of diameter with the target diameter of metal matrix composite. Composite material A359/Al2O3/B4C fabricated by electromagnetic stir casting process was used in the experiment. To select the level of parameter, one-variable-at-a-time analysis was used. The results revealed that the abrasive type had a greater influence on the deviation of diameter from the target diameter as compared to mass flow rate.

Akash Nag, Ashish Kumar Srivastava, Amit Rai Dixit, Somnath Chattopadhyaya, Amitava Mandal, Dagmar Klichová, Petr Hlaváček, Michal Zeleňák, Sergej Hloch

Peristaltic Flow of a Bingham Fluid in Contact with a Jeffrey Fluid

The article concerns the peristaltic transport of two-layered fluid, consisting of a Bingham fluid in the core region and a Jeffrey fluid in the peripheral region through a channel. The flow is analyzed in the wave of reference under the assumptions of long wavelength and low Reynolds number. The analytical expressions for stream function, pressure rise, and the frictional force per wavelength in both the regions are obtained. The effect of physical parameters namely yield stress, Jeffrey parameter associated with the flow are presented graphically. This model helps to understand the behavior of two immiscible physiological fluids in living structures and in modeling the biomechanical instruments.

R. Saravana, P. Hariprabakaran, R. Hemadri Reddy, S. Sreenadh

Performance Analysis of Pulsating Water Jet Machining During Disintegration of Rocks by Means of Acoustic Emission

Over the decades, water jet cutting has been widely used for rock disintegration in mining operations and quarrying purposes. The impact of high-pressure water jet on hard material like rock, coal ruins the original structure of the material; therefore, low-pressure water jet comes into the existence. In recent year, pulsating water jet has been applied in numerous ways such as surface cleaning, exclusion of damaged material layers, preparation of surfaces, and disintegration of materials. It has also a great potential for application in hard rock breakage as conventional methods are cumbersome, not readily accessible and have economical limitations. The performance of the jet increases significantly by the generation of pulses causing disintegration of material at a relatively lower energy and costs. This paper focuses on the study of the disintegration processes of marble and granite by pulsating water jet subjected to erosion via acoustic emission. The experiments are performed by using pulsating water jet with modulation frequency of 20.20 kHz. The MVT circular nozzle with an orifice diameter of 0.9 mm, standoff distance from the target material 6 mm, traverse speed varied from 2 to 16 mm/s, and pump pressure 60 MPa was used for water jetting. The topography of granites and marble on the cut depth and surface quality were investigated by the optical profile meter. Moreover, dependable relations between some physical and mechanical properties of the rocks and the depth of cut were observed. The online monitoring of acoustic emission shows the change in response to the pulse frequency at different time intervals.

Rupam Tripathi, Madhulika Srivastava, Sergej Hloch, Somnath Chattopadhyaya, Alok Kumar Das, Alokesh Pramanik, Dagmar Klichová, Pavel Adamcik

Three-Dimensional Solute Transport Problems in an Aquifer: Numerical Approaches

The solution of solute transport problem in an aquifer with suitable boundary conditions has been dealt by various analytical methods in the past. But, the analytical approach becomes more difficult to apply when either dealing with complex boundary conditions or higher order solute transport problems. The difficulty may be reduced by handling the problem by numerical approaches as in the present paper, forward in time centered in space (FTCS) finite-difference scheme is used to solve the three-dimensional advection-dispersion equation (ADE) with Dirichlet and Neumann boundary conditions. The Dirichlet boundary conditions are taken temporally dependent. The numerical solution is obtained graphically with the help of MATLAB software package, and further under a special case, the numerical solution obtained by FTCS scheme is validated with the solution obtained by PDEtool which is based on the finite-element method.

Mritunjay Kumar Singh, Rakesh Kumar Singh, Vijay P. Singh

Surface Treatment of AISI 304 Using Pulsating Water Jet Peening

Water jet peening has gained attention as a potential surface treatment process for improving the fatigue life of a component. The tensile residual stress in the component initiates the stress corrosion cracking and reduces its fatigue life. The mitigation of this tensile residual stress can be effectively achieved by water jet peening process due to its resistance to corrosion, flexibility in treating complex areas and capability to maintain the eco-friendly environment. In the present work, the AISI 304 plates were treated with pulsating water jet (actuator frequency f = 20.19 Hz) at the pressure of p = 20 MPa with traverse speed of v = 0.5 mm/s and v = 2.5 mm/s using two different types of nozzles; flat nozzle of diameter d = 1 mm (HAMMELMANN) and circular nozzle of diameter d = 1.9 mm (STONEAGE). The microstructural analysis of the treated and untreated region was conducted to analyse the effect of traverse speed and the type of nozzle on the erosion process. The study revealed that more erosion occurs at lower traverse speed; however, fewer surface depressions were observed in the case of flat nozzles. The X-ray diffraction technique was also used to analyse the effect of traverse speed and the type of nozzle on the residual stress of the samples. In addition to this, the acoustic emission during the ongoing process was monitored using LabView 2012 SP1 f5 ver. 12.0.1. The results indicate that acoustically monitored pulsating water jet peening process can be used as tool for the controlled local treatment process arising from the impact of the pulsed water jet on the surface of sample.

Madhulika Srivastava, Rupam Tripathi, Sergej Hloch, Ayush Rajput, Drupad Khublani, Somnath Chattopadhyaya, Amit Rai Dixit, Josef Foldyna, Pavel Adamčík, Jiri Klich, Michal Zelenak, Dagmar Klichová

Pollutant Transport in a Semi-infinite Heterogeneous Porous Media

This study proposed an analytical model of contaminant solute transport with an impact of elemental recharge rate of aquifer. The domain of study is considered as a heterogeneous porous media. Dispersion is directly proportional to the square of the seepage velocity, whereas the velocity is a function of both time and distance variables. Initially, the aquifer is not pollutant free; some background concentration is present there. Temporally dependent exponentially decreasing input source is considered, and the concentration gradient is assumed to be zero at the exit boundary. Laplace transform technique (LTT) is used to obtain the analytical solution and is validated with the numerical solution which is obtained using explicit finite difference method.

S. Begam, S. Ahamad, Chandan Kumar Thakur

Solution to Advection–Dispersion Equation for the Heterogeneous Medium Using Duhamel’s Principle

This work dealt with advection–dispersion problem in heterogeneous medium while the medium is initially considered to be polluted as a functional combination of source term and zero-order production term with distance. Further, Dirichlet-type boundary condition is employed to get insight to the realistic situation for achieving practical solution to the problem. Duhamel’s integration technique has been applied to solve the system. Non-dimensional numbers responsible for the domination of advection and dispersion in the transport of solute have been explored through appropriate graphs. Variability of velocity field and dispersion of the solute due to heterogeneity of the medium has also been taken into consideration while solving the system. The comparison has been made between the different outcomes significantly using graphical approach.

Amit Kumar Pandey, Rohit Kumar, Mritunjay Kumar Singh

Two-Dimensional Solute Transports with Periodic Input Source in Semi-infinite Aquifer

The present study deals with two-dimensional solute transport equation with time-dependent source in homogeneous semi-infinite aquifer. Linear isotherm is taken into consideration due to interaction between solid and liquid phases. Initially, the domain is not solute-free. Initially, space-dependent exponentially increasing form with initial concentration is taken into consideration. At the one end of the domain, time-dependent source concentration is taken into account. Due to no mass flux at the other end of the domain concentration gradient is assumed to be zero. Laplace integral transform technique (LITT) is used for analytical solution, whereas explicit finite difference (EFD) scheme is used for numerical approximation. The exponentially decreasing and asymptotic form velocity function is taken into consideration for the graphical representation of the solutions.

Affreen Akhter, Chandan Kumar Thakur, Mritunjay Kumar Singh

Mathematical Modeling of One-Dimensional Advection Dispersion Equation in Groundwater Contamination Using Different Velocity and Dispersion for Different Zones

Groundwater contamination problem is modeled using advection dispersion equation with different phase velocity and dispersion. This type of flow problem can be occurred or visualized depending upon the geometry as the surface of the aquifer is made of various soil materials. We consider different velocity and dispersion for different zones. Initially, the aquifer is contamination free, and advection dispersion equation is used to model the system subject to the condition that the source is acting at origin and contaminant concentration flux is zero at the semi-infinite part of the boundary. Laplace transform technique is used to solve the system analytically, and graphs are plotted to show the effect in the aquifer with multiphase.

Mritunjay Kumar Singh, Ayan Chatterjee, Priyanka Kumari

Solute Dispersion Along Unsteady Groundwater Flow in a Semi-infinite Homogeneous Aquifer Using Linguistic Hedge by Mamdani Model

In the present study, the analytical solutions for dispersion of contaminants along unsteady flow of groundwater through semi-infinite aquifer are represented by fuzzy linguistic hedges. The sources of pollution are both a point input at origin and a spatially distributed background source. The analytical solutions thus obtained are put into Mamdani model with different linguistic variables, and the model thus formed gives the result of solute concentration in literal sense in different point of time and space. The MATLAB code has been generated to simulate the Mamdani Model and to find the fuzziness of the solution of AD equation (Advection-Dispersion Equation) along unsteady flow.

Abhijit Debnath, Umesh Prasad, Mritunjay Kumar Singh

Effect of Water Pressure During Abrasive Waterjet Machining of Mg-Based Nanocomposite

The pressure of the waterjet influences the overall performance of the abrasive waterjet cutting system through operational and phenomenological effects. In this study, the effect of water pressure in surface quality of Mg-based nanocomposite was investigated. The as-machined surfaces were examined by field emission scanning electron microscope to determine the surface morphology. The surface topography of selected nanocomposite was examined and compared. The results show that the surface quality is better at higher pressure. However, at lower water pressure, there is too much interaction among the low-energy abrasive particles and this may cause insufficient material removal. Abrasive waterjet cutting seems to be promising tool for machining metal matrix composites in terms of no thermal damages, no micro-structural changes and negligible sub-surface damages on the machined surface.

Kumari Bimla Mardi, Amit Rai Dixit, Ashish Kumar Srivastava, Ashish Mallick, Jiri Scucka, Petr Hlaváček, Sergej Hloch, Michal Zeleňák

Analytical Solution for Solute Transport Influenced by Spatially Dependent Dispersion Along Spatiotemporally Dependent Porous Media Flow

One-dimensional pollutant’s solute transport originating from the instantaneous source and the continuous point source is studied in aquifer through the analytical solutions of the advection–diffusion equation (ADE). Dispersion coefficient is considered spatially dependent, and flow velocity is considered spatially and temporally dependent. The solution is obtained in infinite domain using Green’s Function Method (GFM). To use this method, the variable coefficients of the ADE are reduced into constant coefficients through a pertinently developed coordinate transformation equation. The analytical solutions are validated through previously existing analytical solutions.

Abhishek Sanskrityayn, Vinod Kumar Bharati



Surface Wave Propagation in Inhomogeneous Liquid Layer over a Heterogeneous Anisotropic Elastic Half Space

The effect of the inhomogeneity and homogeneity on the dispersion of the Rayleigh-type surface waves in an inhomogeneous liquid layer over a heterogeneous transversely isotopic elastic half space has been discussed. The frequency equation is obtained. The dispersion curve of variation of phase velocity with the wave number is observed and depicted graphically. Also various particular cases have been considered.

Pasupati Paul, Santimoy Kundu, Dinbandhu Mandal

Qualitative Analysis of a Three Species Predator–Prey Model with Stochastic Fluctuation

In this paper, a multi-team predator–prey model, with two preys and one predator species, has been considered within stochastically fluctuating environment. In the first part, we have studied the stability of the model around the equilibrium points and later, introducing white noise terms to the deterministic model, the effects of stochastic fluctuating environment are studied. Numerical simulations have been performed to examine the stability and other properties of the stochastic model.

Soumen Kundu, Sarit Maitra

Plane Wave Propagation in a Rotating Micropolar Microstretch Elastic Solid in Special Case

The present work investigates the propagation of plane waves in a rotating micropolar microstretch elastic solid in a case of irrotational macro-displacements and zero micro-rotations. Three types of basic waves consisting of transverse microstretch waves, transverse micropolar waves, and coupled longitudinal waves are propagated. All these waves are frequency-dependent and hence, dispersive in nature. Except microstretch waves, all these waves are effected by angular rotation of the solid. The variation of these waves with angular frequency and angular rotations has also been depicted graphically for specific models.

K. Somaiah

Possibility and Causes of Backward Bifurcation in a Cholera Model

Backward bifurcation in an epidemiological model is a phenomenon in which the model possesses stable endemic equilibria together with a stable disease-free equilibrium. Till now, this phenomenon has been observed in a number of epidemic models. In this work, we investigate the possibility of backward bifurcation in a cholera model. We also explore the role of various factors, which induce backward bifurcation in other epidemic models. We believe the present work provides an insight of the dynamics of a cholera model and possible causes of backward bifurcation in the same.

Sandeep Sharma, Nitu Kumari

Insights into Ventilation Demand Estimation for High-Speed Supercavitating Underwater Vehicles

The difference between the typical peak speeds of an aerial and an underwater vehicle is enormous. Evidently, the reason behind this huge disparity lies in the tremendous skin friction drag experienced by an underwater vehicle. However, this difference can be bridged if the underwater vehicles were somehow engulfed by elongated gas/vapor bubbles or cavities as these vehicles travel underwater. Such huge cavities or ‘supercavities’ can be generated via two different approaches—cavitation or ventilation. Among the two, the generation of a supercavity through ventilation is more interesting, since it can be accomplished at much lower speeds. For the operation of such underwater vehicles in the ventilation mode, it is imperative to determine the ventilation demand, or the amount of gas to be carried on board. The present study reports some interesting insights into the factors that determine the estimation of this ventilation demand. Two most important factors governing the estimation of ventilation demand are the ventilation requirement for the formation and sustenance of a supercavity. These two factors, in turn, are dependent upon the operational conditions of a vehicle, as well as unsteady state conditions prevailing under the ocean. The current work explores the dependence of the formation and sustenance air entrainment rates of a supercavity at different operational conditions of the supercavitating vehicle.

Ashish Karn, Vishal Narula, Roger E. A. Arndt, Jiarong Hong


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