Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy

https://doi.org/10.1016/j.ijheatmasstransfer.2017.01.029Get rights and content

Highlights

  • Mixed convection in magneto-nanofluid flow past a vertical plate is considered.

  • Aspects of chemical reaction and activation energy are introduced in the model.

  • Brownian motion and thermophoresis effects are addressed.

  • Numerical solutions are obtained by considering zero flux condition for nanoparticles.

Abstract

Here we analyze the mixed convective flow of magneto-nanofluid bounded by a vertical stretchable surface considering Brownian motion and thermophoretic diffusion effects. Additionally, the aspects of chemical reaction and activation energy are introduced. Formulation is made through the newly suggested assumption of zero particle flux at the boundary. Equations governing the locally similar flow are tackled through a numerical approach and the influences of involved parameters on the flow fields are displayed graphically. Buoyancy effects resulting from the temperature and concentration differences accelerate the fluid flow in vertical direction. Brownian motion has no influence on the heat flux from stretching wall. Heat flux from the wall diminishes upon increasing the chemical reaction rate constant. Nanoparticle concentration is directly proportional to the activation energy of chemical reaction and the behavior of Brownian motion on nanoparticle concentration is qualitative opposite to that of thermophoretic force. To our knowledge, the nanofluid flow in the regimes of chemical reaction and activation energy is just discussed in this paper.

Introduction

Recent advancements in nanoscience originate from the examination of physical properties of matter at nanoscale level. Among numerous industrial applications of nanosciences, nanofluids constitute an emerging field in heat transfer. Nanofluids have gained immense interest owing to their remarkable thermal transport and fascinating applications in numerous important fields. Besides anomalously high thermal conductivity, nanofluids have better stability that prevents quick settling and clogging near the boundaries of heat transfer devices. The stimulus in nanofluid research stems from the heat transfer intensification in processes involving microchips in computer processors, micro-manufacturing, space cooling, nuclear engineering, fuel cells, diesel engine oil, hybrid-powered engines, air-conditioners/refrigerators and other high energy devices. Classical theory of single phase fluids can be applied to nanofluids by viewing thermophysical properties of nanofluid as functions of the properties of the base fluids and its constituents. It should be stated here that particle size, thermal conductivity, volume fraction and temperature all contribute to the thermal conductivity enhancement of nanofluids. Buongiorno [1] developed a two-phase model for investigating thermal energy transport via nanofluids. Later, Tiwari and Das [2] put forward a simple model in which thermophysical properties were viewed as functions of nanoparticle volume fraction. Both the above mentioned models have been successfully applied to address several diverse flow problems involving nanofluids in which Kuznetsov and Nield [3] utilized Buongiorno model to describe the aspects of Brownian motion and thermophoretic diffusion on nanofluid flow adjacent to a heated vertical plate in a porous medium. They pointed out that both Brownian motion and thermophoresis cause diminution in heat transfer rate from the plate. Nield and Kuznetsov [4] also addressed the double-diffusive convection in nanofluid adjacent to a vertical surface. Khan and Pop [5] analyzed the nanofluid flow bounded by a stretchable surface using numerical approach. They concluded that Brownian motion and thermophoresis effects enhance the penetration depth of heat. Free convection in nanofluid flow past a flat plate immersed in porous space was examined by Khan and Pop [6]. Aziz and Khan [7] employed practically useful convective type conditions to analyze the buoyancy induced flow of nanofluid bounded by a vertical surface. Series solution for nanofluid flow in the vicinity of stagnation-point on a stretching surface was presented by Mustafa et al. [8]. In another paper, Mustafa et al. [9] presented homotopy based series solutions as well as numerical solutions for exponentially deforming body induced flow of nanofluid. Zheng et al. [10] discussed the consequences of wall slip and temperature jump for nanofluid flow and radiative heat transfer over a deforming surface. They employed homotopy approach to present series solutions comprising exponentially decaying functions. Lin et al. [11] investigated the Marangoni convection flow of pseudo-plastic nanofluid with temperature dependent thermal conductivity utilizing five different kinds of nanoparticles. Kuznetsov and Nield [12] revisited their problem [9] by imposing more realistic condition which requires passive control of nanoparticle concentration at the boundary. Sheikholeslami et al. [13] employed Maxwell model to investigate the heat transfer of Cu-water nanofluid with GMDH-type neural network. Malvandi and Ganji [14] discussed the onset of magnetic (Lorentz) force on the flow of Al2O3-water nanofluid inside a channel. MHD rotating flow of water based nanofluids between parallel plates was observed by Sheikholeslami et al. [15]. Turkyilmazoglu [16] analyzed the swirling flow of nanofluid near a rotating disk by accounting five different types of nanoparticles. In a recent study, Sheremet et al. [17] used Tiwari and Das model to investigate the free convection flow through a square cavity. In another paper, Sheremet et al. [18] discussed the natural convection in a cubical cavity utilizing nanofluid. Lin et al. [19] explored the heat generation effects on MHD flow of pseudo-plastic fluid filled with nanoparticles. The analysis was carried out for both metallic and metal-oxides nanoparticles. They utilized a convenient shooting approach coupled with Runge-Kutta scheme and Newton’s iterative method for presenting numerical solutions. Nanofluid flow and radiative heat transfer near a flat plate immersed in a porous space with first-order chemical reaction was addressed by Zhang et al. [20] utilizing differential transform method. Mixed convection flow of an electrically conducting Al2O3-water nanofluid in a vertical channel was theoretically examined by Rashidi et al. [21]. Recently, Mustafa et al. [22] analyzed the classical Bödewadt flow problem for three different kinds of nanofluids by Keller-Box method.

Mass transfer phenomenon occurs due to concentration difference of species present in a mixture. The species with varying concentration in a mixture transport themselves from a region of higher concentration to a region of lower concentration. Moreover, activation energy can be defined as the least obligatory energy that reactants must acquire before a chemical reaction can take place. Mass transfer process accompanied by chemical reaction with activation energy is often met in applications involving chemical engineering, geothermal reservoirs, mechanics of water and oil emulsions, food processing etc. First of all, Bestman [23] investigated the natural convection flow of binary mixture in a porous space with activation energy. Recent contributions in this direction were made by few authors in which Makinde et al. [24] numerically studied unsteady natural convection flow under the influences of nth-order reaction and activation energy. Maleque [25] investigated the exothermic/endothermic reactions on mixed convection flows in the presence activation energy. Awad et al. [26] examined the unsteady rotating flow of binary fluid past an impulsively stretched surface utilizing modified Arrhenius function. Abbas et al. [27] also studied the binary chemical reaction and activation energy effects on Casson fluid flow in the vicinity of stagnation-point. They provided numerical approximations for developed differential system through spectral-collocation quasi linearization technique. Rotating viscoelastic flow containing chemically reactive species with activation energy was numerically reported by Shafique et al. [28] using numerical approach.

In present framework, we study the onset of activation energy on mixed convection flow of magnetic nanofluid past an isothermal vertical surface utilizing modified Arrhenius function. Buongiorno model is adopted which features the novel aspects of Brownian motion and thermophoresis. Additional, Dirichlet-type condition accounting for zero normal flux of nanoparticles is factored. Computational analysis is performed through shooting approach based on the Runge-Kutta method of fifth-order. Present attempt is novel contribution in the regimes of both magneto-nanofluids and activation energy. Such analysis even in absence of magnetic field and mixed convection is not yet reported.

Section snippets

Problem formulation

Consider the nanofluid flow along a vertical stretchable surface with u and v denoting x- and y-components of velocity respectively, where the coordinate axis x extends along the surface and y is the coordinate axis normal to it (see Fig. 1). A magnetic force having uniform intensity B0 acts normal to the plane of the sheet. We assume that surface stretches in the vertical direction with linear velocity uw = ax, where a > 0 signifies the rate of stretching. The surface temperature, denoted by Tw,

Results and discussion

In this article, mixed convection in the magneto-nanofluid flow over a stretchable sheet is studied in the existence of binary chemical reaction and activation energy. Our simulations are based on practically acceptable assumption of zero particle flux at the stretching boundary. The governing problem comprises of Eqs. (11), (12), (13) subject to the conditions (15) which have been treated numerically through the MATLAB built in routine bvp4c. In Table 1, we include numerical computations for

Concluding remarks

Mixed convective flow of magneto-nanofluid under the influences of chemical reaction and activation energy is addressed numerically. Simulations of this study are based on physically acceptable assumption of zero nanoparticle flux at the boundary. The major results of this work are outlined below:

  • 1.

    Brownian motion parameter has negligible effect on heat flux at the stretching boundary.

  • 2.

    Nanoparticle concentration ϕ is larger when activation energy for chemical reaction is larger. Moreover the

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