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This textbook presents the classical treatment of the problems of heat transfer in an exhaustive manner with due emphasis on understanding of the physics of the problems. This emphasis will be especially visible in the chapters on convective heat transfer. Emphasis is also laid on the solution of steady and unsteady two-dimensional heat conduction problems. Another special feature of the book is a chapter on introduction to design of heat exchangers and their illustrative design problems. A simple and understandable treatment of gaseous radiation has been presented. A special chapter on flat plate solar air heater has been incorporated that covers mathematical modeling of the air heater. The chapter on mass transfer has been written looking specifically at the needs of the students of mechanical engineering. The book includes a large number and variety of solved problems with supporting line diagrams. A number of application-based examples have been incorporated where applicable. The end-of-chapter exercise problems are supplemented with stepwise answers. Though the book has been primarily designed to serve as a complete textbook for undergraduate and graduate students of mechanical engineering, it will also be useful for students of chemical, aerospace, automobile, production, and industrial engineering streams. The book fully covers the topics of heat transfer coursework and can also be used as an excellent reference for students preparing for competitive graduate examinations.

### Chapter 1. Introduction

Abstract
Here, a brief description of three modes of heat transfer is presented. Conduction occurs in all media—solids, liquids, and gases when a temperature gradient exists. In opaque solids, it is the only mechanism by which the heat can flow. In convection, transport of heat takes place as a volume of liquid or gas moves from a region of one temperature to that of another temperature. The thermal radiation is the process of heat propagation by means of electromagnetic waves produced by virtue of the temperature of the body. In contrast to the conduction and convection heat transfers, radiation can take place through a perfect vacuum.
Rajendra Karwa

### Chapter 2. One-Dimensional Steady-State Heat Conduction

Abstract
In this chapter, Fourier’s law has been applied to calculate the conduction heat flow in systems where one-dimensional heat flow occurs. The general heat conduction equations in the rectangular, cylindrical and spherical coordinates have been developed. Considering film coefficients, the equation of overall heat transfer coefficient has been presented. Critical radius of insulation for cylindrical and spherical systems has been defined, and mathematical expressions for the same have been deduced. A number of illustrative examples have been included in one-dimensional steady-state heat conduction. In the end, basic introduction to the thermal contact resistance has been given.
Rajendra Karwa

### Chapter 3. Extended Surfaces (Fins)

Abstract
Fins are widely used in various engineering equipments for increasing heat transfer rate from a surface. In this chapter, mathematical treatments of various types of uniform cross-section, triangular, trapezoidal and annular fins have been presented to determine the temperature variation along the fin length and heat transfer rate from the fin surface assuming one-dimensional steady-state heat flow condition. Fin performance parameters (effectiveness and efficiency) have been defined and discussed. Condition for enhancement of heat transfer from a fin has been deduced. A number of illustrative examples have been given.
Rajendra Karwa

### Chapter 4. Conduction with Heat Generation

Abstract
This chapter is devoted to the heat conduction processes when there is heat generation in the solid itself. Such processes are encountered in many applications. Here the treatment has been presented for plane wall, cylindrical or spherical solids with a uniform rate of heat generation per unit volume with constant and variable thermal conductivity of the solid material. A treatment of the heat transfer through piston crown has been presented to determine the temperature distribution equation. A number of illustrative examples have been given.
Rajendra Karwa

### Chapter 5. Steady-State Two-Dimensional Heat Conduction

Abstract
Previous chapters were devoted to steady-state one-dimensional systems. In this chapter, analytical solution, graphical analysis, method of analogy and numerical solutions have been presented for two-dimensional steady-state conduction heat flow through solids without heat sources. Conduction shape factor has been defined and presented for various physical systems. The presented methods have been supported by a number of numerical examples. Various techniques for the solution of nodal equations developed by the finite-difference method have been given.
Rajendra Karwa

### Chapter 6. Unsteady or Transient Heat Conduction

Abstract
This chapter is devoted to the transient state of heat conduction, i.e. the heating or cooling where the temperature of the solid body varies with time as well as in the space. For bodies with a very high thermal conductivity combined with a low value of the convective heat transfer coefficient, lumped heat capacity analysis has been presented. For determination of temperature variation with time and spatial position in plates (whose thickness is small compared to the other dimensions), cylinders (whose diameter is small compared to its length) and spheres, solution based on Heisler charts has been given. Numerical method of solving transient conduction problems has been presented with a number of illustrative examples.
Rajendra Karwa

### Chapter 7. Convective Heat Transfer

Abstract
Analytical solutions, using the boundary layer equations, of some simple convection heat transfer problems, especially the convection with laminar flow, have been presented in this chapter. Solution of momentum equation for laminar flow over a flat plate by Blasius and solution of the integral momentum equation of laminar flow by von Karman are presented for friction factor determination. Pohlhausen’s solution of energy equation and von Karman integral technique (integral analysis of energy equation) for the laminar boundary layer over a flat plate are presented in Sect. 7.7, and the Nusselt number correlations are derived. Semi-empirical treatment of turbulent flow over a flat plate is presented in Sect. 7.8. Friction factor and Nusselt number have been determined for laminar flow in tubes. Eddy viscosity and eddy thermal diffusivity for momentum and heat exchange in turbulent flow have been defined. Reynolds and other analogies have been presented in next sections. Analytical solution of free convection laminar flow on a vertical plate to obtain the relation of Nusselt number has been presented considering the integral momentum and energy equations. In the end, treatment for liquid metal heat transfer has been presented for laminar flow over a flat plate.
Rajendra Karwa

### Chapter 8. Empirical Relations for Forced Convection Heat Transfer

Abstract
Analytical solutions of some simple convection heat transfer problems, especially the convection with laminar flow, have been presented in Chap. 7. There are a large number of convection problems, especially the convection with turbulent flow, for which the analytical solutions have not met the success. Hence, the technique of dimensional analysis has been applied to develop functional relations in terms of dimensionless numbers. Empirical relations of heat transfer and friction factor have been presented in terms of these dimensionless numbers for flat plates, tubes, annuli, rectangular and parallel plate ducts, submerged bodies and tube banks for different boundary conditions. Nusselt number correlations for fully developed turbulent flow of liquid metals have been given in Sect. 8.11. In the end, effect of wall roughness on friction factor and heat transfer coefficient has been discussed and some correlations have been presented along with the Moody diagram.
Rajendra Karwa

### Chapter 9. Empirical Relations for Natural or Free Convection

Abstract
Flow structure and development of boundary layer for horizontal plates and cylinders, sphere, parallel plate channels and enclosed spaces have been discussed. The technique of dimensional analysis has been applied to develop functional relationship for natural or free convection heat transfer in terms of dimensionless numbers. Experimental schemes for determining heat transfer coefficient have been presented. Heat transfer coefficient correlations for vertical and flat plates, parallel plate open ended channels and enclosed spaces have been given in terms of dimensionless numbers. In Sect. 9.8, problem of combined free and forced convection has been discussed.
Rajendra Karwa

### Chapter 10. Laws of Thermal Radiation

Abstract
All bodies emit radiation to their surroundings through electromagnetic waves due to the conversion of the internal energy of the body into radiation. Reflectivity, absorptivity and transmissivity of bodies are defined. Planck’s law for the spectral distribution of the emissive power of a blackbody is presented in Sect. 10.4, which has been used to determine Stefan–Boltzmann’s equation of the total emissive power of a blackbody. Wein’s displacement law is given in the next section. Concept of gray body has been presented. Kirchhoff’s Law has been stated and proved. Equality of emissivity and absorptivity has been established. Lambert’s cosine law has been presented and utilized to determine the intensity of radiation in terms of total emissive power of a blackbody.
Rajendra Karwa

### Chapter 11. Exchange of Thermal Radiation Between Surfaces Separated by Transparent Medium

Abstract
Radiation heat exchange between two black surfaces depends on the shape and size of the bodies, relative position and distance between them while the radiation exchange between gray bodies also depends on their emissivity. For calculation of the radiation exchange between two black surfaces, basic integral equation of the shape factor has been derived which represents the fraction of the total radiation emitted by a surface intercepted by other surfaces. Salient features of the shape factor have been presented and numbers of illustrative examples on calculation of the shape factor for different systems have been given.
Radiation exchange between gray bodies is a complex process. Electrical analogy-based method is given to solve such problems wherein the actual system is reduced to an equivalent electric network. Concept of radiation shield, which reduces the radiation heat transfer from a body by placing a thin opaque partition between the surfaces, has been explained in Sect. 11.9. In the end of the chapter, Newton’s law of cooling is presented.
Rajendra Karwa

### Chapter 12. Heat Transfer in Absorbing and Emitting Media (Gaseous Radiation)

Abstract
The radiation exchange between an absorbing and emitting gas and a solid surface is considerably more complex than exchanges between solid surfaces through a transparent medium. The specific features of the gaseous radiation have been discussed in this chapter. The procedure for the calculation of net heat exchange, presented by Hottel, between a black enclosure and isothermal (uniform temperature) gas volume consisting of CO2 and/or water vapour is given in Sect. 12.3 followed by a simplified treatment of gay enclosure. In the end, a brief introduction to radiative heat transfer from flames has been presented.
Rajendra Karwa

### Chapter 13. Heat Transfer in Condensing Vapours and Boiling Liquids

Abstract
The chapter has been divided into two parts. In the first part, the basic modes of condensation have been presented followed by the presentation of the analytical solution due to Nusselt for laminar film condensation on a vertical surface. Turbulent film condensation has been discussed and an empirical relation for an estimate of heat transfer coefficient has been given. In the end, the factors affecting film condensation have been discussed. The second part of the chapter deals with heat transfer in boiling liquids. The phenomenon of pool boiling has been discussed followed by a discussion on forced boiling in vertical and horizontal pipes. Relations for boiling heat transfer in pool boiling are presented,
Rajendra Karwa

### Chapter 14. Heat Exchangers

Abstract
Heat exchangers have been classified in various ways. Double pipe and shell-and-tube heat exchangers are most widely used. This chapter deals with heat exchanger fundamentals and design of heat exchangers. Heat transfer equation for double pipe heat exchanger has been presented and log mean temperature difference (LMTD) has been defined in Part 1 of the chapter followed by derivations of equations of LMTD for parallel flow and counterflow exchangers. In Sect. 14.4, graphs of correction factor for calculation of LMTD for other flow arrangements have been presented. Basic treatment of effectiveness-NTU method for counterflow and parallel flow heat exchangers is given in Sect. 14.5. Graphs for determination of effectiveness for other flow arrangements have been given as a function of NTU in Sect. 14.6. In the second part of the chapter, basic considerations for heat exchanger design have been presented followed by defining of fouling factor, and clean and design overall heat transfer coefficients. An illustrative example of double pipe heat exchanger design has been given.
Rajendra Karwa

### Chapter 15. Mass Transfer

Abstract
An introduction and elementary treatment of mass transfer is presented here. The conditions for similarity of concentration and velocity profiles, and temperature and concentration profiles have been discussed and the relevant dimensionless numbers have been defined. Stefan law has been presented in Sect. 15.4, which can be utilized for experimental determination of the diffusion coefficient. Convective mass transfer has been discussed and dimensional analysis has been used to determine functional relations for free and forced flow conditions, which is followed by the presentation of mass transfer correlations. In Sect. 15.8, analogies for convection heat transfer have been extended to the mass transfer problems.
Rajendra Karwa

### Chapter 16. Special Topic: Performance of Solar Air Heater

Abstract
A mathematical model of a smooth duct solar air heater is given in this chapter that can be utilized for the study of the thermohydraulic performance of solar air heaters with the variation of ambient, operating and design parameters. Different correlations for the estimate of the wind heat transfer coefficient and sky temperature and discussions on the same have been given. Artificial roughnesses on the air flow side of solar air heater absorber plate proposed for performance enhancement have been discussed. Heat transfer and friction factor correlations for some roughness geometries have been presented followed by typical results of a performance study of solar air heaters with 60° v-down discrete rectangular cross-section repeated rib roughness on the air flow side of the absorber plate.
Rajendra Karwa