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Steady State Conduction Without

Heat Generation

3.1. Plane Wall. 3.2. Electrical Analogy of Heat Transfer Rate Through a Plane Wall. 3.3. Multilayer Plane Wall—Plane slabs in series—Heat conduction through parallel slabs—Composite wall in series and parallel—Overall heat transfer coefficient.

3.4. Thermal Contact Resistance. 3.5. Long Hollow Cylinder—Electrical analogy for hollow cylinder—Multilayer hollow cylinders—

Overall heat transfer coefficient—Log mean area. 3.6. Critical Thickness of Insulation on Cylinders—Effect of thermal resistances.

3.7. Hollow Sphere—Electrical analogy for hollow sphere—Multilayer hollow sphere—Overall heat transfer coefficient—Critical radius of insulation on sphere. 3.8. Summary—Review Questions—Problems.

Objective of this chapter is to:

• obtain steady state temperature distribution without heat generation in slab, hollow cylinders and spheres.

• obtain heat conduction rate from differential heat conduction equation without heat generation in solids.

• study concept of thermal resistance in series and parallel.

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Mass Transfer


15.1. Introduction. 15.2. Modes of Mass Transfer. 15.3. Comparison between Heat and Mass Transfer. 15.4. Concentrations, Velocities and Fluxes. 15.5. Fick’s Law of Diffusion. 15.6. General Mass Diffusion Equation. 15.7. Boundary Conditions. 15.8. Mass Diffusion without Homogeneous Chemical Reactions—Steady state diffusion through a plane membrane—Water vapour migration—Equimolar counter diffusion—Diffusion through a stagnant gas: Stefan’s flow. 15.9. Mass Diffusion with Homogeneous Chemical Reactions.

15.10. Convective Mass Transfer—Mass transfer coefficient dimensionless parameters in convective mass transfer—Analogy between heat and mass transfer—Correlation for convective mass transfer. 15.11. Dimensional Analysis of Convective Mass Transfer.

15.12. Evaporation of Water into Air. 15.13. Summary—Review Questions—Problems—References and Suggested Reading.



We have so far dealt with conduction, convection and radiation modes of heat transfer, in which energy transfer takes place due to temperature difference in the medium(s). Similarly, if there is a concentration difference within two or more species (components) of a mixture, then mass transfer must occur in order to minimize the concentration difference within the system.

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Steady State Conduction with Heat Generation

4.1. The Plane Wall—Specified temperatures on both sides—Plane wall without heat generation—Plane wall with insulated and convective boundaries—Plane wall exposed to convection environment on its both boundaries—The maximum temperature in the wall. 4.2. The

Cylinder—Solid cylinder with specified surface temperature—Solid cylinder exposed to convection environment. 4.3. Hollow Cylinder with

Heat Generation and Specified Surface Temperatures—Hollow cylinder insulated at its inner surface—The location of maximum temperature in the cylinder—4.4. The Sphere—Solid sphere with convective boundary—Solid sphere with specified surface temperature—4.5. Summary—

Review Questions—Problems—References and Suggested Reading.

Most of the engineering applications involve heat generation in the solids, such as nuclear reactors, resistance heaters etc. In this chapter, we will consider one dimensional steady state heat conduction with heat generation and determination of temperature distribution and heat flow in solids of simple shapes such as plane wall, a long cylinder and a sphere. Such type of problems cannot be solved with electrical analogy concept presented in previous chapter.

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External Flow

8.1. Laminar Flow Over a Flat Plate—Approximate analysis of momentum equation—Approximate analysis of energy equation. 8.2. Reynolds

Colburn Analogy : Momentum and Heat Transfer Analogy for Laminar Flow Over Flat Plate. 8.3. Turbulent Flow Over a Flat Plate.

8.4. Combined Laminar and Turbulent Flow. 8.5. Flow Across Cylinders and Spheres—Drag coefficient—Heat transfer coefficient.

8.6. Summary—Review Questions—Problems—References and Suggested Reading.

When a fluid flows over a body such as plate, cylinder, sphere etc., it is regarded as an external flow. In such a flow, the boundary layer develops freely without any constraints imposed by adjacent surfaces. Accordingly, the region of flow, outside the boundary layer in which the velocity and temperature gradients are negligible is called the free stream region.

In an external flow forced convection, the relative motion between the fluid and the surface is maintained by external means such as a fan or a pump and not by buoyancy forces due to temperature gradients as in natural convection.

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Principles of Convection


7.1. Mechanism of Heat Convection. 7.2. Classification of Convection. 7.3. Convection Heat Transfer Coefficient. 7.4. Convection

Boundary Layers—Velocity boundary layer—Thermal boundary layer—Significance of boundary layers. 7.5. Laminar and Turbulent

Flow—Laminar boundary layer—Turbulent boundary layer. 7.6. Momentum Equation for Laminar Boundary Layer. 7.7. Energy Equation for the Laminar Boundary Layer. 7.8. Boundary Layer Similarities—Friction coefficient—Nusselt number. 7.9. Determination of

Convection Heat Transfer Coefficient—Dimensional analysis—Exact mathematical solutions—Approximate analysis of boundary layers—

Analogy between heat and momentum transfer—Numerical analysis. 7.10. Dimensional Analysis—Primary dimensions and dimensional formulae—Dimensional homogeneity—Rayleigh’s method of dimensional analysis—Buckingham π theorem—Dimensional analysis for forced convection—Dimensional analysis for natural convection. 7.11. Physical Significance of the Dimensionless Parameters—Reynolds number—Critical reynolds number Recr—Prandtl number—Grashof number—Nusselt number—Stanton number—Peclet number—Graetz number. 7.12. Turbulent Boundary Layer Heat Transfer—Prandtl mixing length concept—Turbulent heat transfer. 7.13. Reynolds Colburn

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