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Conduction—Basic Equations

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2.1. Generalised One Dimensional Heat Conduction Equation. 2.2. Three Dimensional Heat Conduction Equation—For the cartesian coordinates—Three dimensional heat conduction equation in cylindrical coordinates—Three dimensional heat conduction equation in spherical coordinates. 2.3. Initial and Boundary Conditions—Prescribed temperature boundary conditions—Prescribed heat flux boundary conditions—Convection boundary conditions : Surface energy balance—Radiation boundary condition—Interface boundary condition. 2.4. Summary—Review Questions—Problems.

The objective of this chapter is to provide a good understanding of the heat conduction equations and boundary conditions for the use in mathematical formulation of heat conduction problems.

2.1.

GENERALISED ONE DIMENSIONAL HEAT

CONDUCTION EQUATION

For the thermal analysis of the bodies having shapes such as slab, rectangle, the cartesian coordinates are used, while for cylindrical and spherical bodies, the polar and spherical coordinate systems are used.

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Transient Heat Conduction

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6.1. Approximate Solution—Systems with negligible internal resistance : lumped system analysis—Dimensionless quantities—Thermal time constant and response of thermocouple—The lumped system analysis for mixed boundary conditions—The validity of lumped system analysis. 6.2. Analytical Solution—Criteria for neglecting internal temperature gradients—Infinite cylinder and sphere with convective boundaries—One term approximation. 6.3. Transient Temperature Charts : Heisler and Gröber Charts—Transient temperature charts for slab—Transient temperature charts for long cylinder and sphere. 6.4. Transient Heat Conduction in Semi Infinite Solids—Penetration depth and penetration time. 6.5. Transient Heat Conduction in Multidimensional Systems. 6.6. Summary—Review Questions—Problems—

References and Suggested Reading.

When the heat energy is being added or removed to or from a body, its energy content (internal energy) changes, resulting into change in its temperature at each point within the body over the time. During this transient period, the temperature becomes function of time as well as direction in the body. The conduction occurred during this period is called transient (unsteady state) conduction. Therefore, in unsteady state

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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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Experiments in

Engineering Heat Transfer

16

Expt. 1 Thermal Conductivity of Metallic Rod. Expt. 2 Thermal Conductivity of Insulating Powder. Expt. 3 Thermal Conductivity of Composite Wall. Expt. 4 Natural Convection Experiment. Expt. 5 Forced Convection Experiment. Expt. 6 Heat Transfer from Pin

Fins. Expt. 7 Stefan Boltzmann Constant. Expt. 8 Measurement of Emissivity of a Test Surface. Expt. 9 Heat Exchanger Experiment.

Expt. 10 Critical Heat Flux. Expt. 11 Heat Pipe. Expt. 12 Thermocouples Calibration Test Rig—Review Questions—References

Engineering education has placed a great emphasis on the ability of an individual to perform experiments along with a theoretical analysis of the problems. The experimental methods have their own importance. They help in better understanding of the basic principles of the subject and to verify the result obtained analytically.

Therefore, in engineering curiculla, the students are expected to devote one laboratory period a week for experimentation. The students are exposed to the basic instruments and get acquainted with the methods used for measuring the physical properties.

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Concepts and Mechanisms of Heat Flow

1.1. What is Heat Transfer ? 1.2. Modes of Heat Transfer. 1.3. Physical Mechanism of Modes of Heat Transfer—Conduction

—Convection—Radiation. 1.4. Laws of Heat Transfer—Law of conservation of mass : Continuity equation—Newton’s second law of motion—Laws of thermodynamics—Fourier law of heat conduction—Newton’s law of cooling—The Stefan Boltzmann law of thermal radiation. 1.5. Combined Convective and Radiation Heat Transfer—Equation of state. 1.6. Thermal

Conductivity—Variation in thermal conductivity—Determination of thermal conductivity—Variable thermal conductivity.

1.7. Isotropic Material and Anisotropic Material. 1.8. Insulation Materials—Superinsulators—Selection of insulating materials—The R-Value of insulation—Economic thickness of insulation. 1.9. Thermal Diffusivity. 1.10. Heat Transfer in

Boiling and Condensation. 1.11. Mass Transfer. 1.12. Summary—Review Questions—Problems—Multiple Choice Questions.

Objective of this chapter is to:

• give an introduction to heat transfer rate, heat flux,

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