Page 1 Chapter 2: Heat Conduction Equation Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Page 2 Chapter 2: Heat Conduction Equation Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Objectives When you finish studying this chapter, you should be able to: â€¢ Understand multidimensionality and time dependence of heat transfer, and the conditions under which a heat transfer problem can be approximated as being one-dimensional, â€¢ Obtain the differential equation of heat conduction in various coordinate systems, and simplify it for steady one-dimensional case, â€¢ Identify the thermal conditions on surfaces, and express them mathematically as boundary and initial conditions, â€¢ Solve one-dimensional heat conduction problems and obtain the temperature distributions within a medium and the heat flux, â€¢ Analyze one-dimensional heat conduction in solids that involve heat generation, and â€¢ Evaluate heat conduction in solids with temperature-dependent thermal conductivity. Page 3 Chapter 2: Heat Conduction Equation Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Objectives When you finish studying this chapter, you should be able to: â€¢ Understand multidimensionality and time dependence of heat transfer, and the conditions under which a heat transfer problem can be approximated as being one-dimensional, â€¢ Obtain the differential equation of heat conduction in various coordinate systems, and simplify it for steady one-dimensional case, â€¢ Identify the thermal conditions on surfaces, and express them mathematically as boundary and initial conditions, â€¢ Solve one-dimensional heat conduction problems and obtain the temperature distributions within a medium and the heat flux, â€¢ Analyze one-dimensional heat conduction in solids that involve heat generation, and â€¢ Evaluate heat conduction in solids with temperature-dependent thermal conductivity. Introduction â€¢ Although heat transfer and temperature are closely related, they are of a different nature. â€¢ Temperature has only magnitude it is a scalar quantity. â€¢ Heat transfer has direction as well as magnitude it is a vector quantity. â€¢ We work with a coordinate system and indicate direction with plus or minus signs. Page 4 Chapter 2: Heat Conduction Equation Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Objectives When you finish studying this chapter, you should be able to: â€¢ Understand multidimensionality and time dependence of heat transfer, and the conditions under which a heat transfer problem can be approximated as being one-dimensional, â€¢ Obtain the differential equation of heat conduction in various coordinate systems, and simplify it for steady one-dimensional case, â€¢ Identify the thermal conditions on surfaces, and express them mathematically as boundary and initial conditions, â€¢ Solve one-dimensional heat conduction problems and obtain the temperature distributions within a medium and the heat flux, â€¢ Analyze one-dimensional heat conduction in solids that involve heat generation, and â€¢ Evaluate heat conduction in solids with temperature-dependent thermal conductivity. Introduction â€¢ Although heat transfer and temperature are closely related, they are of a different nature. â€¢ Temperature has only magnitude it is a scalar quantity. â€¢ Heat transfer has direction as well as magnitude it is a vector quantity. â€¢ We work with a coordinate system and indicate direction with plus or minus signs. Introduction - Continue â€¢ The driving force for any form of heat transfer is the temperature difference. â€¢ The larger the temperature difference, the larger the rate of heat transfer. â€¢ Three prime coordinate systems: â€“ rectangular (T(x, y, z, t)) , â€“ cylindrical (T(r, ?, z, t)), â€“ spherical (T(r, ?, ?, t)). Page 5 Chapter 2: Heat Conduction Equation Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Objectives When you finish studying this chapter, you should be able to: â€¢ Understand multidimensionality and time dependence of heat transfer, and the conditions under which a heat transfer problem can be approximated as being one-dimensional, â€¢ Obtain the differential equation of heat conduction in various coordinate systems, and simplify it for steady one-dimensional case, â€¢ Identify the thermal conditions on surfaces, and express them mathematically as boundary and initial conditions, â€¢ Solve one-dimensional heat conduction problems and obtain the temperature distributions within a medium and the heat flux, â€¢ Analyze one-dimensional heat conduction in solids that involve heat generation, and â€¢ Evaluate heat conduction in solids with temperature-dependent thermal conductivity. Introduction â€¢ Although heat transfer and temperature are closely related, they are of a different nature. â€¢ Temperature has only magnitude it is a scalar quantity. â€¢ Heat transfer has direction as well as magnitude it is a vector quantity. â€¢ We work with a coordinate system and indicate direction with plus or minus signs. Introduction - Continue â€¢ The driving force for any form of heat transfer is the temperature difference. â€¢ The larger the temperature difference, the larger the rate of heat transfer. â€¢ Three prime coordinate systems: â€“ rectangular (T(x, y, z, t)) , â€“ cylindrical (T(r, ?, z, t)), â€“ spherical (T(r, ?, ?, t)). Classification of conduction heat transfer problems: â€¢ steady versus transient heat transfer, â€¢ multidimensional heat transfer, â€¢ heat generation. Introduction - ContinueRead More

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