ABSTRACT
This chapter discusses means for calculating the temperature distribution in a solid body. There are three kinds of the transfer of heat that is conduction, convection, and radiation. The transfer of heat between two particles of the solid body takes place by conduction in which heat flows through the particles of the body. When over-all transfer of the heat in the solid body is considered, the transfer due to radiation is usually negligible. The Fourier heat conduction equation is derived and stated in various coordinate systems. Six sets of boundary conditions, along with the appropriate initial condition, are introduced: prescribed surface temperature; the adiabatic surface; prescribed heat flux; heat transfer by convection; heat transfer by radiation; heat transfer by convection and radiation. Detailed solution methodologies for one-dimensional temperature variations are provided by the separation of variables method and the Laplace transform technique in Cartesian, cylindrical, and spherical coordinate systems.
