Hollow cylinders are useful building structures commonly used for both industrial and domestic purposes. Tanks, cars and some transport machineries are all applications of inner-insulated hollow cylinders to keep contained liquid away from the outer temperature. Food-storage tanks are common applications of these cylinders to ensure the highest level of safety and hygiene. Moreover, Pure transient or periodic heat conduction and simple or complex combinations of them exist in the heat treating of metals, air conditioning, and food processing. Heat transfer problems with time dependence are very common in engineering applications such as hydrocooling of cylindrical food products and heat conduction in composite cylinders under time dependent boundary conditions, which are used in many engineering fields such as aerospace, automobile, chemical, and energy. The heat conduction problems with periodic boundary conditions have some applications in engineering, such as wall temperature oscillation of internal combustion engines, oscillation of environmental temperature in extended surfaces, especially fins, and experimental methods for specifying the thermal diffusivity of material and the temperature field.
Thus an accurate design of heat transfer systems require an appropriate technique. Although a number of analytical solutions for conduction heat transfer problems are available (Carlene and Jaeger 1959;Ozisik 1968),in many practical situations, the geometry and boundary conditions are so complex that an analytical solution in two dimensions is not possible. Even if one could develop analytical relations for such complicated cases, these will invariably involve complex series solutions and would thus be practically difficult to implement. In such situations, conduction heat transfer problems need a numerical solution . The accurate prediction can be achieved using the solutions to mathematical models. The solutions can be obtained by applying mathematical techniques, developing algorithms and implementing these algorithms using computer software.
The implementation of algorithms is achieved with programming ability, which takes advantage of the immense power of today’s computing systems. Programming ability is a should-have for modern Engineers.