Numerical Solution for Nonlinear Transient Heat Transfer in Composite Solids
One dimensional transient heat conduction in composite solids (slabs, cylinders, spheres, hollow cylinders, hollow spheres) with variable thermal properties and internal heat generations subject to simultaneous forced convection, thermal radiation and arbitrary time dependent flux (e.g., periodical heating or cooling) is studied. The contact resistance at the interfaces between the layers and the thermal radiation between the gap are also taken into consideration. In this study the convective heat transfer coefficients and the thermal contact conductance can be functions of time; the initial temperatures of the media can be an arbitrary function of space. Due to the strong nonlinearities which arise from the temperature dependency of the thermal properties, the internal heat sources and the boundary conditions, the analytical solution is not feasible. An explicit finite difference scheme is adapted. A general computer code is developed to accomplish this purpose. Typical numerical results based on this analysis are presented graphically.
Numerical methods for non-linear problems
Yeh, L. T. and Chung, Benjamin T.F., "Numerical Solution for Nonlinear Transient Heat Transfer in Composite Solids" (1980). Mechanical Engineering Faculty Research. 1016.