Diagrams for fast transient conduction in sphere and long cylinder subject to sudden and violent thermal effects on its surface

Analytical solutions for fast transient conduction in spherical and cylindrical geometries subject to sudden and violent thermal effects on its surface are presented in this paper. The numerical solutions are presented in the form of simple diagrams that can be easily and readily used in some engineering applications such as aeronautics, electronics, fire dynamics, tribology, metallurgy or food and agricultural technologies. These data are useful for the optimization of numerical codes in fluid mechanics in association with heat transfer and inverse methods for the determination of thermal characteristics of the surface phenomena in various cases. These diagrams are for specific ranges of Fo and Bi numbers corresponding to the fast transient problems characterized by weak Fourier numbers, associated with a large combination of dimensions of the body and values of thermal surface conductance (large range of Bi). These diagrams constitute a special implementation (violent and sudden thermal effects) of the well known Heisler’s charts and are very useful for understanding and teaching transient heat transfer. A numerical solution is proposed. It overcomes the problems due to a too slow convergence. The main difficulty is encountered when solving characteristic equations based on a combination of the parameters involved in the particular equations of temperature and energy. That may take asymptotic values for the specific phenomenon addressed in this study. The results are successfully compared to those based on a different calculation procedure.