Fast transient conduction in infinite plate subject to violent thermal effects

This work is an implement to a study that was conducted for long cylinders and spheres undergoing fast processes characterized by low Fourier numbers (Fo). It allows to solve some complex 2D and 3D problems involving the specific thermal boundary conditions examined in this survey. Analytical solutions for fast transient conduction in infinite plate 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. 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 low 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 substantial improvement (especially for violent and sudden thermal effects) of the well known Heisler’s charts. 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 which may take asymptotic values for the specific phenomena addressed in this study. The results are successfully compared to those based on a different calculation procedure. It is for example the case for thermo-mechanics problem due to the braking using the tablet-disk system.