Insulated metallic slab - A graphical solution to the transient heat conduction 'inverse problem'

A graphical solution of the inverse problem of heat conduction of an insulated metallic slab exposed to a convective heat flux of Newtonian type is presented. The insulation layer thickness adequate to prevent the metallic wall to exceed a prescribed temperature at the end of the heating process is determined. The quantities defining the required amount of insulation are the characteristic parameters of the heating environment (heat transfer coefficient and adiabatic wall temperature), the thermophysical properties of the materials selected to realize the insulation and the metallic layers, and the assigned thickness and temperature limits of the metallic layer to be protected by the insulation. Three nondimensional parameters, defined as functions of the ratio of the unknown insulation layer thickness to the known metallic layer thickness, are introduced to obtain the solution by means of a graphical procedure in terms of the Biot, the Fourier and the Heat Capacity Ratio numbers. The resulting design chart allows a rapid and accurate solution for a wide range of the basic parameters.