Heat transfer with ablation in a finite slab subjected to time-variant heat fluxes

Abstract

Heat transfer with ablation in a finite slab subjected to time-variant heat fluxes is studied. Three different approaches are employed: the heat balance integral method, the 0-moment integal method, and an implicit finite difference method. Three specific heat fluxes are considered, in terms of linear, exponential, and power law functions of time. Numerical results for ablation distance and speed are presented based on the aforementioned techniques. Nomenclature c = heat capacity per unit volume g = a time dependent parameter H = heat of ablation / = index for dimensionless space j = index for dimensionless time k = thermal conductivity L = thickness of the slab TV = total number of elements q0 = dimensional wall heat flux qr = reference heat flux, = k (Tm — T0) IL Q = dimensionless heat flux, = q0L/k( Tm — T0) 5 = ablation distance s - dimensionless ablation distance, = S/L s =dS/dt t = dimensional time