A singular perturbation solution to a problem of extreme temperatures imposed at the surface of a variable-conductivity halfspace: small surface conductivity

Leonard Y. Cooper
1975 Quarterly of Applied Mathematics  
The transient temperature field resulting from a constant and uniform temperature T, (or time-dependent heat flux H = ht~1/2) imposed at the surface of a halfspace initially at uniform temperature T0 is considered. A temperature-dependent thermal conductivity variation, k(T) = k0 exp [X(T -T0)/To], and a constant product of density and specific heat, pC, are assumed to be accurate models for the halfspace for some useful temperature range. The problem is initially formulated in terms of the
more » ... in terms of the dimensionless conductivity 4> = k(T)/k0 . Attention is then focused on the singular problem resulting from the limits <£s = 4>(T,) J, 0 and , In *.). ■MO *
doi:10.1090/qam/451787 fatcat:anlbq5tmqjegtg5jogj5z47wqm