Constant surface heating of a variable conductivity half-space
A solution to the problem of constant surface heating of an initially constant-temperature, T*0 , half-space where the material in question has a temperaturedependent thermal conductivity is obtained. The thermal conductivity, k*, is specifically given by k* = k% exp [X(T* — T*0)/T%]. The solution is valid for both heating and cooling of the material where X and k% are arbitrary in magnitude, and X can be either positive or negative in sign. The technique of solution of the nonlinear problem considered here is an extension of an integration method used for the boundary layer equations of fluid mechanics. The present success and generality of the technique suggest its use for the solution of more complicated variable property transient heat conduction problems.