Exact solutions to differential-difference heat and mass transfer equations with a finite relaxation time

Abstract

Certain exact solutions to the linear differential-difference heat and mass transfer equations with a finite relaxation time are specified. The exact solution to the one-dimensional Stokes problem with the periodic boundary condition when a first-order volume chemical reaction occurs is given. A wide class of exact solutions to the nonlinear differential-difference heat-conduction equation with the following source is described: $$\Theta _t = div[f(T)\nabla T] + g(\Theta ), = T(r,t + \tau ),$$ where T = T(r, t) is temperature and τ is the relaxation time. Certain more complex heat conduction models with a variable relaxation time that can depend on time and a temperature gradient are also considered.