The heat radiation diffusion equation: Explicit analytical solutions by improved integral-balance method

Approximate explicit analytical solutions of the heat radiation diffusion equation by applying the double integration technique of the integral-balance method have been developed. The method allows approximate closed form solutions to be developed. A problem with a step change of the surface temperature and two problems with time dependent boundary conditions have been solved. The error minimization of the approximate solutions has been developed straightforwardly by minimization of the residual function of the governing equation.