On transient heat conduction in the walls of a rectangular gas channel

In this paper a problem on transient heat conduction in the walls of a gas channel with a rectangular cross-section is solved. The temperature of the gas flow in the channel rises linearly while the temperature of the surrounding open air is constant.The differential equation and its auxiliary conditions are Laplace transformed, the subsidiary equations are solved by a method resembling the two-dimensional relaxation method for steady state heat conduction problems, and the resulting temperatures are obtained by numerical inversion.Numerical results are presented at the end of the paper.