By using methods well known in boundary layer theory, the pressure across a contact region is shown to be approximately constant. A partial differential equation for the temperature is then derived. If the ideal-gas flow external to the contact region is known, the temperature profile can be determined. This can then be used to calculate successively the velocity and a better approximation for the pressure of the gas in the contact region. The theory is illustrated by obtaining the temperature, velocity and pressure distributions for a gas in a contact region moving with uniform velocity. The thermal conductivity of the gas is assumed to vary with the temperature τ like k = knτn, where n = 0, 1 or 2. The results are valid for any temperature ratio across the region.

The general theory is also used to determine the motion of a plane shock which is reflected from a plane-conducting wall. The fluid between the reflected shock and the wall is at a higher temperature than that of the wall and a contact region adjacent to the wall results. Expressions for the temperature, velocity and pressure of the fluid are derived, and it is shown that the effect of heat conduction is to decrease the velocity of the reflected shock by an amount which varies as the inverse square root of the time.