A Problem in Heat Conduction

A steady-state temperature distribution is found for the case of a periodically varying point source of heat, immersed in a homogeneous isotropic infinitely extended fluid, moving with a constant velocity. The phase velocity of the generated temperature wave is discussed. If the phase velocity in a stationary medium is V0, and the fluid velocity v>V0, the phase velocity in a moving medium is given by V=v[1+½(V0/v)4 −(5/8)(V0/v)8+…]. For practical cases one can usually assume V=v, with an error of less than 0.1 percent, even when V0 is as large as 20 percent of v.