Method calculation of a temperatures field of gas flow, in a cylindrical channel in the presence of internal sources of non-uniformly distributed heat in the axial direction

The calculation of a temperature field of gas flow with an internal heat source is generalized in case of a non-uniform axisymmetric heat distribution. The distribution is approximated by a set of segments of various lengths. The source function in each segment is considered constant, in the axial direction, while its radial profile is specific only to that segment. Thus, gas flow sequentially moves through n+2 areas: input z < 0, output z > 1 and the area of the internal heat source 0 <= z <= l, presented by n segments. The obtained analytical solutions provide us with a straightforward way to calculate the heat balance for a wide class of complex problems related to describing air flow in the presence of non-uniform heat source distribution in the axial direction.