Plane problem of the theory of convective heat and mass transfer

A solution is obtained to the plane problem of convective heat transfer from a heated body of arbitrary shape in a flow of ideal incompressible heat-conducting fluid. In Helmholtz variables the initial boundary value problem is reduced to the equivalent problem of convective heat transfer from a heated plate in the flow of an ideal incompressible fluid. This latter problem is solved, after appropriate transformations, by separation of variables in elliptic coordinates and the solution is represented in the form of a Mathieu function series. Simple asymptotic formulas are obtained for small and large Peclet numbers.