Laplace's equation for convective scalar transport in potential flow

Laplace's equation for the stream function and the velocity potential has b een used for a long time for the solution of irrotational flow problems in hydrodynamics. Here, a similar formulation is presented for the convective transport of a scalar such as heat or mass. It is discovered that, in suita ble coordinates, the so-called heat function also satisfies Laplace's equat ion. This function, which was introduced earlier for the visualization of h eat flow in two-dimensional convection, can be used to build up solutions f or scalar transport, both analytical and numerical, by superposition, in mu ch the same way that the stream function or velocity potential can. A vast array of solutions and techniques, developed over centuries, therefore beco mes available for the scalar transport problem.