On the approximate solution of flow and heat transfer through non-circular conduits with uniform wall temperature

The boundary value problem for steady flow and heat transfer through ducts of arbitrary shape is investigated for the case of uniform wall temperature. The use of conformal mapping methods allows for a unified treatment of problems involving ducts of non-circular cross section. A simple approximate technique for solving the formulated eigenvalue problem is proposed. The method is illustrated for slug flows in complex cross sections of practical interest. It is shown that the technique is also applicable to non-uniform flows and the numerical results for the eigenvalues of the Graetz problem are in excellent agreement with the published data.