On approximate solutions of the Graetz problem with axial conduction

Abstract

Two approximate solutions of the Graetz problem with axial conduction and a specified wall temperature (one for low Peclet numbers and the other for high Peclet numbers) are presented and compared favorably with the exact analytical solutions. With the proposed techniques, the approximate eigenvalues and eigenfunctions are obtainable explicitly and readily computable, unlike the methods for the exact results. Both low and high Peclet number approximate solutions give excellent agreements with the exact results when Pe ⩽ 1 and Pe ⩾ 10 respectively. In the limits, both approximate solutions will tend towards those exact ones. For the intermediate range of Peclet numbers between 1 and 10, either approximate technique gives surprisingly satisfactory results.