Semi-analytical solution of the extended Graetz problem for combined electroosmotically and pressure-driven microchannel flows with step-change in wall temperature

Analytical solutions are obtained for the temperature and Nusselt number distribution in the thermal entrance region of a parallel plate microchannell under the combined action of pressure-driven and clectroosinotic transport mechanisms, by taking into account the effects of viscous dissipation, Joule heating and axial conduction simultaneously, in the framework of all extended Graetz problem. Step changes in wall temperature are considered to represent physically conceivable thermal entrance conditions. Tile solution ofthe temperature distributions at tile various channel sections essentially involves the determination of a,set of eigenvalucs and eigenfunctions corresponding to a Sturm Liouiville problem with non self-adjoint operators. The resultant eigenfunctions are non orthogonal in nature, and are obtained in the forms of hypergeometric functions. Parametric variations oil tile effects of tile relative strengths of the pressure gradients and tile electric field, ratio of tile rate of heat generation to the rate of wall heat transfer, and the Peclet number are analyzed in details, in terms of their influences on the temperature field as well as tile Nusselt number distribution. (c) 2008 Elsevier Ltd. All rights reserved.