Thermal effects in StokesÕ second problem for unsteady micropolar fluids flow F.S. Ibrahem a, * , I.A. Hassanien a , A.A. Bakr b a Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt b Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt Abstract The MCF model is used to study the non-classical heat conduction effects in StokesÕ second problem of a micropolar fluid. The effects of the thermal relaxation time and the structure wave on angular velocity, velocity field and temperature are investigated. The skin friction, the displacement thickness and the rate of the heat transfer at the plate are determined. Ó 2005 Elsevier Inc. All rights reserved. Keywords: StokesÕ second problem; Micropolar fluids; Maxwell–Cattaneo–Fox model 1. Introduction FourierÕs law of heat conduction, which has been used to drive the heat con- duction equation in classical unsteady heat transfer problems, results in a par- abolic equation for temperature filed and an infinite speed of heat propagation, thus violating the principle of causality. Maxwell [1] derived the generalization 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.04.024 * Corresponding author. E-mail address: fibrahim@acc.aun.edu.eg (F.S. Ibrahem). Applied Mathematics and Computation 173 (2006) 916–937 www.elsevier.com/locate/amc