Transport in Porous Media 32: 329–355, 1998. c  1998 Kluwer Academic Publishers. Printed in the Netherlands. 329 Mixed Convection Adjacent to a Suddenly Heated Horizontal Circular Cylinder Embedded in a Porous Medium R. BRADEAN 1 , D. B. INGHAM 1 , P. J. HEGGS 2 and I. POP 3 1 Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, U.K. 2 Department of Chemical Engineering, UMIST, Manchester M60 1QD, U.K. 3 Faculty of Mathematics, Babes–Bolyai University, R-3400 Cluj–Napoca, CP 253, Romania (Received: 20 January 1998; in final form: 28 April 1998) Abstract. The mixed convection caused when a horizontal circular cylinder is suddenly heated is investigated in the situation when the initial flow past the cylinder is uniform and its direction either upwards or downwards. An analytical series solution, which is valid at small times, is obtained using the matched asymptotic expansions technique. A numerical solution, which is valid at all times and for any values of the Rayleigh and P´ eclet numbers, is also obtained using a fully implicit finite-difference method. Three different regimes, when either the free or forced convection is dominant or when they have the same order of magnitude, are considered. In the free convection dominated regime, two vortices develop near the sides of the cylinder in both situations of an upward or downward external flow. Comparisons between the analytical and numerical results at small times, as well as a detailed discussion of the evolution of the numerical solution are presented. The numerical results obtained for large Rayleigh, Ra, and P´ eclet, Pe, numbers show that a thermal boundary-layer forms adjacent to the cylinder for any value of the ratio Ra/Pe. The steady state boundary-layer analysis, similar to that performed by Cheng and Merkin, is analysed in comparison to the numerical solution obtained for large values of Ra and Pe at very large times. Key words: mixed convection, asymptotic expansion technique, impulsively heated horizontal circular cylinder. 1. Introduction In recent years, the study of heat convection through porous media has been stim- ulated by the large number of geophysical and engineering applications, such as in geothermal reservoirs, irrigation systems, the exploration of petroleum and gas fields, porous insulations and the cooling of rotating electric windings. Some of the most important analytical, numerical and experimental studies with such applications, which present the current state of the art in this area, have been gathered in the excellent reviews performed by Cheng (1978), Bejan (1987), Tien and Vafai (1990), Kakac et al. (1991) and Nield and Bejan (1992). The free convection from surfaces embedded in porous media has been extensively investigated for many configurations involving different geometries and thermal