Heat Convection from a Sphere Placed in a Fluctuating Free Stream R. S. Alassar Dept. of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia H. M. Badr Dept. of Mechanical Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia DOI 10.1002/aic.11199 Published online May 16, 2007 in Wiley InterScience (www.interscience.wiley.com). The effect of sinusoidal fluctuations superimposed on the average free-stream velocity on mixed convection from a spherical particle is investigated. The parameters considered are the Reynolds number Re, Grashof number Gr, and the relative amplitude of fluctua- tions. The results indicate that due to the adverse pressure gradients created by the decel- eration of the free-stream, separation may occur at a Reynolds number well below that at which it occurs in uniform flow. The rising buoyancy currents, however, weaken and possi- bly destroy the formation of vortices at the rear stagnation point. The average Nusselt number is found to increase with the increase of the amplitude of the free stream fluctua- tions and with the increase of Gr/Re 2 , as along as the flow does not reverse its direction. The time and space averaged Nusselt number increases with Gr/Re 2 , with the effect of the amplitude of the free-stream fluctuations becoming less pronounced at higher values of Gr/Re 2 . Ó 2007 American Institute of Chemical Engineers AIChE J, 53: 1670–1677, 2007 Keywords: heat convection, sphere, fluctuating flow, buoyancy Introduction The problem of heat transfer from a sphere has been the subject of many investigations due to the related engineering applications. Several experimental and theoretical studies can be found which deal with either free, forced, or mixed (com- bined free and forced) convection from a sphere placed in a free-stream. The classical studies which investigate only free convection are those by Potter and Riley, 1 Geoola and Cor- nish 2 and, 3 Riley, 4 Brown and Simpson, 5 Singh and Hasan, 6 and Dudek et al. 7 Representative work on forced convection from a sphere placed in a steady uniform stream are the stud- ies by Dennis and Walker 8 for Reynolds number up to 200, Whitaker, 9 the highly accurate and detailed results by Dennis et al. 10 but for Reynolds number up to 20, and Sayegh and Gauvin. 11 The mixed convection problem was studied at small Reynolds and Grashof numbers by Hieber and Geb- hart. 12 The problem was also solved using the boundary layer approach by Acrivos. 13 Wong and Chen 14 used finite differ- ences to solve the full steady Navier-Stokes and energy equa- tions. Nguyen et al. 15 extended the work of Wong and Chen 14 and solved the transient problem with internal ther- mal resistance. The structure of the flow field under an oscillating free stream is important in understanding the heat convection pro- cess. Several studies on oscillating flow which do not con- sider any heat-transfer processes are available. The interested reader is directed to the studies by Basset, 16 Odar and Hamil- ton, 17 Mei, 18 Lawrence and Mei, 19 Sano, 20 Lovalenti and Brady, 21 Mei et al. 22 Riley, 23 and Chang and Maxey. 24 A review of the literature can be found in Alassar and Badr 25 who extended the work of Chang and Maxey 24 to Reynolds number of 200, and included a detailed analysis of the sepa- ration angle and the wake length. The studies on heat or mass transfer from a sphere in an oscillating free-stream are, on the other hand, few. The two Correspondence concerning this article should be addressed to R. S. Alassar at alassar@kfupm.edu.sa. Ó 2007 American Institute of Chemical Engineers AIChE Journal July 2007 Vol. 53, No. 7 1670