Buoyant Marangoni convection of weakly non-Newtonian power law fluids in a shallow rectangular cavity M. Naı ¨mi Universite ´ Cadi Ayyad, Faculte ´ des Sciences et Techniques de Be ´ni-Mellal, De ´partement de Physique, UFR de Chimie Applique ´e et Sciences de l’Environnement, Laboratoire d’Energe ´tique, Be ´ni-Mellal, Maroc M. Hasnaoui Universite ´ Cadi Ayyad, Faculte ´ des Sciences Semlalia, De ´partement de Physique, UFR de Thermique et Me ´canique des Fluides, Marrakech, Maroc J.K. Platten Universite ´ Mons-Hainaut, Faculte ´ de Me ´decine, Service de Chimie Ge ´ne ´rale, Mons, Belgium Keywords Heat transfer, Non-Newtonian fluids, Buoyancy Abstract Analytical and numerical studies are conducted for two-dimensional steady-state coupled Marangoni and buoyancy convection of a non-Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The results obtained by combining the two basic mechanisms (thermocapillarity and buoyancy) depend on whether their effects are aiding or opposite. The effect of the non-Newtonian behavior on the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations. The current issue and full text archieve of this journal is available at http://www.emeraldinsight.com/0264-4401.htm Nomenclature A = Aspect ratio of the enclosure, Eq. (16) Bi = Biot number, Eq. (14) C = dimensionless horizontal temperature gradient c p = heat capacity (J/kg.K) g = gravitational acceleration (m/s 2 ) h = local heat transfer coefficient at the liquid-gas interface (W/m 2 .K) h 0 = liquid layer height (m) k 0 = consistency index for power-law fluid, Pas n0 L 0 = cavity length (m) Ma = generalized Marangoni number, Eq. (17) n 0 = flow behavior index for power-law fluid Buoyant Marangoni convection 49 Received May 2000 Revised July 2001 Accepted August 2001 Engineering Computations, Vol. 19 No. 1, 2002, pp. 49–91. q MCB UP Limited, 0264-4401 DOI 10.1108/02644400210413658