The onset of Marangoni convection in a horizontal fluid layer with internal heat generation overlying a solid layer heated from below is studied. The upper free surface of a fluid is nondeformable and the bottom boundary are rigid and no-slip. The resulting eigenvalue problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and...

We derive upper bounds for the Nusselt number in innnite Prandtl-number rotating convection. The bounds decay algebraically with Taylor number to the conductive heat transport value; the decay rate depends on boundary conditions. We show moreover that when the rotation is fast enough the purely conductive solution is the globally and nonlinearly attractive xed point; the critical rotation rate ...

In this paper, the problem of forced convection over a horizontal flat plate under condition of variable plate temperature is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This paper provides good supplements to the existing literature and generalizes the previ...

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The problem of steady, laminar, mixed convection flow of a non-Newtonian fluid past a preamble vertical flat plate embedded in a porous medium saturated with a nanofluid is considered. A mixed convection parameter for the entire range of free-forced-mixed convection is employed and a set of non-similar equations are obtained. These equations are solved numerically by an efficient implicit, iter...