Marangoni convection of non‐Newtonian power law fluids in a shallow rectangular cavity

Abstract

Analytical and numerical studies are conducted for two-dimensional steady-state Marangoni 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 effect of the non-Newtonian behavior on the hydrodynamic stability, 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.

Marangoni convection of power law fluids driven by power-law temperature gradient

“…In EMT, Naimi et al [10] studied two-dimensional steady-state Marangoni convection of nonNewtonian power law fluids in a shallow rectangular cavity. Boeck and Thess [11] studied power-law scaling in Benard-Marangoni convection at large Prandtl numbers.…”

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

“…The surface tension was assumed to vary linearly with the temperature and the mass fraction. Naimi et al [13] studied two-dimensional steady-state Marangoni convection of non-Newtonian power-law fluids in a shallow rectangular cavity. Scheid et al [14] presented theoretical study focuses on the dynamics of a thin film falling down a vertical plate with a nonuniform, sinusoidal temperature distribution.…”

Marangoni Convection Flow and Heat Transfer of Power Law Nanofluids Driven by Temperature Gradient with Modified Fourier's Law

“…The basic mechanism of Marangoni convection has been extensively investigated. Recently, Naimi et al [13] studied twodimensional steady-state Marangoni convection of nonNewtonian power law fluids in a shallow rectangular cavity. Marangoni convection over a flat surface due an imposed temperature gradient with the surface tension varies linearly as the temperature was studied in [14][15][16].…”