Effect of radiative heat transfer on thermal-solutal Marangoni convection in a shallow rectangular cavity with mutually perpendicular temperature and concentration gradients

Abstract

A series of three-dimensional numerical simulations considering the effect of radiative heat transfer on the free surface has been carried out to examine the characteristics of thermal-solutal Marangoni convection in a shallow rectangular cavity that is subjected to mutually perpendicular temperature and concentration gradients. In the simulation, the overall contributions of thermal and solutal Marangoni flows are in the same order (Marangoni ratio Maσ=1) for all the cases considered, and the ambient temperature Θa ranges from −1.5 to 1.5, representing the transition from heat loss to heat gain in the whole system. Results show that with the increase of ambient temperature in the case of steady flow, the intensity of the thermal Marangoni effect decreases first, and then increases; furthermore, the flow structure, temperature, and concentration fields in the cavity are significantly affected by the radiative heat transfer on the free surface. When the Marangoni number exceeds a critical value, the flow stability is lost, and a three-dimensional oscillatory flow develops. The critical Marangoni number at which the flow destabilizes highly depends on thermal radiation and exhibits different variation tendencies on the stages of heat loss and gain. For the oscillatory flow, the observed wave patterns of temperature and concentration fluctuations are caused by the coupling effect of thermal-solutal Marangoni flow and radiative heat transfer. Two new types of oscillatory modes with different propagation directions appear in the cases of larger heat loss and gain due to the effect of thermal radiation. In addition, a sudden drop in the frequency is observed at a higher thermal Marangoni number.