We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.

This article describes the impact of slip conditions on nanofluid flow through a stretching sheet. Nanofluids are very helpful to enhance the convective heat transfer in a boundary layer flow. Prandtl number also play a major role in controlling the thermal and momentum boundary layers. For this purpose, we have considered a model for effective Prandtl number which is borrowed by means of exper...

The unsteady free convection flow with thermal radiation past a vertical plate with Newtonian heating has been studied. The governing equations have been solved numerically by the implicit finite difference method of CrankNicolson's type. The variations of the fluid velocity and temperature are presented graphically. It is found that the fluid velocity decreases near the plate and it incre...

Over the past 10 years, geodynamo simulations have grown rapidly in sophistication. However, it is still necessary to make certain approximations in order to maintain numerical stability. In addition, models are forced to make assumptions about poorly known parameters for the Earth’s core. Different magnetic Prandtl numbers have been used and different assumptions about the presence of radiogen...

Full simulations of homogeneous isotropic turbulence containing a homogeneous passive scalar were made at low Reynolds numbers and various Prandtl numbers. The results show that the spectral behavior of the two fields are quite similar; both fields decay as power-law functions of time. However. the decay exponent is quite dependent on both the Reynolds and Prandtl numbers. The decay exponent of...