Abstract
In the current research, the effect of thermophoretic motion combined with temperature-dependent thermal conductivity on natural convection flow around the surface of a sphere at several circumferential locations has been presented. The modeled nonlinear governing partial differential has been transformed into a dimensionless form with the help of appropriate non-dimensional variables. Later, the finite difference method is applied to solve the proposed model. The effect of controlling parameters, such as thermal conductivity variation parameter γ, Prandtl number Pr, Schmidt number Sc, thermophoretic coefficient k, and thermophoresis parameter Nt on the velocity field, temperature distribution, mass concentration, skin friction, rate of heat transfer, and rate of mass transfer has been highlighted. The estimations of the emerging parameters on the physical properties are displayed in graphical and in tabular forms. It has been predicted that the rise in γ, Nt, Sc, Pr, and k increases the velocity distribution, but the reverse behavior has been seen in the temperature field. The enhancement in Nt, Sc, Pr, and k boosts up the curves of mass concentration, and the rise in γ suppresses the concentration function. It has been observed that an increase in γ reduces the skin friction and the rate of mass transfer but opposite behavior of the rate of heat transfer occurs. Furthermore, increasing values of Sc cause the skin friction to lose the dominance in the rate of heat and mass transfer. It has been also noticed that increasing values of Nt strengthen the skin friction and rate of heat transfer, and attenuation occurs in the case of the rate of mass transfer.
Highlights
The phenomenon observed in mixtures of moving submicron particles in which these particles move away or come toward the surface due to temperature gradient is termed nanoparticle motion commonly known as thermophoresis
It has been noticed that increasing values of Nt strengthen the skin friction and rate of heat transfer, and attenuation occurs in the case of the rate of mass transfer
We have focused on the study of the physical behavior of the combined effects of nanoparticle motion and variable thermal conductivity on natural convection flow around a sphere for different values of parameters involved in the flow model, and they are displayed in the tabular form as well as graphically
Summary
The phenomenon observed in mixtures of moving submicron particles in which these particles move away or come toward the surface due to temperature gradient is termed nanoparticle motion commonly known as thermophoresis. Kuznetsov and Nield examined the revised model of the free convection boundary layer flow of nano-fluids over a vertical plate discussed in Ref. 7. Ashraf et al. proposed the model of convective flow over a magnetized surface by taking the effect of variable viscosity and temperature-dependent thermal conductivity. Li et al. discussed the model of force convection flow of the power-law of non-Newtonian fluid through semi-infinite parallel plates with the consideration of variable thermal conductivity. Malik et al. studied the effect of variable thermal conductivity on heat transfer and fluid flow mechanism in Sisko fluid in the presence of an applied magnetic field
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