HEAT AND MASS TRANSPORT IN A NANOFLUID LAYER USING A THERMAL NONEQUILIBRIUM MODEL CONFINED WITHIN A HELE-SHAW CELL UNDER THE EFFECT OF GRAVITY MODULATION

Abstract

The local thermal nonequilibrium (LTNE) condition is the temperature difference between the base fluid and the nanoparticle. In the present research article, linear analysis was done to know about the onset of convection in the system, and a weakly nonlinear stability analysis was done to know about heat and mass transport in the system for both the unsteady and steady case. Here we have taken temperature to be constant and nanoparticle flux to be zero at the upper and lower boundaries of the system. The normal mode technique is used for linear analysis, and the truncated Fourier series method is used for nonlinear analysis; plot streamlines, isotherms, and isohaline are used to visualize the conduction, convection, and steady state. We found that the behavior of Hele-Shaw cell is the same in the case of LTNE and local thermal equilibrium (LTE). The effect of Hele-Shaw number, interphase heat transfer coefficient, modified thermal capacity ratio, thermal diffusivity ratio, amplitude, and frequency of modulation on the onset of convection, heat, and mass transfer are depicted graphically. We found that the effect of LTNE can be seen only for the intermediate values of the interphase heat transfer coefficient, and this region is called the LTNE region. We also discuss the result of thermal Nusselt number, streamlines, and isothermals of fluid and particle phase for steady case and plot the graphs with respect to the Hele-Shaw cell Rayleigh number. Rate of heat transfer for the particle phase is higher than the fluid phase for both the unsteady and steady state. In this research paper we find the result for both LTE and LTNE conditions with unsteady and steady cases, while in the previous study we analyzed only for the LTE condition.