Local Thermal Non-Equilibrium and Internal Heating Impact on Thermal Instability of Jeffrey Nanofluid Saturated Porous Media Under Different Gravity Modulations

Abstract

In the present study, we have implied internal heating and different types of gravity modulation on a Jeffrey nanofluid saturating porous media under three field temperature models i.e., fluid, solid-matrix, and particle phases. Normal mode technique is applied for linear analysis and the truncated Fourier series method is used for non-linear analysis. Numerical values are obtained to compare the convection rate between LTNE and LTE models. Jeffrey parameter and internal heating enhance the stationary rate of convection. Analytically the effect of internal heating and the Jeffrey parameter is obtained and compared with graphical results. Effect of rate of convection at ɛp = 0.1 is observed more earlier than convection at ɛp = 0.4. Opposite impact of the Jeffrey parameter is obtained in the graph of interface heat transfer for particle phase (NHS) and critical wave number (ac). Three types of gravity modulation (day-night, saw-tooth, sinusoidal) are applied to investigate the earlier influence of modulation on the system for Nusselt number for concentration, fluid, solid-matrix, and particle phase and we obtain day-night profile has an earlier rate of heat and mass transfer than the other two profiles. No effect of frequency of modulation is observed for steady-state analysis. Comparison of heat transfer rate for Nusselt number was obtained using RKF-45 method and NDSolve Mathematica.