Combined Effect of Internal Heating and Through-flow in a Nanofluid Saturated Porous Medium Under Local Thermal Non-equilibrium

2021 ◽  
Author(s):  
Beer Bhadauria ◽  
Anurag Srivastava
Keyword(s):  
Porous Medium ◽  
Saturated Porous Medium ◽  
Combined Effect ◽  
Internal Heating ◽  
Through Flow ◽  
Non Equilibrium

scholarly journals Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

2016 ◽  
Vol 21 (4) ◽  
pp. 785-803 ◽  
Author(s):  
B.S. Bhadauria ◽  
M.K. Singh ◽  
A. Singh ◽  
B.K. Singh ◽  
P. Kiran
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Landau Equation ◽  
Power Series Expansion ◽  
Gravity Modulation ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Fluid Saturated Porous Medium

Abstract In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

scholarly journals Weakly Nonlinear Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium with Throughflow and Temperature Modulation

2018 ◽  
Vol 23 (3) ◽  
pp. 635-653 ◽  
Author(s):  
P. Kiran ◽  
Y. Narasimhulu ◽  
S.H. Manjula
Keyword(s):  
Porous Medium ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Landau Equation ◽  
Oscillatory Mode ◽  
Stationary Mode ◽  
Temperature Modulation ◽  
Through Flow ◽  
Fluid Saturated Porous Medium

Abstract The effect of vertical throughfow and temperature modulation on a viscoelastic fluid saturated porous medium has been investigated. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non autonomous complex Ginzburg- Landau equation, is calculated. The effect of vertical through flow is found to stabilize the system irrespective of the direction of through flow in the case of permeable boundary conditions. The time relaxation has a destabilizing effect, while the time retardation parameter has a stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat transport have been analyzed and depicted graphically. The study shows that the heat transport can be controlled effectively by a mechanism that is external to the system. Further, it is also found that heat transfer is more in oscillatory mode of convection rather than in stationary mode of convection.

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