Effect of Internal Heat Source on the Onset of Convection in a Nanofluid Layer

2011 ◽  
Vol 110-116 ◽  
pp. 1827-1832
Author(s):  
Dhananjay ◽  
G.S. Agrawal ◽  
R. Bhargava
Keyword(s):  
Brownian Motion ◽  
Stability Analysis ◽  
Rayleigh Number ◽  
Heat Source ◽  
Lower Boundary ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Onset Of Convection ◽  
Diffusivity Ratio ◽  
Upper Boundary

Effect of internal heat source on the onset of convection in nanofluid layer heated from below is studied. The lower boundary and upper boundary are assumed to be rigid and free respectively. The two important effects namely the Brownian motion and thermophoresis have been included in the model of nanofluid. Linear stability analysis has been made to investigate the effect of internal heat source on the onset of convection. Galerkin method is used to obtain the analytical expression for Rayleigh number in the non-oscillatory mode and result are depicted graphically. It has been shown that the internal heat source, nanoparticle Rayleigh number and modified diffusivity ratio have a destabilizing effect depending upon the values of various nanofluid parameters.

scholarly journals Linear and Nonlinear Stability Analysis of Double Diffusive Convection in a Maxwell Fluid Saturated Porous Layer with Internal Heat Source

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Moli Zhao ◽  
Qiangyong Zhang ◽  
Shaowei Wang
Keyword(s):  
Rayleigh Number ◽  
Heat Source ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Maxwell Fluid ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Linear And Nonlinear ◽  
Double Diffusive

The onset of double diffusive convection is investigated in a Maxwell fluid saturated porous layer with internal heat source. The modified Darcy law for the Maxwell fluid is used to model the momentum equation of the system, and the criterion for the onset of the convection is established through the linear and nonlinear stability analyses. The linear analysis is obtained using the normal mode technique, and the nonlinear analysis of the system is studied with the help of truncated representation of Fourier series. The effects of internal Rayleigh number, stress relaxation parameter, normalized porosity, Lewis number, Vadasz number and solute Rayleigh number on the stationary, and oscillatory and weak nonlinear convection of the system are shown numerically and graphically. The effects of various parameters on transient heat and mass transfer are also discussed and presented analytically and graphically.

scholarly journals Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
I. K. Khalid ◽  
N. F. M. Mokhtar ◽  
I. Hashim ◽  
Z. B. Ibrahim ◽  
S. S. A. Gani
Keyword(s):  
Feedback Control ◽  
Heat Source ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Density Ratio ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Onset Of Convection ◽  
Double Diffusive

A linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Bénard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below and the model used for the nanofluid layer incorporates the effects of thermophoresis and Brownian motion. Three types of bounding systems of the model have been considered which are as follows: both the lower and upper bounding surfaces are free, the lower is rigid and the upper is free, and both of them are rigid. The eigenvalue equations of the perturbed state were obtained from a normal mode analysis and solved using the Galerkin method. It is found that the effect of internal heat source and Soret parameter destabilizes the nanofluid layer system while increasing the Coriolis force, feedback control, and Dufour parameter helps to postpone the onset of convection. Elevating the modified density ratio hastens the instability in the system and there is no significant effect of modified particle density in a nanofluid system.

Onset of Convection in a Porous Medium With Internal Heat Generation

1976 ◽  
Vol 98 (1) ◽  
pp. 49-54 ◽  
Author(s):  
R. D. Gasser ◽  
M. S. Kazimi
Keyword(s):  
Porous Medium ◽  
Heat Generation ◽  
Lower Boundary ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Rigid Surface ◽  
Onset Of Convection ◽  
Rayleigh Numbers ◽  
Upper Boundary ◽  
Small Disturbances

The conditions leading to onset of thermal convection in a horizontal porous layer are determined analytically using the method of linear stability of small disturbances. The lower boundary is treated as a rigid surface and the upper boundary as a free surface. The critical internal and external Rayleigh numbers are determined for both stabilizing and destabilizing boundary temperatures. The predicted critical external Rayleigh number in the limit of no heat generation is in agreement with the critical number predicted for a porous medium heated from below.

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