Onset of Darcy-Brinkman Convection in a Binary Viscoelastic Fluid-Saturated Porous Layer with Internal Heat Source

2013 ◽  
Vol 42 (8) ◽  
pp. 676-703 ◽  
Author(s):  
S.N. Gaikwad ◽  
Shaheen Kouser
Keyword(s):  
Heat Source ◽  
Porous Layer ◽  
Viscoelastic Fluid ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Saturated Porous Layer

scholarly journals Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
B. S. Bhadauria
Keyword(s):  
Heat Source ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Momentum Equation ◽  
Darcy Law ◽  
Chaotic Convection ◽  
Saturated Porous Layer ◽  
Truncated Fourier Series

Chaotic convection in a viscoelastic fluid saturated porous layer, heated from below, is studied by using Oldroyd’s type constituting relation and in the presence of an internal heat source. A modified Darcy law is used in the momentum equation, and a heat source term has been considered in energy equation. An autonomous system of fourth-order differential equations has been deduced by using a truncated Fourier series. Effect of internal heat generation on chaotic convection has been investigated. The asymptotic behavior can be stationary, periodic, or chaotic, depending upon the flow parameters. Construction of four-scroll, or “two-butterfly,” and chaotic attractor has been examined.

scholarly journals Cross Diffusion Effect on Linear and Nonlinear Double Diffusive Convection in a Viscoelastic Fluid Saturated Porous Layer with Internal Heat Source

Fluids ◽  
2021 ◽  
Vol 6 (5) ◽  
pp. 182
Author(s):  
A. A. Altawallbeh
Keyword(s):  
Mass Transfer ◽  
Heat Source ◽  
Viscoelastic Fluid ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Cross Diffusion ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Heat Parameter ◽  
Linear And Nonlinear

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode technique, while the nonlinear theory is based on a minimal representation of truncated double Fourier series. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is considered to model the momentum equation. The onset criterion for stationary and oscillatory convection and steady heat and mass transfer have been obtained analytically using linear and nonlinear theory, respectively. The combined effect of an internal heat source and cross diffusion is investigated. The effects of Dufour, Soret, internal heat, relaxation and retardation time, Lewis number and concentration Rayleigh number on stationary, oscillatory, and heat and mass transport are depicted graphically. Heat and mass transfer are presented graphically in terms of Nusselt and Sherwood numbers, respectively. It is reported that the stationary and oscillatory convection are significantly influenced with variation of Soret and Defour parameters. An increment of the internal heat parameter has a destabilizing effect as well as enhancing the heat transfer process. On the other hand, an increment of internal heat parameter has a variable effect on mass transfer. It is found that there is a critical value for the thermal Rayleigh number, below which increasing internal heat decreases the Sherwood number, while above it increasing the internal heat increases the Sherwood number.

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