The Effect of Local Thermal Nonequilibrium on the Stability of Convection in a Vertical Porous Channel

2010 ◽  
Vol 87 (2) ◽  
pp. 459-464 ◽  
Author(s):  
D. Andrew S. Rees
Keyword(s):  
Porous Channel ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium ◽  
The Stability

scholarly journals Effect of Local Thermal Nonequilibrium on the Stability of Natural Convection in an Oldroyd-B Fluid Saturated Vertical Porous Layer

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
B. M. Shankar ◽  
I. S. Shivakumara
Keyword(s):  
Natural Convection ◽  
Solid Phase ◽  
Viscoelastic Fluids ◽  
Maxwell Fluid ◽  
Base Flow ◽  
Temperature Fields ◽  
Thermal Nonequilibrium ◽  
Interphase Heat Transfer ◽  
Local Thermal Nonequilibrium ◽  
The Stability

The effect of local thermal nonequilibrium (LTNE) on the stability of natural convection in a vertical porous slab saturated by an Oldroyd-B fluid is investigated. The vertical walls of the slab are impermeable and maintained at constant but different temperatures. A two-field model that represents the fluid and solid phase temperature fields separately is used for heat transport equation. The resulting stability eigenvalue problem is solved numerically using Chebyshev collocation method as the energy stability analysis becomes ineffective in deciding the stability of the system. Despite the basic state remains the same for Newtonian and viscoelastic fluids, it is observed that the base flow is unstable for viscoelastic fluids and this result is qualitatively different from Newtonian fluids. The results for Maxwell fluid are delineated as a particular case from the present study. It is found that the viscoelasticity has both stabilizing and destabilizing influence on the flow. Increase in the value of interphase heat transfer coefficient Ht, strain retardation parameter Λ2 and diffusivity ratio α portray stabilizing influence on the system while increasing stress relaxation parameter Λ1 and porosity-modified conductivity ratio γ exhibit an opposite trend.

Thermomagnetic Convection in Porous Media: Effect of Anisotropy and Local Thermal Nonequilibrium

2017 ◽  
Vol 378 ◽  
pp. 137-156
Author(s):  
M. Ravisha ◽  
I.S. Shivakumara ◽  
A.L. Mamatha
Keyword(s):  
Media Effect ◽  
Thermal Nonequilibrium ◽  
Interphase Heat Transfer ◽  
Thermomagnetic Convection ◽  
Thermal Anisotropy ◽  
Local Thermal Nonequilibrium ◽  
The Stability ◽  
Exchange Of Stability ◽  
Convection In Porous Media ◽  
Good Agreement

The onset of thermomagnetic convection in an anisotropic layer of Darcy porous medium in the presence of a uniform vertical magnetic field is investigated using a local thermal nonequilibrium (LTNE) model for energy equation representing the solid and fluid phases separately. Anisotropies in permeability as well as in fluid and solid thermal conductivities are considered. The principle of exchange of stability is shown to be valid. Asymptotic solutions for the Rayleigh number for both small and large values of scaled interphase heat transfer coefficient are presented and the comparison of results with those computed numerically shows good agreement. The mechanical and thermal anisotropy parameters have opposing influence on the stability characteristics of the system. Besides, the influence of magnetic parameters on the instability of the system is also reported.

A Discussion of Transpiration Cooling Problems through an Analytical Solution of Local Thermal Nonequilibrium Model

2006 ◽  
Vol 128 (10) ◽  
pp. 1093-1098 ◽  
Author(s):  
J. H. Wang ◽  
H. N. Wang
Keyword(s):  
Analytical Solution ◽  
Biot Number ◽  
Thermal Conduction ◽  
Porous Plate ◽  
Local Thermal Equilibrium ◽  
Transpiration Cooling ◽  
Thermal Nonequilibrium ◽  
Cooling Effects ◽  
Local Thermal Nonequilibrium ◽  
Hot Surface

To study transpiration cooling problems, an analytical solution of the local thermal nonequilibrium (LTNE) model with the second or third boundary conditions is presented. This solution is obtained through neglecting the thermal conduction of the fluid coolant in porous media. By the analytical solution, two problems are investigated. At first, the parameters which influence transpiration cooling effects are analyzed, and the analysis indicates that the cooling effects are dominated by coolant mass flow rate, the Biot number at the hot surface of porous plate, and the Biot number in the pores. Second, the error caused by the assumption of the local thermal equilibrium (LTE) model is quantitatively discussed, and the variation trend of the LTE error is analyzed. Based on the analytical solution and the error analysis, a quantitative criterion to choose the LTNE or LTE model is suggested, and the corresponding expression is also given in this paper.

Convective Instability of the Darcy Flow in a Horizontal Layer With Symmetric Wall Heat Fluxes and Local Thermal Nonequilibrium

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
A. Barletta ◽  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Solid Phase ◽  
Fluid Phase ◽  
Heat Fluxes ◽  
Local Thermal Equilibrium ◽  
Neutral Stability ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium ◽  
Darcy Rayleigh Number

The linear stability of the parallel Darcy throughflow in a horizontal plane porous layer with impermeable boundaries subject to a symmetric net heating or cooling is investigated. The onset conditions for the secondary thermoconvective flow are expressed through a neutral stability bound for the Darcy–Rayleigh number associated with the uniform heat flux supplied or removed from the walls. The study is performed by taking into account a condition of local thermal nonequilibrium between the solid phase and the fluid phase. The linear stability analysis is carried out according to the normal modes' decomposition of the perturbations to the basic state. The governing equations for the disturbances are solved numerically as an eigenvalue problem leading to the neutral stability condition. If compared with the asymptotic condition of local thermal equilibrium, the regime of local nonequilibrium manifests an enhanced instability. This behavior is displayed by lower critical values of the Darcy–Rayleigh number, eventually tending to zero when the thermal conductivity of the solid phase is much larger than the conductivity of the fluid phase. In this special limit, which can be invoked as an approximate model of a gas-saturated metallic foam, the basic throughflow is always unstable to external disturbances of arbitrarily small amplitude.

scholarly journals New Study of the Stability of Fluid Flow in a Porous Channel under Effects of Magnetic Field and Radiation

OALib ◽  
2020 ◽  
Vol 07 (05) ◽  
pp. 1-9
Author(s):  
Iman Hashim AL-Obeide ◽  
Alaa Abdul-Raheem Hammodat
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Porous Channel ◽  
The Stability
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