Double-Diffusive Natural Convection in Anisotropic Porous Medium Bounded by Finite Thickness Walls: Validity of Local Thermal Equilibrium Assumption

Harzallah, Mounira; Jbara, Abdessalem; Slimi, Khalifa

doi:10.1007/s11242-014-0298-3

Cited by 22 publications

(10 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A description of the flow and heat transfer inside a porous medium can be modeled using local thermal equilibrium (LTE) (Beckermann et al , 1987; Ghalambaz et al , 2015) or local thermal non-equilibrium (LTNE) (Buonomo et al , 2014; Ouarzazi et al , 2017; Zargartalebi et al , 2017; Tahmasebi et al , 2018; Zargartalebi et al , 2016; Zargartalebi et al , 2017; Mehryan et al , 2018). Thus, the LTNE model is a physically approved approach for problems with an essential difference in the thermophysical properties of working liquid and solid porous matrix, while LTE approach has many limitations (Harzallah et al , 2014). As a result, using LTE approach can lead to some non-physical results.…”

Section: Introductionmentioning

confidence: 99%

Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

Astanina

Sheremet

Umavathi

2019

HFF

View full text Add to dashboard Cite

Purpose The purpose of this study is a numerical analysis of transient natural convection in a square partially porous cavity with a heat-generating and heat-conducting element using the local thermal non-equilibrium model under the effect of cooling from the vertical walls. It should be noted that this research deals with a development of passive cooling system for the electronic devices. Design/methodology/approach The domain of interest is a square cavity with a porous layer and a heat-generating element. The vertical walls of the cavity are kept at constant cooling temperature, while the horizontal walls are adiabatic. The heat-generating solid element is located on the bottom wall. A porous layer is placed under the clear fluid layer. The governing equations, formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions, are solved using implicit finite difference schemes of the second order accuracy. The governing parameters are the Darcy number, viscosity variation parameter, porous layer height and dimensionless time. The effects of varying these parameters on the average total Nusselt number along the heat source surface, the average temperature of the heater, the fluid flow rate inside the cavity and on the streamlines and isotherms are analyzed. Findings The results show that in the case of local thermal non-equilibrium the total average Nusselt number is an increasing function of the interphase heat transfer coefficient and the porous layer thickness, while the average heat source temperature decreases with the Darcy number and viscosity variation parameter. Originality/value An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady natural convection within a partially porous cavity using the local thermal non-equilibrium model in the presence of a local heat-generating solid element. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer in enclosures with local heat-generating heaters and porous layers, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

show abstract

Section: Introductionmentioning

confidence: 99%

Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

Astanina

Sheremet

Umavathi

2019

HFF

View full text Add to dashboard Cite

show abstract

“…Since many real porous materials display strong anisotropy this focus of attention is natural and is studied by e.g. [176,193,214,226,228,370,387,394,395,398,400,404,439] and [485], and the references therein. These articles concentrate mainly on anisotropy of the permeability tensor or thermal conductivity.…”

Section: Fig 19mentioning

confidence: 99%

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Straughan

2015

Advances in Mechanics and Mathematics

111

View full text Add to dashboard Cite

In this chapter we describe work of [366] and of [393] on thermal convection in a Darcy porous material in a vertical layer subject to different temperatures on the vertical walls.For the case of a single temperature the problem where the porous medium occupies a vertical layer subject to differential heating from one side to the other has attracted much attention. This problem has much application to insulation, such as in the area of building design, and is of importance in window double glazing. For the single temperature situation the first proof that a vertical porous slab of Darcy type which is held at fixed but different temperatures on the vertical walls is stable to perturbations from the equilibrium state is due to [156]. His analysis is based on the linear theory and analyses the two-dimensional problem.[409] further analysed this problem but in three-dimensions and he treated the completely nonlinear situation by employing energy-like integral methods. In particular, [409] produced a threshold for the Rayleigh number which guarantees global nonlinear stability, i.e. regardless of how large the initial perturbation may be. He also employed a generalized energy method to demonstrate that the result of [156] is true in the fully three-dimensional case although the initial data must be restricted. Articles dealing with other interesting aspects of convection in a vertical porous slab or pipe involving effects like double diffusion, and LTNE, include the papers by [32, 33, 36, 46, 211, 220, 221, 329, 330, 362] and [460]. The methods of energy stability techniques applied specifically to convection in a vertical porous slab are addressed in [144, 229] and [356], and these are discussed in detail in the book by [414, pp. 126-134].The analogous problem in LTNE to that of [156] was first addressed by [366]. Specifically [366] dealt with the [156] problem of thermal convection in a vertical porous medium, but he employed the theory of local thermal non-equilibrium, allowing for different fluid and solid temperatures. The interesting work of [366] demonstrates that the vertical configuration is always stable according to linear theory, even with the much more complicated LTNE theory. [393] continued the problem of [366] but they analysed the complete nonlinear three-dimensional situation.

show abstract

“…The thermo‐solute natural convection is a process induced by combining temperature and solute gradient that collectively produced buoyancy; hence it is a resilience‐mediated process. Various fields like geophysics, 1,2 solar collector, 3 drying technology, 4 food engineering, 5 biomechanics, 6 distillation, 7 and building engineering 8 are based on thermo‐solute natural convection. Among these, rectangular systems that are based on thermo‐solutes natural convection like tank storage, energy transfer devices, reactor systems, solar collectors, and cooling systems of the engine have large industrial applications.…”

Section: Introductionmentioning

confidence: 99%

Modified class of explicit and enhanced stability region schemes: Application to mixed convection flow in a square cavity with a convective wall

Nawaz

Arif

2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

A modification of Adams–Bashforth methods is given to construct time discretization schemes for partial differential equations. The second‐order modified method is shown to have a larger stability region than second‐order standard Adams–Bashforth for the two‐dimensional heat equation. Later the scheme is applied on considered flow problem in a square cavity. The flow problem is a modified mathematical model of the heat and mass transfer of mixed convection flow in a square cavity with effects of the inclined magnetic field and thermal radiations. In addition to this, another feature of the present contribution is to apply the coupling approach for employing a mixture of stable and unstable schemes. This coupling approach is based upon the difference quotient that has been used in the literature to construct flux limiters for reducing oscillations in the discontinuous solutions of hyperbolic conservation laws. Since proposed scheme produces oscillation in the beginning and then diverges for the chosen diffusion number that falls in the unstable region, so these oscillations, due to instability, is reduced by coupling it with the scheme that can produce the convergent solution. The convergence of the proposed scheme for the considered modified nondimensional mathematical model of mixed convection flow is also given. The improvement is shown in graphs when proposed second order in time scheme is compared with the standard second order in time Adams–Bashforth method. Also, the mixture of first‐order and unconditionally unstable Richardson's schemes is applied, and the solution is obtained, and some plots are provided.

show abstract

Double-Diffusive Natural Convection in Anisotropic Porous Medium Bounded by Finite Thickness Walls: Validity of Local Thermal Equilibrium Assumption

Cited by 22 publications

References 27 publications

Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Modified class of explicit and enhanced stability region schemes: Application to mixed convection flow in a square cavity with a convective wall

Contact Info

Product

Resources

About