Steady-state conjugate natural convection in a fluid-saturated porous cavity

Al-Amiri, Abdalla M.; Khanafer, Khalil; Pop, Ioan

doi:10.1016/j.ijheatmasstransfer.2007.12.026

Cited by 44 publications

(30 citation statements)

References 26 publications

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“…They found that the critical Rayleigh number of the buoyancy-driven onset approached the well known Lapwood value (4p 2 ). Al-Amiri et al [24] extended the problem of references [22] by assuming the Forchheimer-Brinkman extended Darcy model. They established a correlation for the average Nusselt number for a wide range of dimensionless parameters.…”

Section: Introductionmentioning

confidence: 99%

Conjugate Heat Transfer in a Porous Cavity Heated by a Triangular Thick Wall

Chamkha

Ismael

2013

Numerical Heat Transfer, Part A: Applications

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The conjugate natural convection-conduction heat transfer in a square domain composed of a cavity heated by a triangular solid wall is studied under steady state condition. The vertical and horizontal walls of the triangular solid are kept isothermal and at the same hot temperature T h . The other boundaries surrounding the porous cavity are kept adiabatic except the right vertical wall, where it is kept isothermally at the lower temperature T c . Equations governing the heat transfer in the triangular wall and heat and fluid flow, based on the Darcy model, in the fluid-saturated porous medium together with the derived relation of the interface temperature are solved numerically using the second order central differences finite difference scheme with the successive over relaxation (SOR) method. The investigated parameters are the Rayleigh number Ra (100-1000), solid to fluid saturated porous medium thermal conductivity ratio Kr (0.1-10), and the triangular wall thickness D (0.05-1). The results are presented in the conventional form; contours of streamlines and isotherms and the local and average Nusselt numbers. An uncommon behavior of the heat transfer in the porous medium with the triangular wall thickness D is observed and accounted.

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Section: Introductionmentioning

confidence: 99%

Conjugate Heat Transfer in a Porous Cavity Heated by a Triangular Thick Wall

Chamkha

Ismael

2013

Numerical Heat Transfer, Part A: Applications

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“…Malatip et al [3] also developed a fractional step method to analyze the unsteady conjugate heat transfer problems. Al-Amiri et al [4] used the finite element method to study the steady-state natural convection in a fluid-saturated porous cavity of a conducting vertical wall. Schäfer and Teschauer [5] employed the finite volume method to analyze both the fluid flow phenomenon and the solid heat transfer behavior.…”

Section: Introductionmentioning

confidence: 99%

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

Malatip

Wansophark

Dechaumphai

2012

Appl. Math. Mech.-Engl. Ed.

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An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin (SUPG) method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid are performed by the Galerkin method. The second-order semiimplicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are linearized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

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“…It has been shown that the value of the mean Nusselt number decreases with the increase of thermal conductivity ratio. Al-Amiri et al [13] considered the steady-state conjugate natural convection in a fluid-saturated porous cavity. The configuration consists of two insulated horizontal walls and two vertical walls one of which has a finite thickness.…”

Section: Introductionmentioning

confidence: 99%

Visualization of heat flow using Bejan’s heatline due to natural convection of water near 4 °C in thick walled porous cavity

Varol

Öztop

Mobedi

et al. 2010

International Journal of Heat and Mass Transfer

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a b s t r a c tA numerical study on natural convection heat transfer of cold water near 4°C in a thick bottom walled cavity filled with a porous medium has been performed. It is assumed that the cavity is isothermally heated from the outside of the thick bottom wall and cooled from ceiling. The finite-difference method has been used to solve the governing partial differential equations of heat and fluid flow. Effects of thermal conductivity ratio, Rayleigh number and bottom wall thickness on heat transfer from the bottom to the ceiling have been studied. The heatline visualization technique has been used to demonstrate the path of heat transport through the enclosure. Moreover, streamlines and isotherms have been used to present fluid flow and temperature distributions. The obtained results show that multiple circulation cells are formed in the cavity and the local Nusselt numbers at the bottom wall and solid-fluid interface are highly affected by formed cells. The increase of Rayleigh number and thermal conductivity ratio increases heat transfer through the cavity. However, the increase of thickness of the bottom wall reduces the mean Nusselt number. Almost one-dimensional conduction heat transfer is observed in the solid bottom wall of the cavity.

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Steady-state conjugate natural convection in a fluid-saturated porous cavity

Cited by 44 publications

References 26 publications

Conjugate Heat Transfer in a Porous Cavity Heated by a Triangular Thick Wall

Conjugate Heat Transfer in a Porous Cavity Heated by a Triangular Thick Wall

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

Visualization of heat flow using Bejan’s heatline due to natural convection of water near 4 °C in thick walled porous cavity

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