Natural Convection in a Cavity Partially Filled with a Vertical Porous Medium

The shear stress jump boundary condition that must be imposed at an interface between a porous medium and a free fluid in an enclosure is investigated. Two-domain approach is founded and finite element method is used to solve the problem. Three stress jump coefficients 0, 1, -1 are analyzed for different Rayleigh number, permeability and thickness of porous layer. Variation of Maximum stream function and Nusselt number show stronger convection and heat transfer when the stress jump coefficient is positive. There is little distinctive in flow and heat transfer when the value of coefficient is equal to 0 and -1.

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Analysis of Heat Transfer and Entropy Generation in a Channel Partially Filled With N-Layer Porous Media

Journal of Heat Transfer ◽

10.1115/1.4038909 ◽

2018 ◽

Vol 140 (8) ◽

Cited By ~ 4

Author(s):

Kun Yang ◽

Hao Chen ◽

Jiabing Wang

Keyword(s):

Heat Transfer ◽

Boundary Condition ◽

Heat Flux ◽

Porous Medium ◽

Porous Media ◽

Entropy Generation ◽

Entropy Generation Rate ◽

Free Fluid ◽

Bejan Number ◽

Stress Jump

Convective heat transfer in a channel partially filled with porous medium has received a lot of attention due to its wide engineering applications. However, most researches focused on a channel partially filled with single layer porous medium. In this paper, we will analyze the heat transfer and entropy generation inside a channel partially filled with N-layer porous media. The flow and the heat transfer in the porous region are described by the Darcy–Brinkman model and the local thermal nonequilibrium model, respectively. At the porous-free fluid interface, the momentum and the heat transfer are described by the stress jump boundary condition and the heat flux jump boundary condition, respectively; while at the interface between two different porous layers, the momentum and the heat transfer are described by the stress continuity boundary condition and the heat flux continuity boundary condition, respectively. The analytical solutions for the velocity and temperature in the channel are derived and used to calculate the overall Nusselt number, the total entropy generation rate, the Bejan number, and the friction factor. Furthermore, the performances of the flow and heat transfer of a channel partially filled with third-layer porous media are studied.

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CREEPING FLOW PAST A POROUS APPROXIMATELY SPHERICAL SHELL: STRESS JUMP BOUNDARY CONDITION

The ANZIAM Journal ◽

10.1017/s144618111100071x ◽

2011 ◽

Vol 52 (3) ◽

pp. 289-300 ◽

Cited By ~ 3

Author(s):

D. SRINIVASACHARYA ◽

M. KRISHNA PRASAD

Keyword(s):

Boundary Condition ◽

Spherical Shell ◽

Stokes Equations ◽

Jump Condition ◽

Creeping Flow ◽

Navier Stokes ◽

Free Fluid ◽

Stress Jump ◽

Navier Stokes Equations ◽

Stress Jump Boundary Condition

AbstractThe creeping flow of an incompressible viscous liquid past a porous approximately spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier–Stokes equations. The flow within the porous annular region of the shell is governed by Brinkman’s model. The boundary conditions used at the interface are continuity of the velocity, continuity of the pressure and Ochoa-Tapia and Whitaker’s stress jump condition. An exact solution for the problem and an expression for the drag on the porous approximately spherical shell are obtained. The drag is evaluated numerically for several values of the parameters governing the flow.

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Boundary-Layer Flow and Heat Transfer of Nanofluid Over a Vertical Plate With Convective Surface Boundary Condition

Journal of Fluids Engineering ◽

10.1115/1.4007075 ◽

2012 ◽

Vol 134 (8) ◽

Cited By ~ 22

Author(s):

Wubshet Ibrahim ◽

Bandari Shanker

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Boundary Condition ◽

Nusselt Number ◽

Sherwood Number ◽

Vertical Plate ◽

Lewis Number ◽

Convective Heating ◽

Flow And Heat Transfer ◽

Layer Flow

The problem of boundary layer flow and heat transfer induced due to nanofluid over a vertical plate is investigated. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. We used a convective heating boundary condition instead of a widely employed thermal conduction of constant temperature or constant heat flux. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., convective heating parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, buoyancy ratio parameter Nr, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order ordinary differential equations. These equations were solved numerically using Runge-Kutta fourth order method with shooting technique. The effects of the governing parameters on flow field and heat transfer characteristics were obtained and discussed. Numerical results are obtained for velocity, temperature, and concentration distribution as well as the local Nusselt number and Sherwood number. It is found that the local Nusselt number and Sherwood number increase with an increase in convective parameter A and Lewis number Le. Likewise, the local Sherwood number increases with an increase in both A and Le. A comparison with the previous study available in literature has been done and we found an excellent agreement with them.

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Natural Convection Heat and Mass Transfer in the Vertical Cylindrical Porous Channel Under the Effects of Time-Periodic Boundary Condition

Journal of Heat Transfer ◽

10.1115/1.4044705 ◽

2019 ◽

Vol 141 (12) ◽

Author(s):

Hayder I. Mohammed ◽

Donald Giddings

Keyword(s):

Heat Transfer ◽

Mass Transfer ◽

Boundary Condition ◽

Porous Medium ◽

Nusselt Number ◽

Natural Convection ◽

Rayleigh Number ◽

Aspect Ratio ◽

Heat And Mass Transfer ◽

Vertical Wall

Abstract Heat and mass transfer are investigated numerically with steady-state laminar natural convection through a vertical cylindrical enclosure filled with a liquid-saturated porous medium. The vertical wall is under a constant magnetic field and various durations of periodic heating boundary condition; the top and bottom surfaces are kept at a constant cold temperature. Continuity, momentum, and energy equations are transformed to dimensionless equations. The finite difference approach with the line successive over-relaxation (LSOR) method is used to obtain the computational results. This study covers the heat transfer, the temperature distribution, and the velocity field in the domain under the variation of different parameters. The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et al. (1998, “Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium,” Int. J. Heat Fluid Flow, 19(6), pp. 629–635). This work shows that Nusselt number decreases (with varying gradient) as the aspect ratio increases, and that it increases as the Rayleigh number increases. The centerline temperature has a proportional relationship with the heating amplitude and the heating period (as the system receives more heat) and is inversely proportional with Rayleigh number. Increasing the Rayleigh number causes increased convective velocity, which affects the position of the hot region, and causes a decrease in the temperature field. Increasing the aspect ratio results in a warm stream at the center of the cylinder, and when the time period of the heating increases, the circulation becomes faster and the intensity of the temperature contour layers decreases. In this work, a correlation for Nu as a function of the mentioned parameters is developed.

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MHD Natural Convective Flow in an Isosceles Triangular Cavity Filled with Porous Medium due to Uniform/Non-Uniform Heated Side Walls

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0232 ◽

2015 ◽

Vol 70 (11) ◽

pp. 919-928 ◽

Cited By ~ 17

Author(s):

Tariq Javed ◽

Muhammad Arshad Siddiqui ◽

Ziafat Mehmood ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Porous Medium ◽

Nusselt Number ◽

Bottom Wall ◽

Physical Parameters ◽

Uniform Heating ◽

Weighted Residual Method ◽

Flow And Heat Transfer ◽

Side Walls ◽

Limiting Case

AbstractIn this article, numerical simulations are carried out for fluid flow and heat transfer through natural convection in an isosceles triangular cavity under the effects of uniform magnetic field. The cavity is of cold bottom wall and uniformly/non-uniformly heated side walls and is filled with isotropic porous medium. The governing Navier Stoke's equations are subjected to Penalty finite element method to eliminate pressure term and Galerkin weighted residual method is applied to obtain the solution of the reduced equations for different ranges of the physical parameters. The results are verified as grid independent and comparison is made as a limiting case with the results available in literature, and it is shown that the developed code is highly accurate. Computations are presented in terms of streamlines, isotherms, local Nusselt number and average Nusselt number through graphs and tables. It is observed that, for the case of uniform heating side walls, strength of circulation of streamlines gets increased when Rayleigh number is increased above critical value, but increase in Hartmann number decreases strength of streamlines circulations. For non-uniform heating case, it is noticed that heat transfer rate is maximum at corners of bottom wall.

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