Study on Natural Convection in Horizontal Parallel Plate Channels Heated on Upper Wall and Partially Filled With Metal Foam

2020 ◽  
Author(s):  
Bernardo Buonomo ◽  
Vincenzo Fardella ◽  
Oronzio Manca ◽  
Sergio Nardini ◽  
Salvatore Pragliola
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Metal Foam ◽  
Open Cavity ◽  
Temperature Fields ◽  
Local Thermal Equilibrium ◽  
Uniform Heat Flux

Abstract In this work, a numerical investigation on two-dimensional steady state natural convection in a horizontal channel partially filled with a porous medium and heated at uniform heat flux from above is carried out. The lower plate is adiabatic. The porous medium is modeled using the Brinkman–Forchheimer-extended Darcy model and the local thermal equilibrium (LTE) hypothesis is assumed. The structure of the porous medium is homogenous and isotropic, the thermophysical properties of the air and the porous medium are temperature independent and the fluid flow is laminar and incompressible. The aluminum foam has 10, 20 and 40 pore per inches (PPI) and its porosity ranges from 0.90 and 0.95. Rayleigh number values are examined, from 6.0 × 104 and 1.2 × 107. Results are presented in terms of velocity and temperature fields, temperature and velocity profiles at different significant sections are shown, to obtain a description of the natural convection inside the open-ended cavity. Finally, Average Nusselt number values are evaluated. The horizontal open cavity partially filled with metal foam presents improved heat transfer behavior for higher Rayleigh numbers. The enhancement depends on the porosity and pore density. The average Nusselt number for the partially filled open cavity is the double of the configuration without the foam, clear configuration, for the highest considered Rayleigh number.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

Numerical Study on Mixed Convection in Porous Media in a Channel With an Open Cavity Below

2010 ◽  
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Paolo Mesolella ◽  
Sergio Nardini
Keyword(s):  
Mixed Convection ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Vertical Wall ◽  
Open Cavity ◽  
Temperature Fields ◽  
Forced Flow ◽  
Heated Wall ◽  
Local Thermal Equilibrium ◽  
Uniform Heat Flux

A numerical analysis of mixed convection in gas saturated metal foam in a horizontal channel with an open cavity heated at uniform heat flux on a vertical wall is studied numerically. Non-local thermal equilibrium and Brinkman-Forchheimer-extended Darcy model are assumed. Boussinesq approximation with constant thermophysical proprieties are considered. Results are carried out for an aluminium foam with 10 PPI and ε = 0.909, the fluid is air and for the assisting case. Results, for different Peclet and Rayleigh numbers, are given in terms of solid and fluid wall temperatures and local Nusselt numbers and stream function and temperature fields. Results show that diffusive effect determined lower temperature values inside the solid and the fluid temperatures are higher in all considered cases. The interaction between the forced flow in the channel and the buoyancy due to the heated wall determines different thermal and fluid dynamic behaviors.

Natural Convection in a Partitioned Vertical Enclosure Heated With a Uniform Heat Flux

2006 ◽  
Vol 129 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Kamil Kahveci
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Thermal Resistance ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

This numerical study looks at laminar natural convection in an enclosure divided by a partition with a finite thickness and conductivity. The enclosure is assumed to be heated using a uniform heat flux on a vertical wall, and cooled to a constant temperature on the opposite wall. The governing equations in the vorticity-stream function formulation are solved by employing a polynomial-based differential quadrature method. The results show that the presence of a vertical partition has a considerable effect on the circulation intensity, and therefore, the heat transfer characteristics across the enclosure. The average Nusselt number decreases with an increase of the distance between the hot wall and the partition. With a decrease in the thermal resistance of the partition, the average Nusselt number shows an increasing trend and a peak point is detected. If the thermal resistance of the partition further declines, the average Nusselt number begins to decrease asymptotically to a constant value. The partition thickness has little effect on the average Nusselt number.

scholarly journals Prediction of Natural Convection Heat Transfer Phenomena of Nanofluids in Corrugated Annulus

2020 ◽  
Author(s):  
Sattar Aljobair ◽  
Akeel Abdullah Mohammed ◽  
Israa Alesbe
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Outer Cylinder ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Abstract The natural convection heat transfer and fluid flow characteristic of water based Al2O3 nano-fluids in a symmetrical and unsymmetrical corrugated annulus enclosure has been studied numerically using CFD. The inner cylinder is heated isothermally while the outer cylinder is kept constant cold temperature. The study includes eight models of corrugated annulus enclosure with constant aspect ratio of 1.5. The governing equations of fluid motion and heat transfer are solved using stream-vorticity formulation in curvilinear coordinates. The range of solid volume fractions of nanoparticles extends from PHI=0 to 0.25, and Rayleigh number varies from 104 to 107. Streamlines, isotherms, local and average Nusselt number of inner and outer cylinder has been investigated in this study. Sixty-four correlations have been deduced for the average Nusselt number for the inner and outer cylinders as a function of Rayleigh number have been deduced for eight models and five values of volume fraction of nano particles with an accuracy range 6-12 %. The results show that, the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. Also, increase the number of undulations in unsymmetrical annuli reduces the heat transfer rates which remain higher than that in symmetrical annuli. There is no remarkable change in isotherms contour with increase of volume fraction of nanofluid.

scholarly journals Effect of Various Tilted Positions of a Thin Fin on Natural Convection of Laminar Viscous Flow in a Square Cavity

2021 ◽  
Vol 39 (5) ◽  
pp. 1634-1642
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G Sankara Sekhar Raju
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Finite Difference ◽  
Average Nusselt Number ◽  
Vertical Position ◽  
Inclination Angles ◽  
Rayleigh Numbers

An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.

Natural Convection in a Porous Medium Bounded by a Long Vertical WavyWall and a Parallel Flat Wall

2010 ◽  
Vol 65 (10) ◽  
pp. 800-810 ◽  
Author(s):  
Ambrish K. Tiwari ◽  
Ashok K. Singh
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Study ◽  
Temperature Fields ◽  
Wavy Wall ◽  
Heat Flows ◽  
Flat Wall ◽  
Porous Region ◽  
Parallel Wall

This paper presents natural convection in a porous medium bounded by a long vertical wavy wall and a parallel wall. The shape of the wavy wall is assumed to follow a profile of cosine curve. The wall is kept at a constant heat flux while the parallel wall is kept at a constant temperature. The governing systems of nonlinear partial differential equations in their non-dimensional form are linearised by using the perturbation method in terms of amplitude and the analytical solutions for velocity and temperature fields have been obtained in terms of various parameters occurring in the model. A numerical study of the analytical solution is performed with respect to the realistic fluid air in order to illustrate the interactive influences of governing parameters on the temperature and velocity fields as well as skin friction and Nusselt number. It is found that in the case of maximum waviness (positive and negative), the velocity component along the wall has a reverse trend near the flat wall. It is observed that the parallel flow through the channel at zero waviness is greater than at maximum waviness (positive and negative) while the same trend occurs for perpendicular flow in the opposite direction. Examination of the Nusselt number shows that in the presence and absence of a heat source, the heat flows from the porous region towards the walls but in the presence of a sink, the heat flows from the walls into the porous region.

Natural Convection at the Interface Between a Vertical Porous Layer and an Open Space

1983 ◽  
Vol 105 (1) ◽  
pp. 124-129 ◽  
Author(s):  
A. Bejan ◽  
R. Anderson
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Open Space ◽  
Saturated Porous Medium ◽  
Temperature Fields ◽  
Interface Temperature ◽  
Fluid Systems ◽  
Two Fluid ◽  
Fluid Reservoir

This paper examines the interaction by natural convection between a fluid-saturated porous medium and a fluid reservoir separated by a vertical impermeable partition. The two fluid systems are maintained at different temperatures. The analysis is simplified by assuming Pr > > 1 in the fluid reservoir. It is shown analytically that the flow and temperature fields in the boundary layer regime consist of two fluid layers in counterflow. The interface temperature is shown to increase monotonically with altitude. The important dimensionless group which governs the fluid mechanics is B = (kRaK1/2) / (k′Ra1/4), where k, k′, RaK and Ra are, respectively, the porous medium conductivity, reservoir fluid conductivity, Darcy-modified Rayleigh number based on partition height, and the reservoir Rayleigh number based on partition height. The effect of parameter, B, on the flow, temperature, and heat transfer is documented in the range 0 < B < ∞.

High Rayleigh Number Laminar Natural Convection in an Asymmetrically Heated Vertical Channel

1989 ◽  
Vol 111 (3) ◽  
pp. 649-656 ◽  
Author(s):  
B. W. Webb ◽  
D. P. Hill
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Channel ◽  
Local Heat Transfer ◽  
Heated Wall ◽  
Uniform Heat Flux ◽  
Parallel Plates ◽  
Heating Rates ◽  
Wide Range

Experiments have been performed to determine local heat transfer data for the natural convective flow of air between vertical parallel plates heated asymmetrically. A uniform heat flux was imposed along one heated wall, with the opposing wall of the channel being thermally insulated. Local temperature data along both walls were collected for a wide range of heating rates and channel wall spacings corresponding to the high modified Rayleigh number natural convection regime. Laminar flow prevailed in all experiments. Correlations are presented for the local Nusselt number as a function of local Grashof number along the channel. The dependence of both average Nusselt number and the maximum heated wall temperature on the modified Rayleigh number is also explored. Results are compared to previous analytical and experimental work with good agreement.

Natural Convection in a Stably Heated Corner Filled With Porous Medium

1985 ◽  
Vol 107 (2) ◽  
pp. 293-298 ◽  
Author(s):  
S. Kimura ◽  
A. Bejan
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Single Cell ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Number Range ◽  
Corner Flow ◽  
Horizontal Wall

This is a study of the single-cell natural convection pattern that occurs in a “stably heated” corner in a fluid-saturated porous medium, i.e., in the corner formed between a cold horizontal wall and a hot vertical wall situated above the horizontal wall, or in the corner between a hot horizontal wall and a cold vertical wall situated below the horizontal wall. Numerical simulations show that this type of corner flow is present in porous media heated from the side when a stabilizing vertical temperature gradient is imposed in order to suppress the side-driven convection. Based on numerical solutions and on scale analysis, it is shown that the single cell corner flow becomes increasingly more localized as the Rayleigh number increases. At the same time, the mass flow rate engaged in natural circulation and the conduction-referenced Nusselt number increase. Numerical results for the flow and temperature fields and for the net heat transfer rate are reported in the Darcy-Rayleigh number range 10–6000.

Thermal Viscous Dissipative Couette Flow in a Porous Medium Filled Microchannel

2016 ◽  
Author(s):  
Farrukh Mirza Baig ◽  
G. M. Chen ◽  
B. K. Lim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Couette Flow ◽  
Viscous Dissipation ◽  
Saturated Porous Medium ◽  
Local Thermal Equilibrium ◽  
Uniform Heat Flux ◽  
Brinkman Number ◽  
Essential Information

The increasing demand for high-performance electronic devices and surge in power density accentuates the need for heat transfer enhancement. In this study, a thermal viscous dissipative Coeutte flow in a micochannel filled with fluid saturated porous medium is looked into. The study explores the fluid flow and heat transfer phenomenon for a Coeutte flow in a microchannel as well as to establish the relationship between the heat convection coefficient and viscous dissipation. The moving boundary in this problem is subjected to uniform heat flux while the fixed plate is assumed adiabatic. In order to simplify the problem, we consider a fully developed flow and assume local thermal equilibrium in the analysis. An analytical Nusselt number expression is developed in terms of Brinkman number as a result of this study, thus providing essential information to predict accurately the thermal performance of a microchannel. The results obtained without viscous dissipation are in close agreement with published results whereas viscous dissipation has a more significant effect on Nusselt number for a porous medium with higher porous medium shape factor. The Nusselt number versus Brinkman number plot shows an asymptotic Brinkman number, indicating a change in sign of the temperature difference between the bulk mean temperature and the wall temperature. The effects of Reynolds number on the two dimensional temperature profile for a Couette flow in a microchannel are investigated. The temperature distribution of a microscale duct particularly along the axial direction is a strong function of viscous dissipation. The significance of viscous dissipation to a microscale duct as compared to a conventional scale duct is also discussed and compared in this study.

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