Effects of Nonuniform Heating and Wall Conduction on Natural Convection in a Square Porous Cavity Using LTNE Model

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
A. I. Alsabery ◽  
A. J. Chamkha ◽  
I. Hashim ◽  
P. G. Siddheshwar
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Wall Thickness ◽  
Solid Wall ◽  
Finite Thickness ◽  
Weighted Average ◽  
Nonuniform Heating ◽  
Conductivity Ratio ◽  
Cold Temperatures ◽  
Porous Cavity

The effects of nonuniform heating and a finite wall thickness on natural convection in a square porous cavity based on the local thermal nonequilibrium (LTNE) model are studied numerically using the finite difference method (FDM). The finite-thickness horizontal wall of the cavity is heated either uniformly or nonuniformly, and the vertical walls are maintained at constant cold temperatures. The top horizontal insulated wall allows no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The results of this study are obtained for various parametric values of the Rayleigh number, thermal conductivity ratio, ratio of the wall thickness to its height, and the modified conductivity ratio. Comparisons with previously published work verify good agreement with the proposed method. The effects of the various parameters on the streamlines, isotherms, and the weighted-average heat transfer are shown graphically. It is shown that a thicker bottom solid wall clearly inhibits the temperature gradient which then leads to the thermal equilibrium case. Further, the overall heat transfer is highly affected by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer.

Conjugate Natural Convection in a Square Porous Cavity Filled with a Nanofluid in the Presence of Two Isothermal Cylindrical Sources

2021 ◽  
Vol 80 (1) ◽  
pp. 147-164
Author(s):  
Islam Bouafia ◽  
Razli Mehdaoui ◽  
Syham Kadri ◽  
Mohammed Elmir
Keyword(s):  
Natural Convection ◽  
Wall Thickness ◽  
Numerical Study ◽  
Solid Wall ◽  
Finite Thickness ◽  
Convection Heat Transfer ◽  
Thick Wall ◽  
Thermal Conductivity Ratio ◽  
Porous Cavity ◽  
Conjugate Natural Convection

In this work, a numerical study has been performed for the problem of steady-state natural convection in a square porous cavity having a solid wall of finite thickness and conductivity filled by a nanofluid in the presence of two isothermal cylindrical sources. The external walls of the cavity are considered adiabatic and the circular sources are maintained at a hot and cold uniform temperatures. The internal thick wall has been a conducting solid. The governing dimensionless equations are solved using Galerkin finite element method and Darcy-Brinkman model assumed to be adopted. The results are presented as isotherms, streamlines, stream function values, average and local Nusselt number for various combinations of Rayleigh and Darcy numbers, concentration of nanoparticles, Thermal conductivity ratio, and dimensionless wall thickness of the solid portion. The convection heat transfer can be enhanced by increasing of these parameters except for the wall thickness.

Numerical Study on Conjugate Conduction–Convection in a Cubic Enclosure Submitted to Time-Periodic Sidewall Temperature

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Wei Zhang ◽  
Zhu Huang ◽  
Chuhua Zhang ◽  
Guang Xi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Wall Thickness ◽  
Numerical Study ◽  
Finite Thickness ◽  
Pseudospectral Method ◽  
Thermal Conductivity Ratio ◽  
Conjugate Conduction ◽  
Time Periodic ◽  
Diffusivity Ratio

The laminar conjugate conduction-natural convection heat transfer in a cubic enclosure of finite thickness conductive walls and central cavity filled with fluid is comprehensively studied by using recently developed high accuracy temporal-spatial multidomain pseudospectral method. The enclosure is assumed to have one sidewall submitted to time-periodic pulsating temperature and the opposing sidewall constant temperature, and the top, bottom and two lateral sidewalls are adiabatic. The present study is devoted to explore the fluid mechanics and heat transfer mechanisms of the time-periodic conjugate conduction-natural convection in the enclosure, with particular highlights on the heat transfer resonance and back heat transfer phenomena, the perturbation propagation patterns and the three-dimensional characteristics. The computations are performed for wide ranges of controlling parameters of engineering significance, i.e., the dimensionless wall thickness 0 ≤ s ≤ 0.10, the solid–fluid thermal conductivity ratio 10 ≤ k ≤ 50 and diffusivity ratio 0.001 ≤ a ≤ 0.1, and the sidewall temperature pulsating period 1 ≤ P ≤ 103. Numerical results reveal that the time-periodic fluid flow and conjugate heat transfer performances of the enclosure system are greatly affected by the conductive walls and complexly dependent on the controlling parameters. The thickness and thermophysical properties of the conductive walls, together with the pulsating period of the sidewall temperature, govern the sidewall temperature disturbance propagation patterns (amplitude, phase position and speed) within the enclosure. The heat transfer resonance only appears in cases of large diffusivity ratio, but the variation of period-averaged heat transfer rate with respect to the pulsating period is quite different from that of the zero wall thickness enclosure. The back heat transfer exists in region close to the corners formed by either the top or bottom walls and the enclosure hot sidewall, and the former is more remarkable in both scale and duration and is gradually disappearing as the pulsating period increases.

Natural Convection Heat Transfer in a Vertical Air Layer Partitioned Into Cubical Enclosures of Finite Wall Thermal Conductivity and Thickness

1999 ◽  
Author(s):  
Y. Yamaguchi ◽  
Y. Asako
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Natural Convection ◽  
Wall Thickness ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Wide Range

Abstract Three-dimensional natural convection heat transfer characteristics in a vertical air layer partitioned into cubical enclosures of finite wall thermal conductivity and finite thickness were obtained numerically. The outer surfaces of the enclosure are prescribed at different temperatures. These walls are often encountered in applications such as door panels and thermal insulation boards. The analyses were performed for finite wall thickness and conductivity, for Ra = 104 and 105 and for a wide range of wall thickness and thermal. The results were presented in form of temperature distributions and contour plots of Num and Qwall/Qtotal. From comparison of the results with ideal boundary conditions, a correlation for heat transfer for partitioned walls was developed. It was shown from the results that the ratio of heat transfer into the partition walls to the total heat transfer from the hot wall is a function of the product of wall thermal conductivity and thickness.

Natural Convection in an Anisotropic Porous Enclosure Due to Nonuniform Heating From the Bottom Wall

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Ashok Kumar ◽  
P. Bera
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Principal Direction ◽  
Orientation Angle ◽  
Bottom Wall ◽  
Nonuniform Heating ◽  
Material Derivative ◽  
Porous Enclosure

A comprehensive numerical investigation on the natural convection in a hydrodynamically anisotropic porous enclosure is presented. The flow is due to nonuniformly heated bottom wall and maintenance of constant temperature at cold vertical walls along with adiabatic top wall. Brinkman-extended non-Darcy model, including material derivative, is considered. The principal direction of the permeability tensor has been taken oblique to the gravity vector. The spectral element method has been adopted to solve numerically the governing conservative equations of mass, momentum, and energy by using a stream-function vorticity formulation. Special attention is given to understand the effect of anisotropic parameters on the heat transfer rate as well as flow configurations. The numerical experiments show that in the case of isotropic porous enclosure, the maximum rates of bottom as well as side heat transfers (Nub and Nus) take place at the aspect ratio, A, of the enclosure equal to 1, which is, in general, not true in the case of anisotropic porous enclosures. The flow in the enclosure is governed by two different types of convective cells: rotating (i) clockwise and (ii) anticlockwise. Based on the value of media permeability as well as orientation angle, in the anisotropic case, one of the cells will dominate the other. In contrast to isotropic porous media, enhancement of flow convection in the anisotropic porous enclosure does not mean increasing the side heat transfer rate always. Furthermore, the results show that anisotropy causes significant changes in the bottom as well as side average Nusselt numbers. In particular, the present analysis shows that permeability orientation angle has a significant effect on the flow dynamics and temperature profile and consequently on the heat transfer rates.

Effect of Wall Heat Conduction on Natural Convection Heat Transfer in a Square Enclosure

1985 ◽  
Vol 107 (1) ◽  
pp. 139-146 ◽  
Author(s):  
D. M. Kim ◽  
R. Viskanta
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Natural Convection ◽  
Solid Wall ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Square Enclosure ◽  
Void Fractions ◽  
Aspect Ratios

This paper presents numerical and experimental results for buoyancy-induced flow in a two-dimensional, fluid-filled enclosure. Rectangular cavities formed by finite conductance walls of different void fractions and aspect ratios are considered. Parametric heat transfer calculations have been performed and results are presented and discussed. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The temperatures in the walls were measured with thermocouples, and the temperature distributions in the air-filled cavity were determined using a Mach-Zehnder interferometer. Good agreement has been obtained between the measured and the predicted temperatures in both the solid wall and in the fluid using the mathematical model. Wall heat conduction reduces the average temperature differences across the cavity, partially stabilizes the flow, and decreases natural convection heat transfer.

Numerical computation of natural convection inside a curved-shape nanofluid-filled enclosure with nonuniform heating of the bottom wall

2019 ◽  
Vol 30 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Abdellaziz Yahiaoui ◽  
Mahfoud Djezzar ◽  
Hassane Naji
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Pure Water ◽  
Bottom Wall ◽  
Working Fluid ◽  
Nonuniform Heating ◽  
Square Enclosure ◽  
Nusselt Numbers

This paper performs a numerical analysis of the natural convection within two-dimensional enclosures (square enclosure and enclosures with curved walls) full of a H2O-Cu nanofluid. While their vertical walls are isothermal with a cold temperature [Formula: see text], the horizontal top wall is adiabatic and the bottom wall is kept at a sinusoidal hot temperature. The working fluid is assumed to be Newtonian and incompressible. Three values of the Rayleigh number were considered, viz., 103, 104, 105, the Prandtl number is fixed at 6.2, and the volume fraction [Formula: see text] is taken equal to 0% (pure water), 10% and 20%. The numerical simulation is achieved using a 2D-in-house CFD code based on the governing equations formulated in bipolar coordinates and translated algebraically via the finite volume method. Numerical results are presented in terms of streamlines, isotherms and local and average Nusselt numbers. These show that the heat transfer rate increases with both the volume fraction and the Rayleigh number, and that the average number of Nusselt characterizing the heat transfer raises with the nanoparticles volume fraction.

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

2019 ◽  
Vol 29 (6) ◽  
pp. 1902-1919 ◽  
Author(s):  
Marina S. Astanina ◽  
Mikhail Sheremet ◽  
C. Jawali Umavathi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Porous Layer ◽  
Equilibrium Model ◽  
Local Heat ◽  
Darcy Number ◽  
Content Type ◽  
Porous Cavity ◽  
Variation Parameter ◽  
Non Equilibrium

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.

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