Thermal Convection in an Infinite Porous Medium Induced by a Heated Sphere

1997 ◽  
Vol 119 (3) ◽  
pp. 647-650 ◽  
Author(s):  
R. Ganapathy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Free Convection ◽  
Wall Temperature ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Series Expansions ◽  
Medium Permeability ◽  
Velocity And Temperature Fields

This paper investigates the transient behavior of the free convection motion and heat transfer induced by a heated sphere with prescribed wall temperature embedded instantaneously in an infinite porous medium. Solutions for the velocity and temperature fields have been obtained in the form of series expansions in Rayleigh number which is based on the medium permeability and the temperature of the sphere. All discussions are based on the assumption that the flow is governed by Darcy's law and the thermal Rayleigh number is small.

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.

scholarly journals Control of the free convective heat transfer using a U-shaped obstacle in an Al2O3-water nanofluid filled cubic cavity

2021 ◽  
Vol 8 (7) ◽  
pp. 23-30
Author(s):  
Rajab Al-Sayagh ◽  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Free Convection ◽  
Convective Heat Transfer ◽  
Volume Fraction ◽  
Temperature Fields ◽  
Flow Structures ◽  
Nanoparticles Volume Fraction ◽  
Al2o3 Nanofluid

This paper deals with the study of free convection in a 3D enclosure filled with Al2O3-nanofluid and equipped with a U-shaped obstacle. The used U-shaped obstacle is considered perfectly conductive. The effect of the dimension and the orientation of the obstacle is investigated. In addition, the parameters governing the problem are varied as Rayleigh number (103 to 106), and nanoparticles volume fraction (0 to 7.5%). Results are depicted in terms of flow structures, temperature fields, and Nusselt number. Results show that the obstacle dimension and orientation can control the flow and optimize the heat transfer and the addition of nanoparticles enhances significantly Nusselt number.

Experimental Study of Free Convection from a Vertical Flat Plate in Porous Media

2008 ◽  
Vol 273-276 ◽  
pp. 796-801
Author(s):  
L.B.Y. Aldabbagh ◽  
Mohsen Sharifpur ◽  
Mahdi Zamani
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Free Convection ◽  
Flat Plate ◽  
Saturated Porous Medium ◽  
Convection Heat Transfer ◽  
Steady State Condition ◽  
Free Convection Heat ◽  
Vertical Flat Plate

A set of experiments is done to study the phenomenon of free convection heat transfer from an isothermal vertical flat plate embedded in a saturated porous medium in steady state condition. The porous medium consisting of 0.8 cm spheres. The aspect ratio of the isothermal flat plate, H/W, is equal to 2. Where H is the height and W is the width of the vertical plate. The investigations were cared out for Darcy modified Rayleigh number between 100 and 500. The results indicate that heat transfer increases linearly with increasing the Darcy modified Rayleigh number. In addition, the present results are in good agreement with the higher-order boundary layer theory obtained by Cheng and Hsu [1].

scholarly journals Mixed Convective Flow of Unsteady Hydromagnetic Couple Stress Fluid Through a Vertical Channel Filled with Porous Medium

2020 ◽  
Vol 25 (4) ◽  
pp. 148-161
Author(s):  
C.R. Makhalemele ◽  
L. Rundora ◽  
S.O. Adesanya
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Convective Flow ◽  
Couple Stress ◽  
Saturated Porous Medium ◽  
Vertical Channel ◽  
Temperature Fields ◽  
Couple Stress Fluid ◽  
Medium Permeability ◽  
Mixed Convective Flow

AbstractIn this paper, the mixed convective flow of an electrically conducting, viscous incompressible couple stress fluid through a vertical channel filled with a saturated porous medium has been investigated. The fluid is assumed to be driven by both buoyancy force and oscillatory pressure gradient parallel to the channel plates. A uniform magnetic field of strength B0 is imposed transverse to the channel boundaries. The temperature of the right channel plate is assumed to vary periodically, and the temperature difference between the plates is high enough to induce radiative heat transfer. Under these assumptions, the equations governing the two-dimensional couple stress fluid flow are formulated and exact solutions of the velocity and the temperature fields are obtained. The effects of radiation, Hall current, porous medium permeability and other various flow parameters on the flow and heat transfer are presented graphically and discussed extensively.

scholarly journals Free convection in a vertical cylindrical annulus filled with anisotropic porous medium

2009 ◽  
Vol 13 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Rathinam Thansekhar ◽  
Babu Mahesh ◽  
Sekhar Chandra
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Temperature Distribution ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Free Convection ◽  
Numerical Study ◽  
Radius Ratio ◽  
Permeability Ratio ◽  
Cylindrical Annulus

A numerical study has been carried out for free convection in a vertical cylindrical annulus filled with a porous medium and whose inner wall is isothermally heated and the outer wall is isothermally cooled, the horizontal walls being insulated. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. Numerical results are reported for 0.1 ? K*? 10, 0.1 ? ? ? 10,1 ? A ? 20,2 ? Rr ? 20, and Ra*? 10000. Anisotropy of the porous medium is found to affect fluid flow, temperature distribution and heat transfer significantly. Higher permeability in the vertical direction enhances convective flow intensity and heat transfer inside the annulus. Average Nusselt number on the inner hot wall increases with increase in Rayleigh number or radius ratio, while it decreases with increase in aspect ratio or permeability ratio. The influence of thermal anisotropy is not so significant as that of hydrodynamic anisotropy. The numerically predicted temperature distribution at various locations inside the annulus shows reasonable agreement with experimental results available for isotropic porous medium. Based on a parametric study, correlation for heat transfer is presented in terms of Rayleigh number, aspect ratio, radius ratio, and permeability ratio.

scholarly journals Free Convection Heat Transfer from Horizontal Cylinders

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 559
Author(s):  
Janusz T. Cieśliński ◽  
Slawomir Smolen ◽  
Dorota Sawicka
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Free Convection ◽  
Convection Heat Transfer ◽  
Horizontal Tube ◽  
Correlation Equations ◽  
Convection Heat ◽  
Number Range ◽  
Heated Cylinder ◽  
Free Convection Heat

The results of experimental investigation of free convection heat transfer in a rectangular container are presented. The ability of the commonly accepted correlation equations to reproduce present experimental data was tested as well. It was assumed that the examined geometry fulfils the requirement of no-interaction between heated cylinder and bounded surfaces. In order to check this assumption recently published correlation equations that jointly describe the dependence of the average Nusselt number on Rayleigh number and confinement ratios were examined. As a heat source served electrically heated horizontal tube immersed in an ambient fluid. Experiments were performed with pure ethylene glycol (EG), distilled water (W), and a mixture of EG and water at 50%/50% by volume. A set of empirical correlation equations for the prediction of Nu numbers for Rayleigh number range 3.6 × 104 < Ra < 9.2 × 105 or 3.6 × 105 < Raq < 14.8 × 106 and Pr number range 4.5 ≤ Pr ≤ 160 has been developed. The proposed correlation equations are based on two characteristic lengths, i.e., cylinder diameter and boundary layer length.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

New benchmark solutions for transient natural convection in partially porous annuli

2016 ◽  
Vol 26 (3/4) ◽  
pp. 1187-1225 ◽  
Author(s):  
Nicola Massarotti ◽  
Michela Ciccolella ◽  
Gino Cortellessa ◽  
Alessandro Mauro
Keyword(s):  
Natural Convection ◽  
Free Convection ◽  
Transient Flow ◽  
Flow Behavior ◽  
Outer Radius ◽  
Temperature Fields ◽  
Content Type ◽  
Transient Natural Convection ◽  
Velocity And Temperature Fields ◽  
Benchmark Solutions

Purpose – The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro-ri. Moreover, several Darcy numbers have been considered. Design/methodology/approach – A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement. Findings – For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number. Research limitations/implications – A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems. Practical implications – The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility. Originality/value – This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

Development of Convective Heat Transfer Near Suddenly Heated, Vertically Aligned Horizontal Wires

1987 ◽  
Vol 109 (4) ◽  
pp. 912-918 ◽  
Author(s):  
J. R. Parsons ◽  
M. L. Arey
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Fluid Layer ◽  
Convective Motion ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Heat Sources ◽  
Transfer Coefficients ◽  
Vertically Aligned ◽  
The Wire

Experiments have been performed which describe the transient development of natural convective flow from both a single and two vertically aligned horizontal cylindrical heat sources. The temperature of the wire heat sources was monitored with a resistance bridge arrangement while the development of the flow field was observed optically with a Mach–Zehnder interferometer. Results for the single wire show that after an initial regime where the wire temperature follows pure conductive response to a motionless fluid, two types of fluid motion will begin. The first is characterized as a local buoyancy, wherein the heated fluid adjacent to the wire begins to rise. The second is the onset of global convective motion, this being governed by the thermal stability of the fluid layer immediately above the cylinder. The interaction of these two motions is dependent on the heating rate and relative heat capacities of the cylinder and fluid, and governs whether the temperature response will exceed the steady value during the transient (overshoot). The two heat source experiments show that the merging of the two developing temperature fields is hydrodynamically stabilizing and thermally insulating. For small spacing-to-diameter ratios, the development of convective motion is delayed and the heat transfer coefficients degraded by the proximity of another heat source. For larger spacings, the transient behavior approaches that of a single isolated cylinder.

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