The aim of this article is to present the results of a parametric analysis of the entropy generation due to mixed convection in the entry‐developing region between two…
Abstract
Purpose
The aim of this article is to present the results of a parametric analysis of the entropy generation due to mixed convection in the entry‐developing region between two differentially heated isothermal vertical plates.
Design/methodology/approach
The entropy generation was estimated via a numerical solution of the mass, momentum and energy conservation equations governing the flow and heat transfer in the vertical channel between the two parallel plates. The resultant temperature and velocity profiles were used to estimate the entropy generation and other heat transfer parameters over a wide range of the operating parameters. The investigated parameters include the buoyancy parameter (Gr/Re), Eckert number (Ec), Reynolds number (Re), Prandtl number (Pr) and the ratio of the dimensionless temperature of the two plates (θT).
Findings
The optimum values of the buoyancy parameter (Gr/Re) optimum at which the entropy generation assumes its minimum for the problem under consideration have been obtained numerically and presented over a wide range of the other operating parameters. The effect of the other operating parameters on the entropy generation is presented and discussed as well.
Research limitations/implications
The results of this investigation are limited to the geometry of vertical channel parallel plates under isothermal boundary conditions. However, the concept of minimization of entropy generation via controlling the buoyancy parameter is applicable for any other geometry under any other thermal boundary conditions.
Practical implications
The results presented in this paper can be used for optimum designs of heat transfer equipment based on the principle of entropy generation minimization with particular focus on the optimum design of plate and frame heat exchanger and the optimization of electronic packages and stacked packaging of laminar‐convection‐cooled printed circuits.
Originality/value
This paper introduces the entropy generation minimization via controlling the operating parameters and clearly identifies the optimum buoyancy parameter (Gr/Re) at which entropy generation assumes its minimum under different operating conditions.
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Keywords
Maged A.I. El‐Shaarawi, Esmail M.A. Mokheimer and Ahmad Jamal
To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal…
Abstract
Purpose
To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal boundary conditions with one cylinder heated isothermally while the other cylinder is kept at the inlet fluid temperature.
Design/methodology/approach
A finite‐difference algorithm has been developed to solve the bipolar boundary‐layer equations for the conjugate laminar free convection heat transfer in vertical eccentric annuli.
Findings
Numerical results are presented for a fluid of Prandtl number, Pr=0.7 in eccentric annuli. The geometry parameters of NR2 and E (the fluid‐annulus radius ratio and the eccentricity, respectively) have considerable effects on the results.
Practical implications
Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.
Originality/value
The paper presents results that are not available in the literature for the problem of conjugate laminar free convection in open‐ended vertical eccentric annular channels. Geometry effects having been investigated by considering fluid annuli having radii ratios NR2=0.1 and 0.3, 0.5 and 0.7 and four values of the eccentricity E=0.1, 0.3, 0.5 and 0.7. Moreover, practical ranges of the solid‐fluid conductivity ratio (KR) and the wall thicknesses that are commonly available in pipe standards have been investigated. Such results are very much needed for design purposes of heat transfer equipment.
Details
Keywords
Esmail M.A. Mokheimer and Maged El‐Shaarawi
Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the…
Abstract
Purpose
Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature). Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature).
Design/methodology/approach
The fully‐developed laminar free convection momentum equation has been solved numerically using an analytical solution of the governing energy equation.
Findings
Results are presented to show the effect of the annulus radius ratio and the dimensionless eccentricity on the induced flow rate, the total heat absorbed by the fluid, and the fully developed Nusselt numbers on the two boundaries of the annulus for a fluid of Prandtl number 0.7.
Practical implications
Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.
Originality/value
The paper presents a solution that is not available in the literature for the problem of fully developed free convection in open‐ended vertical eccentric annular channels under thermal boundary conditions of the fourth kind. Also presents the maximum possible induced flow rates, the total heat absorbed by the fluid, and the Nusselt numbers on the two boundaries of the annulus. The effects of N and E (the radius ratio and eccentricity, respectively) on these results are presented. Such results are very much needed for design purposes of heat transfer equipment.
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Keywords
Esmail M.A. Mokheimer, S. Sami and B.S. Yilbas
This paper's aim is to examine flow and heat transfer through vertical channels between parallel plates, which is of prime importance in the design of cooling systems for…
Abstract
Purpose
This paper's aim is to examine flow and heat transfer through vertical channels between parallel plates, which is of prime importance in the design of cooling systems for electronic equipment such as that of finned cold plates in general, plate‐and‐frame heat exchangers, etc.
Design/methodology/approach
Numerical and analytical solutions are presented to investigate the heat transfer enhancement and the pressure drop reduction due to buoyancy effects (for buoyancy‐aided flow) for the developing laminar mixed convection in vertical channel between parallel plates in the vicinity of the critical values of the buoyancy parameter (Gr/Re)crt that are obtained analytically. The numerical solutions are presented for a wide range of the buoyancy parameters Gr/Re that cover both of buoyancy‐opposed and buoyancy‐aided flow situations under each of the isothermal boundary conditions under investigation.
Findings
Buoyancy parameters greater than the critical values result in building‐up the pressure downstream of the entrance such that the vertical channel might act as a thermal diffuser with possible incipient flow reversal. Locations at which the pressure gradient vanishes and the locations at which the pressure‐buildup starts have been numerically obtained and presented for all the investigated cases.
Research limitations/implications
The study is limited to the laminar flow situation.
Practical implications
The results clearly show that for buoyancy‐aided flow, the increase of the buoyancy parameter enhances the heat transfer and reduces the pressure drop across the vertical channel. These findings are very useful for cooling channel or chimney designs.
Originality/value
The study is original and presents new findings, since none of the previous studies reported the conditions for which pressure buildup might take place due to mixed convection in vertical channels between parallel plates.
Details
Keywords
Maged A.I. El‐Shaarawi and Esmail M. A. Mokheimer
The paper utilizes a boundary‐layer model in bipolar coordinates to study the developing laminar free convection in vertical open‐ended eccentric annuli with one of the boundaries…
Abstract
The paper utilizes a boundary‐layer model in bipolar coordinates to study the developing laminar free convection in vertical open‐ended eccentric annuli with one of the boundaries uniformly heated while the other boundary is cooled and kept isothermal at the ambient temperature. This model has been solved numerically using finite‐difference techniques. Results not available in the literature are presented for a fluid of Prandtl number 0.7 in an annulus of radius ratio 0.5 for three values of the dimensionless eccentricity, namely, 0.1, 0.5 and 0.7. These results include the developing velocity profiles and the pressure along the annulus, the channel heights required to naturally induce different flow rates and the variation of the total heat absorbed by the fluid with the channel height.
Details
Keywords
M.T. Darvishi, R.S.R. Gorla and F. Khani
The purpose of this paper is to conduct a numerical study of the convection heat transfer in porous media by the homotopy analysis method (HAM). The geometry considered is that of…
Abstract
Purpose
The purpose of this paper is to conduct a numerical study of the convection heat transfer in porous media by the homotopy analysis method (HAM). The geometry considered is that of a rectangular profile fin. The porous fin allows the flow to infiltrate through it and solid-fluid interaction takes place. This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The theory section addresses the derived governing equation. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation. The auxiliary parameter in the HAM is derived by using the averaged residual error concept which significantly reduces the computational time. The use of optimal auxiliary parameter provides a superior control on the convergence and accuracy of the analytic solution.
Design/methodology/approach
This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed.
Findings
The HAM has been successfully applied for the thermal performance of a porous fin of rectangular profile. Solutions are derived for three cases of tip condition: an infinitely long fin with tip in thermal equilibrium with the ambient, a finite fin with an insulated tip and a finite fin with a convective tip. The performance of the fin depends on three dimensionless parameters; porosity parameter Sh, radiation-conduction parameter G and a dimensionless temperature relating the ambient and base temperatures. The results show that the base heat flow increases when the permeability of the medium is high and/or when the buoyancy effect induced in the fluid is strong. The base heat flow is enhanced as the surface radiation or the tip Biot number increases.
Research limitations/implications
The analysis is made for the Darcy's model. Non-Darcy effects will be investigated in a future work.
Practical implications
The approach is useful in enhancing heat transfer rates.
Originality/value
The results of the study will be interested to the researchers of the field of heat exchanger designers.