Thermal Optimization of a Circular-Sectored Finned Tube Using a Porous Medium Approach

2002 ◽  
Vol 124 (6) ◽  
pp. 1026-1033 ◽  
Author(s):  
Sung Jin Kim ◽  
Jae Wook Yoo ◽  
Seok Pil Jang
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Effective Conductivity ◽  
Saturated Porous Medium ◽  
Finned Tube ◽  
Uniform Heat Flux ◽  
Total Thermal Resistance

The present work investigates the heat transfer characteristics of a laminar fully developed forced convection in a circular-sectored finned tube with axially uniform heat flux and peripherally uniform wall temperature. The tubes with circular-sectored fins are modeled as a fluid-saturated porous medium. Using the Brinkman-extended Darcy model for fluid flow and the two-equation model for heat transfer, the analytical solutions for both velocity and temperature distributions are obtained and compared with the exact solution for fluid flow and the numerical solutions for conjugate heat transfer in order to validate the porous medium approach. The agreement between the solutions based on the porous medium approach and the conventional method is close within 5.3 percent. Based on the analytical solutions, parameters of engineering importance are identified to be the angle of the circular sector α and the effective conductivity ratio C, and their effects on fluid flow and heat transfer are studied. Also, the total thermal resistance is derived from the analytical solutions and minimized in order to optimize the thermal performance of a tube with circular-sectored fins.

Thermal Optimization of an Internally Finned Tube Using Analytical Solutions Based on a Porous Medium Approach

2007 ◽  
Vol 129 (10) ◽  
pp. 1408-1416 ◽  
Author(s):  
Kyu Hyung Do ◽  
Jung Yim Min ◽  
Sung Jin Kim
Keyword(s):  
Porous Medium ◽  
Analytical Solutions ◽  
Saturated Porous Medium ◽  
Equation Model ◽  
Finned Tube ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Thermal Optimization ◽  
Internally Finned Tube ◽  
Cylindrical Region

The present work deals with thermal optimization of an internally finned tube having axial straight fins with axially uniform heat flux and peripherally uniform temperature at the wall. The physical domain was divided into two regions: One is the central cylindrical region of the fluid extending to the tips of the fins and the other constituted the remainder of the tube area. The latter region including the fins was modeled as a fluid-saturated porous medium. The Brinkman-extended Darcy equation for fluid flow and two-equation model for heat transfer were used in the porous region, while the classical Navier–Stokes and energy equations were used in the central cylindrical region. The analytical solutions for the velocity and temperature profiles were in close agreement with the corresponding numerical solution as well as with existing theoretical and experimental data. Finally, optimum conditions, where the thermal performance of the internally finned tube is maximized, were determined using the developed analytical solutions.

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.

Film Boiling Heat Transfer From a Sphere and a Horizontal Cylinder Embedded in a Liquid-Saturated Porous Medium

1988 ◽  
Vol 110 (4a) ◽  
pp. 961-967 ◽  
Author(s):  
J. Orozco ◽  
R. Stellman ◽  
M. Gutjahr
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Porous Medium ◽  
Theoretical Model ◽  
Layer Thickness ◽  
Numerical Solutions ◽  
Saturated Porous Medium ◽  
Horizontal Cylinder ◽  
Film Boiling ◽  
Vapor Layer

This paper analyses both theoretically and experimentally the problem of film boiling from a body embedded in a liquid-saturated porous medium. Two body geometries are investigated thoroughly: a horizontal cylinder and a sphere. The theoretical model relies on the Brinkman-extended flow model to describe the flow field inside the thin vapor layer occupying the neighborhood near the heated surface. The theoretical model also includes an improved formulation of the effective conductivity in the vicinity of the heater as a function of the vapor layer thickness and the geometry of the porous medium material. Solutions are obtained for the vapor layer thickness and the local Nusselt number as a function of angular position. Numerical solutions are also obtained for the overall heat transfer rates from the surface to the fluid for a given vapor superheat. Experimental data for a 12.70 mm stainless steel cylindrical heater embedded in a 3-mm glass particle porous medium were obtained under steady—state operation. The experimental data obtained are compared with the theoretical analysis. The comparison shows that there is a good agreement between theory and experiments. The theoretical model is also compared with the experimental data obtained by other investigators for a spherical geometry. Excellent results are obtained in such comparison.

Forced Convection in Microstructures for Electronic Equipment Cooling

1999 ◽  
Vol 121 (3) ◽  
pp. 639-645 ◽  
Author(s):  
S. J. Kim ◽  
D. Kim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Thermal Resistance ◽  
Analytical Solutions ◽  
Heat Sink ◽  
Microchannel Heat Sink ◽  
Fluid Temperature ◽  
Medium Model ◽  
Porous Medium Model

This paper reports analytical solutions for both velocity and temperature profiles in Microchannel heat sinks by modeling the Microchannel heat sink as a fluid-saturated porous medium. The analytical solutions are obtained based on the modified Darcy model for fluid flow and the two-equation model for heat transfer. To validate the porous medium model and the analytical solutions based on that model, the closed-form solution for the velocity distribution in the fully-developed channel flow and the numerical solutions for the conjugate heat transfer problem, comprising the solid fin and the fluid, are also obtained. The analytical solutions based on the porous medium model are shown to predict the volume-averaged velocity and temperature distributions quite well. Using the analytical solutions, the aspect ratio and the effective thermal conductivity ratio are identified as variables of engineering importance and their effects on fluid flow and heat transfer are studied. As either one of these variables increases, the fluid temperature is shown to approach the solid temperature. Finally, the expression for the total thermal resistance, derived from the analytical solutions and the geometry of the microchannel heat sink for which the thermal resistance of the heat sink is minimal, is obtained.

Analysis of Fluid Flow in Composite Channels: Comparision of Analytical and Numerical Approaches

1999 ◽  
Author(s):  
A. V. Kuznetsov ◽  
Ming Xiong
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Saturated Porous Medium ◽  
Single Domain ◽  
Fluid Viscosity ◽  
Clear Fluid ◽  
Composite Channels ◽  
Model Fluid ◽  
Forced Convective Flow

Abstract In this work, comparisons between the numerical solutions for forced convective flow in composite channels, partly occupied by a homogeneous (clear) fluid and partly by a fluid saturated porous medium, and the exact solutions for the same problems are carried out. This is done to establish limitations of the single-domain approach utilized to obtain the numerical solutions. These limitations result from the assumptions which are implicitly invoked once the single-domain approach is utilized to model fluid flow in the interface region between the porous medium and a clear fluid. It is shown that the single-domain approach results in correct matching of the shear stress at the porous/fluid interface only if the adjustable coefficient in the representation for the excess stress equals zero and also if the effective viscosity of the porous medium equals to the fluid viscosity.

scholarly journals Modelling fluid flow and heat transfer in a saturated porous medium

2000 ◽  
Vol 4 (2) ◽  
pp. 165-173 ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Viscous Dissipation ◽  
Single Phase ◽  
Saturated Porous Medium ◽  
Inertial Effects ◽  
Flow And Heat Transfer ◽  
Phase Fluid

Since the days of Darcy, many refinements have been made to the equations used to model single-phase fluid flow and heat transfer in a saturated porous medium, to allow for such basic things as inertial effects, boundary friction and viscous dissipation, and also additional effects such as those due to rotation or a magnetic field. These developments are reviewed.

Natural Convection Around a Heated Cylinder in a Saturated Porous Medium

1988 ◽  
Vol 110 (3) ◽  
pp. 642-648 ◽  
Author(s):  
B. Farouk ◽  
H. Shayer
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Water Distribution ◽  
Numerical Solutions ◽  
Saturated Porous Medium ◽  
Convection Heat Transfer ◽  
Governing Equations ◽  
Heated Cylinder ◽  
Finite Difference Equations

Numerical solutions are presented for the natural convection heat transfer from a heated cylinder buried in a semi-infinite liquid-saturated porous medium. The governing equations are expressed in the stream function–temperature formulation and finite difference equations are obtained by integrating the governing equations over finite cells. The heat transfer characteristics of the heated cylinder are studied as functions of the Rayleigh number and the vertical depth of the cylinder center from a permeable surface. The numerical scheme involves the use of a cylindrical network of nodes in the vicinity of the cylinder with a Cartesian mesh covering the remainder of the flow domain. The results are of use in the design of underground electrical cables, power plant steam, and water distribution lines, among others.

scholarly journals Homotopy perturbation and numerical solutions for MHD flow of PTT fluid through a channel embedded in a porous medium

2021 ◽  
Author(s):  
Swain B.K ◽  
◽  
Das M ◽  
Dash G.C ◽  
◽  
...  
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Viscous Dissipation ◽  
Flow Model ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Saturated Porous Medium ◽  
Deborah Number ◽  
Homotopy Perturbation ◽  
Ptt Fluid

An analysis is made of the steady one dimensional flow and heat transfer of an incompressible viscoelastic electrically conducting fluid (PTT model) in a channel embedded in a saturated porous medium. The pressure driven flow is subjected to a transverse magnetic field of constant magnetic induction (field strength). The heat transfer accounts for the viscous dissipation. The governing equation (a non-linear ordinary differential equation) is solved analytically (Homotopy Perturbation Method) and numerically (Runge-Kutta method with shooting technique) providing the consistency of the result. The role of Deborah number substantiates both Newtonian and non-Newtonian aspects of the flow model. The inclusion of two body forces affects rheological property of the flow model considered. Temperature distribution in the boundary layer is shown when the channel surfaces are held at constant temperatures. A novel result of the analysis is that the contribution of viscous dissipation is found to be negligible as the variation of temperature is almost linear across the flow field in the present PTT fluid model indicating preservation of thermal energy loss.

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