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.

Subcooled Flow Film Boiling Across a Horizontal Cylinder: Part I—Analytical Model

1995 ◽  
Vol 117 (1) ◽  
pp. 167-174 ◽  
Author(s):  
X. S. Chou ◽  
L. C. Witte
Keyword(s):  
Heat Transfer ◽  
Layer Thickness ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Temperature Fields ◽  
Film Boiling ◽  
Wake Region ◽  
Vapor Layer ◽  
Subcooled Flow

An analytical model of stable subcooled flow film boiling on the front of a horizontal cylinder and a model for the wake region downstream of the flow separation points were developed. The flow and temperature fields upstream of the separation points were represented by a “local-similarity” solution obtained through a rigorous mathematical transformation. The transformed governing equations were solved numerically using a finite-difference scheme. Numerical solutions for the vapor layer thickness, the velocity, and the temperature fields were obtained for both the liquid and vapor layers. The results showed that the liquid boundary layer was thicker than the vapor film. Increases in the liquid subcooling and in the free-stream velocity decreased the vapor layer thickness. The influence of convection in the vapor layer is small yielding a near-linear temperature distribution. A two-dimensional vapor wake model was developed based on mass and energy balances. Numerical solutions, including the vapor layer thickness and the temperature field of the front part and the wake part, were matched at the separation points. The results showed that increases in the liquid subcooling decreased the vapor layer thickness. Heat transfer in the wake region can amount up to 20 percent of the heat transfer in the forward region and should not be neglected especially at high subcooling.

A General Correlation for Pool Film Boiling Heat Transfer From a Horizontal Cylinder to Subcooled Liquid: Part 2—Experimental Data for Various Liquids and Its Correlation

1990 ◽  
Vol 112 (2) ◽  
pp. 441-450 ◽  
Author(s):  
A. Sakurai ◽  
M. Shiotsu ◽  
K. Hata
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Analytical Solution ◽  
Boiling Heat Transfer ◽  
Radiation Effects ◽  
Approximate Analytical Solution ◽  
Horizontal Cylinder ◽  
Film Boiling ◽  
System Pressure ◽  
Horizontal Cylinders

Experimental data of pool film boiling heat transfer from horizontal cylinders in various liquids such as water, ethanol, isopropanol, Freon-113, Freon-11, liquid nitrogen, and liquid argon for wide ranges of system pressure, liquid subcooling, surface superheat and cylinder diameter are reported. These experimental data are compared with a rigorous numerical solution and an approximate analytical solution derived from a theoretical model based on laminar boundary layer theory for pool film boiling heat transfer from horizontal cylinders including the effects of liquid subcooling and radiation from the cylinder. A new correlation was developed by slightly modifying the approximate analytical solution to agree better with the experimental data. The values calculated from the correlation agree with the authors’ data within ± 10 percent, and also with other researchers’ data for various liquids including those with large radiation effects, though these other data were obtained mainly under saturated conditions at atmospheric pressure.

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.

A General Correlation for Pool Film Boiling Heat Transfer From a Horizontal Cylinder to Subcooled Liquid: Part 1—A Theoretical Pool Film Boiling Heat Transfer Model Including Radiation Contributions and Its Analytical Solution

1990 ◽  
Vol 112 (2) ◽  
pp. 430-440 ◽  
Author(s):  
A. Sakurai ◽  
M. Shiotsu ◽  
K. Hata
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Theoretical Model ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Numerical Solution ◽  
Boiling Heat Transfer ◽  
Approximate Analytical Solution ◽  
Horizontal Cylinder ◽  
Film Boiling

A rigorous numerical solution of a theoretical model based on laminar boundary layer theory for pool film boiling heat transfer from a horizontal cylinder including the contributions of liquid subcooling and radiation from the cylinder was obtained. The numerical solution predicted accurately the experimental results of pool film boiling heat transfer from a horizontal cylinder in water with high radiation emissivity for a wide range of liquid subcooling in the range of nondimensional cylinder diameters around 1.3, where the numerical solution was applicable to the pool film boiling heat transfer from a cylinder with negligible radiation emissivity. An approximate analytical solution for the theoretical model was also derived. It was given by the sum of the pool film boiling heat transfer coefficient if there were no radiation and the radiation heat transfer coefficient for parallel plates multiplied by a nondimensional radiation parameter similar to the expression for saturated pool film boiling given by Bromley. The approximate analytical solution agreed well with the rigorous numerical solution for various liquids of widely different physical properties under wide ranges of conditions.

Forced Convection Film Boiling Heat Transfer From Single Horizontal Cylinders in Saturated and Subcooled Liquids: Part 1 — Experimental Data and Its Correlation for Saturated Liquids

2008 ◽  
Author(s):  
Qiusheng Liu ◽  
Katsuya Fukuda
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Forced Convection ◽  
Boiling Heat Transfer ◽  
Horizontal Cylinder ◽  
Film Boiling ◽  
Two Phase ◽  
Saturated Water ◽  
Horizontal Cylinders ◽  
Flow Velocities

Forced convection film boiling heat transfer on a horizontal cylinder in saturated water and Freon-113 flowing upward perpendicular to the cylinder was measured for the flow velocities ranging from zero to 1 m/s at the system pressures ranging from 100 to 500 kPa: the platinum cylinders with the diameters ranging from 0.7 to 5 mm were used as the test cylinder heaters. The existing correlation for forced convection film boiling heat transfer given by Bromley et al. could not well describe the experimental data obtained, especially those for the higher pressures. The forced convection film boiling heat transfer correlation including the radiation contribution from the cylinders with various diameters for saturation conditions was developed based on forced convection two-phase laminar boundary layer film boiling model and the experimental data obtained. The experimental data agreed with the corresponding values derived from the correlation within ±15% for the flow velocities below 0.7 m/s, and within −30% to +15% for higher flow velocities. It was confirmed that the experimental data obtained by Bromley et al. for the horizontal carbon cylinders with the diameters ranging from 9.83 to 16.2 mm and with the significant radiation effect from the cylinder surfaces in various liquids for the various flow velocities up to 4.4 m/s at an atmospheric pressure agreed with the corresponding values derived from the new correlation within ±20%.

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.

Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell

1969 ◽  
Vol 39 (3) ◽  
pp. 477-495 ◽  
Author(s):  
R. A. Wooding
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Saturated Porous Medium ◽  
Mean Amplitude ◽  
Wave Number ◽  
Two Fluids ◽  
Averaged Equations ◽  
The Mean ◽  
Hele Shaw Cell

Waves at an unstable horizontal interface between two fluids moving vertically through a saturated porous medium are observed to grow rapidly to become fingers (i.e. the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approximately as (time)2, followed by a transition to a growth proportional to time. Correspondingly, the mean wave-number decreases approximately as (time)−½. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an unclosed set, but closure is achieved by assuming a law for the mean wave-number based on similarity. It is found that the mean amplitude is fairly insensitive to changes in wave-number. Numerical solutions of the averaged equations give more detailed information about the growth behaviour, in excellent agreement with the similarity results and with the Hele-Shaw experiments.

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