Performance of Asymmetrically Heated Extended Surface With Temperature Dependent Thermal Conductivity

2006 ◽  
Author(s):  
A. Aziz
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Heat Exchangers ◽  
Numerical Solutions ◽  
Temperature Dependent ◽  
Compact Heat Exchangers ◽  
Extended Surface ◽  
Temperature Dependent Thermal Conductivity ◽  
Perturbation Solutions

The effect of temperature dependent thermal conductivity on the performance of an asymmetrically heated extended surface which is commonly encountered in compact heat exchangers is studied both analytically and numerically. The surface is assumed to extend between two primary surfaces at different temperatures and to operate in a convective environment. The nonlinear differential equation governing the thermal performance of the extended surface is solved by carrying out a perturbation analysis in which the perturbation parameter is the dimensionless measure of thermal conductivity variation with temperature. Two-term analytical solutions for the temperature distribution and the convective heat dissipation are presented. The problem is also solved numerically for a range of conventional fin parameter, thermal asymmetry parameter, and thermal conductivity-temperature variation parameter to assess the accuracy of the perturbation solutions. Graphical results illustrating the effect of these parameters on the temperature distribution, heat transfer rates from the end primary surfaces, and the total heat transfer from the extended surface are provided and discussed. For the thermal conductivity variations encountered in compact heat exchangers, the two-term perturbation solutions are accurate with 2% of the numerical solutions.

Exact solution of a nonlinear fin problem of temperature-dependent thermal conductivity and heat transfer coefficient

2020 ◽  
Vol 98 (7) ◽  
pp. 700-712 ◽  
Author(s):  
Sheng-Wei Sun ◽  
Xian-Fang Li
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Temperature Distribution ◽  
Transfer Coefficient ◽  
Power Law ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Special Cases ◽  
Temperature Dependent Thermal Conductivity

This paper studies a class of nonlinear problems of convective longitudinal fins with temperature-dependent thermal conductivity and heat transfer coefficient. For thermal conductivity and heat transfer coefficient dominated by power-law nonlinearity, the exact temperature distribution is obtained analytically in an implicit form. In particular, the explicit expressions of the fin temperature distribution are derived explicitly for some special cases. An analytical expression for fin efficiency is given as a function of a thermogeometric parameter. The influences of the nonlinearity and the thermogeometric parameter on the temperature and thermal performance are analyzed. The temperature distribution and the fin efficiency exhibit completely different behaviors when the power-law exponent of the heat transfer coefficient is more or less than negative unity.

scholarly journals Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 111-115 ◽  
Author(s):  
Domiri Ganji ◽  
Ziabkhsh Ganji ◽  
Domiri Ganji
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Variable Thermal Conductivity ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Annular Fin ◽  
Temperature Dependent Thermal Conductivity

In this paper, homotopy perturbation method has been used to evaluate the temperature distribution of annular fin with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. This method is useful and practical for solving the nonlinear heat transfer equation, which is associated with variable thermal conductivity condition. The homotopy perturbation method provides an approximate analytical solution in the form of an infinite power series. The annular fin heat transfer rate with temperature-dependent thermal conductivity has been obtained as a function of thermo-geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity

Effect of Variable Thermal Conductivity on Heat Transfer From a Hollow Sphere With Heat Generation Using Homotopy Perturbation Method

2008 ◽  
Author(s):  
Zafar H. Khan ◽  
Rahim Gul ◽  
Waqar A. Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Homotopy Perturbation Method ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Generation Parameter ◽  
Dimensionless Heat ◽  
Temperature Dependent Thermal Conductivity

Homotopy perturbation method (HPM) is employed to investigate steady-state heat conduction with temperature dependent thermal conductivity and heat generation in a hollow sphere. Analytical models are developed for dimensionless temperature distribution and heat transfer using mixed boundary conditions (Dirichlet, Neumann and Robin). The effects of dimensionless heat generation parameter and temperature dependent thermal conductivity on temperature distribution and heat transfer from hollow spheres are analyzed graphically. It is demonstrated that the heat transfer is strongly dependent on the dimensionless heat generation parameter and temperature dependent thermal conductivity. Finally the HPM results are compared with Kirchhoff Transformation results.

Sixty-Five Years of Extended Surface Technology (1922–1987)

1988 ◽  
Vol 41 (9) ◽  
pp. 321-364 ◽  
Author(s):  
Allan D. Kraus
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Heat Exchangers ◽  
Electronic Equipment ◽  
Numerical Analyses ◽  
Compact Heat Exchangers ◽  
Extended Surface ◽  
Mathematical Techniques

The extended surface literature from 1922 to 1987 is reviewed. The review begins with the classic NACA report of Harper and Brown published in 1922 and concludes with the works of Marto, Wanniarachchi, Rose, Mitrou, and Razelos published in 1986. A section entitled “The Beginnings” traces the accomplishments of the pioneers and it covers the period from 1922 to 1945 which coincides with the publication of Gardner’s landmark paper. At this point, a chronological approach is abandoned in favor of a categorization into topical areas. These are the elimination of the Murray–Gardner assumptions, boiling and condensation, experimental endeavors, compact heat exchangers, internally finned configurations, numerical analyses, optimizations, analyses of finned arrays, and additional topics including the use of extended surface to augment heat transfer, heat transfer in electrical and electronic equipment, purely mathematical techniques, and heat and mass transfer.

Sign in / Sign up

Export Citation Format

Share Document