Optimum Dimensions of Extended Surfaces Operating in a Convective Environment

1992 ◽  
Vol 45 (5) ◽  
pp. 155-173 ◽  
Author(s):  
A. Aziz
Keyword(s):  
Heat Dissipation ◽  
State Of The Art ◽  
Internal Heat ◽  
Optimization Procedure ◽  
Review Of The Literature ◽  
Temperature Dependent ◽  
Dual Purpose ◽  
Extended Surface ◽  
Extended Surfaces ◽  
Temperature Dependent Thermal Conductivity

This article is devoted to the review of the literature on optimum dimensions of extended surfaces losing heat by pure convection to the surroundings. The review covers straight (longitudinal) fins, annular (radial) fins, and spines of different profile shapes. The optimum dimensions for each shape are given both in terms of the volume of the material as well as the heat dissipation. The effects of tip heat loss, variable heat transfer coefficient, internal heat generation, temperature dependent thermal conductivity, base convection, and primary surface thickness on the optimum dimensions are discussed. The optimization procedure is illustrated with several numerical examples. Areas of extended surface technology where further optimization studies are needed are identified. It is hoped that the article would serve the dual purpose of the state-of-the-art as well as a pedagogical review.

scholarly journals A Study on Convective-Radial Fins with Temperature-dependent Thermal Conductivity and Internal Heat Generation

2019 ◽  
Vol 8 (1) ◽  
pp. 145-156
Author(s):  
Trushit Patel ◽  
Ramakanta Meher
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Fractional Order ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Temperature Dependent Thermal Conductivity

Abstract In this paper, the temperature distribution in a convective radial fins is analyzed through a fractional order energy balance equation with the consideration of internal heat generation and temperature dependent thermal conductivity. Adomian decomposition Sumudu transform method is used to study the influence of temperature distribution and the efficiency of radial fins for different values of thermal conductivity and to determine the role of thermal conductivity, thermo-geometric fin parameter as well as fractional order values in finding the temperature distribution and the fin efficiency of the convective radial fins. Finally, the efficiency of this proposed method has been studied by comparing the obtained results with the classical order results obtained by using numerical method and Variational Iteration Method (Coskun and Atay, 2007).

The exact closed solution in the analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation

2019 ◽  
Vol 97 (5) ◽  
pp. 566-575
Author(s):  
S. Abbasbandy ◽  
E. Shivanian
Keyword(s):  
Thermal Conductivity ◽  
Natural Convection ◽  
Thermal Behaviour ◽  
Heat Generation ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Porous Fin ◽  
Temperature Dependent Thermal Conductivity

In the current work, thermal behaviour analysis of a natural convection porous fin with internal heat generation and temperature-dependent thermal conductivity is studied. The developed symbolic heat transfer models are for the purpose of the investigation of the effects of various parameters on the thermal behaviour of the porous fin. It is shown that its governing nonlinear differential with proper boundary conditions is exactly solvable. To this aim, we reduce the order of differential equations first and then convert into a total differential equation by multiplying a convenient integrating factor. A full discussion and exact analytical solution in the implicit form is given for further physical interpretation and it is proved that a solution to the problem may not exist or the solution is mathematically unique depending on the values of the parameters of the model.

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.

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