scholarly journals Steady Thermal Analysis of Two-Dimensional Cylindrical Pin Fin with a Nonconstant Base Temperature

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Raseelo J. Moitsheki ◽  
Charis Harley
Keyword(s):  
Heat Transfer ◽  
Separation Of Variables ◽  
Invariant Solution ◽  
Base Temperature ◽  
Lie Point Symmetries ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Pin Fin ◽  
Sink Term ◽  
Steady Heat

Steady heat transfer through a pin fin is studied. Thermal conductivity, heat transfer coefficient, and the source or sink term are assumed to be temperature dependent. In the model considered, the source or sink term is given as an arbitrary function. We employ symmetry techniques to determine forms of the source or sink term for which the extra Lie point symmetries are admitted. Method of separation of variables is used to construct exact solutions when the governing equation is linear. Symmetry reductions result in reduced ordinary differential equations when the problem is nonlinear and some invariant solution for the linear case. Furthermore, we analyze the heat flux, fin efficiency, and the entropy generation.

scholarly journals Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
A. Moradi ◽  
H. Ahmadikia
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Data ◽  
Transformation Method ◽  
Base Temperature ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Runge Kutta Method ◽  
Range Of Values ◽  
Temperature Dependent Thermal Conductivity

Three different profiles of the straight fin that has a temperature-dependent thermal conductivity are investigated by differential transformation method (DTM) and compared with numerical solution. Fin profiles are rectangular, convex, and exponential. For validation of the DTM, the heat equation is solved numerically by the fourth-order Runge-Kutta method. The temperature distribution, fin efficiency, and fin heat transfer rate are presented for three fin profiles and a range of values of heat transfer parameters. DTM results indicate that series converge rapidly with high accuracy. The efficiency and base temperature of the exponential profile are higher than the rectangular and the convex profiles. The results indicate that the numerical data and analytical method are in agreement with each other.

scholarly journals Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
M. D. Mhlongo ◽  
R. J. Moitsheki
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Dirichlet Boundary Conditions ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Highly Nonlinear ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Steady Heat

One-dimensional steady-state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The effects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.

Effect of Absorptive Coating of the Hot Fluid Passage of a Heat Exchanger Employing Exergy-Optimized Pin Fins in High Temperature Applications

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Nwosu P. Nwachukwu ◽  
Samuel O. Onyegegbu
Keyword(s):  
Heat Transfer ◽  
High Temperature ◽  
Simple Relation ◽  
Base Temperature ◽  
Minimum Entropy ◽  
Pin Fin ◽  
Temperature Heat ◽  
Pin Fins ◽  
Minimum Entropy Generation ◽  
Fluid Parameters

An expression for the optimum pin fin dimension is derived on exergy basis for a high temperature exchanger employing pin fins. The present result differs from that obtained by Poulikakos and Bejan (1982, “Fin Geometry for Minimum Entropy Generation in Forced Convection,” ASME J. Heat Transfer, 104, pp. 616–623) for a low temperature heat recovery application. Also, a simple relation is established between the amounts the base temperature of the optimized pin fin is raised for a range of absorptive coating values. Employing this relation, if the absorptivity of the coating, the plate emissivity, the number of protruding fins, and some area and fluid parameters are known, the corresponding value for the base temperature of the fin is immediately obtained. The analysis shows that the thermal performance of the exchanger improves substantially with a high absorptivity coating hence can be seen as a heat transfer enhancement feature of the exchanger operating with radiation dominance.

Experimental Study of Threaded and Grooved Radiating Pin Fin

2007 ◽  
Author(s):  
J. Ganesh Murali ◽  
S. Katte Subrahmanya
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Steady State ◽  
Vacuum Chamber ◽  
Unit Mass ◽  
Test Facility ◽  
Temperature Control System ◽  
Base Temperature ◽  
Total Heat Transfer ◽  
Pin Fin

An experimental study was performed to provide information on the heat radiated to the space from grooved pin fin radiator of three different geometries. Since mass is at a premium on spacecraft, the space radiator used in its temperature control system needs to be optimized with respect to mass. A literature review shows that much of work on radiating fins has been carried out analytically and numerically. Presently, a radiating pin fin with threads and grooves on its outside surface is investigated experimentally. A test facility with a vacuum chamber and instrumentation is fabricated. The heat input to the fin is varied such that the base temperature is maintained constant under steady state. Based on a study of effect of vacuum, using available resources, the chamber is designed for a vacuum of 680 mm Hg such that the contribution of convection to the total heat transfer could be ignored. The study shows that there exists optimum thread per inch (TPI), angle of threads and depth of grooves for which the heat loss per unit mass is a maximum. The threaded and grooved radiating fin loses 1.2 to 1.34 times greater heat per unit mass, respectively, compared to the bare pin fin.

Study of PCM-Based Pin-Fin Heat Sinks

2009 ◽  
Author(s):  
V. Dubovsky ◽  
G. Barzilay ◽  
G. Granot ◽  
G. Ziskind ◽  
R. Letan
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Material Properties ◽  
Heat Fluxes ◽  
Heat Sinks ◽  
Base Temperature ◽  
Pin Fin ◽  
Dependent Parameter ◽  
Set Up ◽  
Change Material

This study deals with heat transfer from pin-fin aluminum heat sinks to a phase-change material (PCM) which fills the inter-fin space. The sinks have a horizontal base and accordingly their fins are vertical. The sink base dimensions are 100 mm by 100 mm, with fin height of 10 mm, 20 mm or 30 mm, and cross section of 4 mm×4 mm. The number of fins varies, e.g. 49, 64, 81, etc. The applied power is between 50 W to 250 W, corresponding to the heat fluxes of 5–25 kW/m2. The present paper reports mostly numerical results, but the numerical model is validated using the findings from an ongoing experimental investigation, in which a commercially available paraffin wax RT-35 is used as the PCM, with the melting temperature of about 35 °C. The simulations reflect the material properties, geometry, and other features of the experimental set-up, including heating with an electrical foil heater. Accordingly, the base temperature serves as the dependent parameter. Numerical simulations, performed using the Fluent 6.2 software, serve to obtain detailed melting patterns and explain the effect of fin size and number on sink performance.

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.

Cooling Performance of an Integrated Impingement and Pin Fin Cooling Configuration

2003 ◽  
Author(s):  
Shigemichi Yamawaki ◽  
Chiyuki Nakamata ◽  
Ryouji Imai ◽  
Shinsuke Matsuno ◽  
Toyoaki Yoshida ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Unit Area ◽  
Rapid Prototype ◽  
Cooling Effectiveness ◽  
Impingement Cooling ◽  
Casting Technique ◽  
Fin Efficiency ◽  
Pin Fin ◽  
Pin Geometry ◽  
Efficiency Theory

The cooling configuration adopted in this study integrates impingement cooling and pin fin cooling devices into one body, the aim being enhancement of the effective heat transfer area. The purpose of the study is to confirm improvement of cooling effectiveness for two different pin density configurations by experimental verification. Experiments were conducted in similar conditions to actual engines using large-scaled flat-plate specimens manufactured by a new rapid prototype casting technique. The results were compared with predictions by one-dimensional analysis adopting the fin efficiency theory. Although the coarse pin density, one pin in a unit area, shows good agreement with the prediction, the fine pin density, four pins in the unit area, was overpredicted. It was found by numerical analysis that heat transfer of the new pin geometry did not increase, so that its surface area increased. CFD-aided prediction was proposed and validated with two specimen’s data.

scholarly journals Enhancement of Heat Transfer Characteristics of Plain Fin Coated with Brass and Aluminium

2019 ◽  
Vol 8 (4) ◽  
pp. 6030-6035
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Power Plants ◽  
Heat Transfer Characteristics ◽  
Thermal Systems ◽  
Air Conditioners ◽  
Fin Efficiency ◽  
Pin Fin ◽  
Transfer Characteristics

Rate of heat transfer plays a very important role in the performance of thermal systems like heat engines, steam power plants, refrigerators, air conditioners etc. Continuous efforts are being made to improve the effectiveness of the mentioned systems. Thermal conductivity of material effects the heat transfer characteristics the most and can be enhanced by surface coating of various materials. Materials with high thermal conductivity are preferable for providing coating on substrate to improve heat transfer rate. In present work, fins made of Stainless Steel 304 coated with Brass and Aluminum (250 micrometers thickness) by Twin wire arc coating process, is investigated. Experiments were conducted with and without coating at different heat input using Pin Fin Apparatus and calculated Nusselt number, Reynolds number, thermal conductivity, heat transfer coefficient, fin efficiency. From the results obtained, it is concluded that Nusselt number in case of S.S coated with Aluminium is increased by 1.36% compared with coated with brass and 2.1% compared without coating and there is an increase in efficiency of fin coated brass and Aluminium materials by 14-73% compared to without coating.

Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Mahdi Anbarloei ◽  
Elyas Shivanian
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Temperature Dependent Thermal Conductivity

In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.

Homotopy Perturbation Method for the Analysis of Heat Transfer in an Annular Fin With Temperature-Dependent Thermal Conductivity

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Rishi Roy ◽  
Sujit Ghosal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Base Temperature ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Annular Fin ◽  
Temperature Dependent Thermal Conductivity

A recent mathematical technique of homotopy perturbation method (HPM) for solving nonlinear differential equations has been applied in this paper for the analysis of steady-state heat transfer in an annular fin with temperature-dependent thermal conductivity and with the variation of thermogeometric fin parameters. Excellent benchmark agreement indicates that this method is a very simple but powerful technique and practical for solving nonlinear heat transfer equations and does not require large memory space that arises out of discretization of equations in numerical computations, particularly for multidimensional problems. Three conditions of heat transfer, namely, convection, radiation, and combined convection and radiation, are considered. Dimensionless parameters pertinent to design optimization are identified and their effects on fin heat transfer and efficiency are studied. Results indicate that the heat dissipation under combined mode from the fin surface is a convection-dominant phenomenon. However, it is also found that, at relatively high base temperature, radiation heat transfer becomes comparable to pure convection. It is worth noting that, for pure radiation condition, the dimensionless parameter of aspect ratio (AR) of a fin is a more desirable controlling parameter compared to other parameters in augmenting heat transfer rate without much compromise on fin efficiency.

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