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.

scholarly journals Transient Formulations for a Heat-Generating Fin with a Temperature-Dependent Heat Transfer Coefficient and Thermal Conductivity

2019 ◽  
Vol 2 (2) ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Governing Equation ◽  
Neumann Boundary ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Temperature Dependent ◽  
Discrete Equations ◽  
Highly Nonlinear ◽  
Temporal Derivative

Numerical calculations and scalar transport analyses are carried out for transient heat transfer in a heat generating fin with a temperature-dependent heat transfer and conduction coefficients. The highly nonlinear governing equation, satisfies the Dirichlet and Neumann boundary conditions at both ends of the problem domain.Integral representation of the governing equation over the discretized problem domain is achieved via the Green’s second identity together with the so called free- space Green function . This element-driven approach togetherwith the finite difference approximation of the temporal derivative result in discrete equations which are recursive in nature. At the boundaries of any of the adjacent elements, compatibility conditions and/or boundary conditions are enforced to guarantee scalar continuity. After the resulting system of discrete equations are numerically solved and assembled, they yield the transient history of the scalar variables at any particular point in time. Several numerical tests are carried out to ensure the convergence and accuracy of the formulation by comparing numerical results with those found in literature.

scholarly journals STEADY-STATE HEAT TRANSFER IN A PLATE WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY (AN EXACT SOLUTION)

2019 ◽  
Vol 18 (2) ◽  
pp. 85
Author(s):  
A. Miguelis ◽  
R. Pazetto ◽  
R. M. S. Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Transfer Problem ◽  
Internal Heat ◽  
Temperature Dependent ◽  
State Heat ◽  
Kirchhoff Transformation ◽  
Steady State Heat ◽  
Steady State Heat Transfer

This work presents the solution of the steady-state heat transfer problem in a rectangular plate with an internal heat source in a context in which the thermal conductivity depends on the local temperature. This generalization of one of the most classical heat transfer problems is carried out with the aid of the Kirchhoff transformation and employs only well known tools, as the superposition of solutions and the Fourier series. The obtained results illustrate how the usual procedures may be extended for solving more realistic physical problems (since the thermal conductivity of any material is temperature-dependent). A general formula for evaluating the Kirchhoff transformation as well as its inverse is presented too. This work has a strong didactical contribution since such analytical solutions are not found in any classical heat transfer book. In addition, the main idea can be used in a lot of similar problems.

scholarly journals A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
R. M. S. Gama ◽  
R. Pazetto
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Robin Boundary Conditions ◽  
Temperature Dependent ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems ◽  
Robin Boundary ◽  
Temperature Dependent Thermal Conductivity

This work presents an useful tool for constructing the solution of steady-state heat transfer problems, with temperature-dependent thermal conductivity, by means of the solution of Poisson equations. Specifically, it will be presented a procedure for constructing the solution of a nonlinear second-order partial differential equation, subjected to Robin boundary conditions, by means of a sequence whose elements are obtained from the solution of very simple linear partial differential equations, also subjected to Robin boundary conditions. In addition, an a priori upper bound estimate for the solution is presented too. Some examples, involving temperature-dependent thermal conductivity, are presented, illustrating the use of numerical approximations.

scholarly journals Asymptotic and Dynamical Analyses of Heat Transfer through a Rectangular Longitudinal Fin

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
C. Harley
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Ordinary Differential Equation ◽  
Heat Transfer Coefficient ◽  
Dynamical Analysis ◽  
Temperature Dependent ◽  
Highly Nonlinear ◽  
The Relationship ◽  
Steady Heat

The steady heat transfer through a rectangular longitudinal fin is studied. The thermal conductivity and heat transfer coefficient are assumed to be temperature dependent making the resulting ordinary differential equation (ODE) highly nonlinear. An asymptotic solution is used as a means of understanding the relationship between key parameters. A dynamical analysis is also employed for the same purpose.

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.

An Investigation of the Effect of interrupted fin arrangements on the Thermal Performance of a Heat Sink under a Free Convection Condition

2019 ◽  
Vol 7 (1) ◽  
pp. 43-53
Author(s):  
Abbas Jassem Jubear ◽  
Ali Hameed Abd
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Thermal Performance ◽  
Heat Sink ◽  
Numerical Study ◽  
Ansys Fluent ◽  
Fluent Software ◽  
Steady State Heat ◽  
Steady State Heat Transfer

The heat sink with vertically rectangular interrupted fins was investigated numerically in a natural convection field, with steady-state heat transfer. A numerical study has been conducted using ANSYS Fluent software (R16.1) in order to develop a 3-D numerical model.  The dimensions of the fins are (305 mm length, 100 mm width, 17 mm height, and 9.5 mm space between fins. The number of fins used on the surface is eight. In this study, the heat input was used as follows: 20, 40, 60, 80, 100, and 120 watts. This study focused on interrupted rectangular fins with a different arrangement and angle of the fins. Results show that the addition of interruption in fins in various arrangements will improve the thermal performance of the heat sink, and through the results, a better interruption rate as an equation can be obtained.

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