Analysis of Heat Transfer in a Cylindrical Spine Fin with Variable Thermal Properties

2018 ◽  
Vol 387 ◽  
pp. 10-22 ◽  
Author(s):  
Nkejane Fallo ◽  
Raseelo Joel Moitsheki ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Techniques ◽  
Temperature Dependent ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
The Heat Transfer Coefficient

In this paper we analyse the heat transfer in a cylindrical spine fin. Here, both the heat transfer coefficient and thermal conductivity are temperature dependent. The resulting 2+1 dimension partial differential equation (PDE) is rendered nonlinear and difficult to solve exactly, particularly with prescribed initial and boundary conditions. We employ the three dimensional differential transform methods (3D DTM) to contract the approximate analytical solutions. Furthermore we utilize numerical techniques to determine approximate numerical solutions. The effects of parameters, appearing in the boundary value problem (BVP), on temperature profile of the fin are studied.

Analysis of Nonlinear Heat Transfer in Solids of Various Geometries with Variable Thermal Conductivity and Heat Source

2017 ◽  
Vol 377 ◽  
pp. 1-16
Author(s):  
Raseelo Joel Moitsheki ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Exact Solutions ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Power Law Function

In this paper we consider heat transfer in a hot body with different geometries. Here, the thermal conductivity and internal heat generation are both temperature-dependent. This assumption rendered the model considered to be nonlinear. We assume that thermal conductivity is given by a power law function. We employ the preliminary group classification to determine the cases of internal heat generation for which the principal Lie algebra extends by one. Exact solutions are constructed for the case when thermal conductivity is a differential consequence of internal heat generation term. We derive the approximate numerical solutions for the cases where exact solutions are difficult to construct or are nonexistent. The effects of parameters appearing in the model on temperature profile are studied.

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.

A Study of Transient Heat Transfer through a Moving Fin with Temperature Dependent Thermal Properties

2020 ◽  
Vol 401 ◽  
pp. 1-13
Author(s):  
Luyanda Partner Ndlovu ◽  
Raseelo Joel Moitsheki
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Heat Dissipation ◽  
Numerical Solutions ◽  
Solution Technique ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Transform Method ◽  
Differential Transform ◽  
Numerical Solver

In this article, heat transfer through a moving fin with convective and radiative heat dissipation is studied. The analytical solutions are generated using the two-dimensional Differential Transform Method (2D DTM) which is an analytical solution technique that can be applied to various types of differential equations. The accuracy of the analytical solution is validated by benchmarking it against the numerical solution obtained by applying the inbuilt numerical solver in MATLAB ($pdepe$). A good agreement is observed between the analytical and numerical solutions. The effects of thermo-physical parameters, such as the Peclet number, surface emissivity coefficient, power index of heat transfer coefficient, convective-conductive parameter, radiative-conductive parameter and non-dimensional ambient temperature on non-dimensional temperature is studied and explained. Since numerous parameters are studied, the results could be useful in industrial and engineering applications.

scholarly journals Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces

2021 ◽  
Author(s):  
Raseelo Joel Moitsheki ◽  
Partner Luyanda Ndlovu ◽  
Basetsana Pauline Ntsime
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Properties ◽  
Analytical Solutions ◽  
Nonlinear Problems ◽  
Transient Heat Transfer ◽  
Temperature Dependent ◽  
Approximate Analytical Solutions ◽  
Extended Surfaces ◽  
Insight Into

In this chapter we provide the review and a narrative of some obtained results for steady and transient heat transfer though extended surfaces (fins). A particular attention is given to exact and approximate analytical solutions of models describing heat transfer under various conditions, for example, when thermal conductivity and heat transfer are temperature dependent. We also consider fins of different profiles and shapes. The dependence of thermal properties render the considered models nonlinear, and this adds a complication and difficulty to solve these model exactly. However, the nonlinear problems are more realistic and physically sound. The approximate analytical solutions give insight into heat transfer in fins and as such assist in the designs for better efficiencies and effectiveness.

Analysis of a Nonlinear Model of Heat Transfer Through a Rectangular Fin: Exact Solutions and Their Multiplicity

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Mohammad Danish ◽  
Shashi Kumar ◽  
Surendra Kumar
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Substitution Method ◽  
Porous Catalyst ◽  
Exact Analytical Solutions ◽  
The Heat Transfer Coefficient

Abstract Exact analytical solutions for the temperature profile and the efficiency of a nonlinear rectangular fin model have been obtained in the forms of well-known algebraic/non-algebraic functions. In the considered nonlinear fin model, the thermal conductivity and the heat transfer coefficient have been assumed to vary as distinct power-law functions of temperature thereby yielding a nonlinear BVP in a 2nd order ODE (ordinary differential equation). These exact solutions have been obtained by employing the derivative substitution method which not only include the solutions of previously studied simplified cases of the same problem but also the solutions of a similar problem of reaction-diffusion process occurring in a porous catalyst slab. These exact solutions have been successfully validated against their numerical counterparts. Besides, effects of various parameters on the obtained solutions have been studied, and the conditions for their existence, uniqueness/multiplicity and stability/instability are analyzed and discussed in detail.

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.

A Method for the Evaluation of Heat Transfer Coefficient by Optimization Algorithm

2007 ◽  
Vol 124-126 ◽  
pp. 1637-1640 ◽  
Author(s):  
Jeong Tae Kim ◽  
Chae Ho Lim ◽  
Jeong Kil Choi ◽  
Young Kook Lee
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Optimization Algorithm ◽  
Heat Conduction Problem ◽  
Three Dimensional ◽  
Temperature History ◽  
Temperature Dependent ◽  
The Heat Transfer Coefficient

New method for evaluation of heat transfer coefficient is proposed. In general, many researchers have been studied about inverse problem in order to calculate the heat transfer coefficient on three-dimensional heat conduction problem. But they can get the time-dependent heat transfer coefficient only through inverse problem. In order to acquire temperature-dependent heat transfer coefficient, it requires much time for numerous repetitive calculation and inconvenient manual modification. In order to solve these problems, we are using the SQP(Sequential Quadratic Programming) as an optimization algorithm. When the temperature history is given by experiment, the optimization algorithm can evaluate the temperature-dependent heat transfer coefficient with automatic repetitive calculation until difference between calculated temperature history and experimental ones is minimized. Finally, temperature-dependent heat transfer coefficient evaluated by developed program can used on the real heat treatment process of casting product.

scholarly journals Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet

2020 ◽  
Vol 9 (1) ◽  
pp. 233-243 ◽  
Author(s):  
Nainaru Tarakaramu ◽  
P.V. Satya Narayana ◽  
Bhumarapu Venkateswarlu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Variable Thermal Conductivity ◽  
Normal Velocity ◽  
Transfer Coefficients ◽  
Similarity Transformations ◽  
Frictional Coefficients ◽  
The Impact

AbstractThe present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu-water nanoparticles is more than that of Al2O3- water nanofluid. On the other hand, the axial velocity of the fluid in case of Al2O3- water nanofluid is more than that of TiO2nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.

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