scholarly journals Analytical solution to convection-radiation of a continuously moving fin with temperature-dependent thermal conductivity

2013 ◽  
Vol 17 (4) ◽  
pp. 1049-1060 ◽  
Author(s):  
Amir Moradi ◽  
Reza Rafiee
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Analytic Solution ◽  
Radiation Heat Transfer ◽  
Numerical Data ◽  
Transformation Method ◽  
Variable Thermal Conductivity ◽  
Temperature Dependent ◽  
Runge Kutta Method ◽  
Good Agreement

In this article, the simultaneous convection-radiation heat transfer of a moving fin of variable thermal conductivity is studied. The differential transformation method (DTM) is applied for an analytic solution for heat transfer in fin with two different profiles. Fin profiles are rectangular and exponential. The accuracy of analytic solution is validated by comparing it with the numerical solution that is obtained by fourth-order Runge-Kutta method. The analytical and numerical results are shown for different values of the embedding parameters. DTM results show that series converge rapidly with high accuracy. The results indicate that the fin tip temperature increases when ambient temperature increases. Conversely, the fin tip temperature decreases with an increase in the Peclet number, convection-conduction and radiation-conduction parameters. It is shown that the fin tip temperature of the exponential profile is higher than the rectangular one. The results indicate that the numerical data and analytical method are in a good agreement with each other.

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 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

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.

scholarly journals A numerical analysis of a convective straight fin with temperature-dependent thermal conductivity

2017 ◽  
Vol 21 (2) ◽  
pp. 939-952 ◽  
Author(s):  
Gokhan Sevilgen
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Cfd Analysis ◽  
Flow Conditions ◽  
Heat Transfer Characteristics ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Conductivity Property ◽  
Temperature Dependent Thermal Conductivity ◽  
Good Agreement

In this paper, heat transfer characteristics of a straight fin having temperature-dependent thermal conductivity were computed by using 3-D CFD analysis and MATLAB differential equation solver. The computations were performed with two different cases having both constant and linear function for thermal conductivity property. The CFD and MATLAB results were in good agreement with the data available in the literature. With the help of using these numerical techniques, fin efficiency can be improved and heat transfer rate of fins can be augmented by changing fin materials with variable thermal properties and air-flow conditions. Application of the proposed method can be effectively extended to solve the class of similar non-linear fin problems in engineering and sciences.

scholarly journals Effect of variable thermal conductivity on the mhd boundary layer of casson-nanofluid over a moving plate with variable thickness

2019 ◽  
pp. 293-293
Author(s):  
Hassan Ismail ◽  
M. Abdel-Wahed ◽  
M. Omama
Keyword(s):  
Mechanical Properties ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Transformation Method ◽  
Variable Thermal Conductivity ◽  
Moving Plate ◽  
Casson Nanofluid ◽  
Runge Kutta Method ◽  
Mhd Boundary Layer ◽  
Physical Quantities

The effect of variable thermal conductivity on the characteristics of heat transfer and mechanical properties of a moving surface on a casson-nanofluid flow as a coolant has been studied in this paper. We used similarity transformation method to transform the equations of the governing boundary layer into ordinary differential equations which are solved numerically using a mix of fourth order Runge Kutta method and find root technique. Different values relevant parameters have been studied on the features of velocity, temperature and the profiles of concentration and discussed in details for different values of various parameter as shape parameter, heat source parameter, radiation parameter and magnetic parameter. The results were compared with previous published researches and obtained it in a good agreement and the results were tabulated. Furthermore, Nusselt number, Sherwood number and the Skin friction values with different parameters were calculated and the influence of theses physical quantities on the mechanical properties on the surface are analyzed and discussed in details.

Collocation Spectral Method for the Transient Conduction–Radiation Heat Transfer With Variable Thermal Conductivity in Two-Dimensional Rectangular Enclosure

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Guo-Jun Li ◽  
Jian Ma ◽  
Ben-Wen Li
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Spectral Method ◽  
Radiation Heat Transfer ◽  
Variable Thermal Conductivity ◽  
Two Dimensional ◽  
Radiation Heat ◽  
Rectangular Enclosure ◽  
Collocation Spectral Method ◽  
Transient Conduction

The collocation spectral method (CSM) is further developed to solve the transient conduction–radiation heat transfer in a two-dimensional (2D) rectangular enclosure with variable thermal conductivity. The energy equation and the radiative transfer equation (RTE) are all discretized by Chebyshev–Gauss–Lobatto collocation points in space after the discrete ordinates method (DOM) discretization of RTE in angular domain. The treatment of variable thermal conductivity is executed using the array multiplication. The present method can deal with different boundary conditions with high accuracy, the Dirichlet one and mixed one, for example. Based on our new method, the effects of several parameters on heat transfer processes are analyzed.

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