Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Sinan Deniz
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Optimal Perturbation ◽  
Transfer Equations ◽  
Better Than ◽  
Good Agreement ◽  
Distribution Equation

In this paper, the new optimal perturbation iteration method (OPIM) is introduced and applied for solving nonlinear differential equations arising in heat transfer. The effectiveness of the proposed method will be tested by considering two specific applications: the temperature distribution equation in a thick rectangular fin radiation to free space and cooling of a lumped system with variable specific heat. Comparing different methods shows that the results obtained by optimal perturbation iteration method are very good agreement with the numerical solutions and perform better than the most existing analytic methods.

Analysis of Heat Transfer by Natural Convection Across Vertical Fluid Layers

1977 ◽  
Vol 99 (2) ◽  
pp. 287-293 ◽  
Author(s):  
G. D. Raithby ◽  
K. G. T. Hollands ◽  
T. E. Unny
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Average Nusselt Number ◽  
Vertical Temperature ◽  
The Core ◽  
Aspect Ratios ◽  
Fluid Layers ◽  
Transfer Equations ◽  
Vertical Temperature Distribution ◽  
Good Agreement

An analysis is presented which predicts the heat transfer across fluid layers bounded laterally by vertical isothermal surface and adiabatic surfaces on the top and bottom. The vertical temperature distribution in the core of the cavity is also predicted. Extensive comparisons of average Nusselt number and temperature distribution are made with experimental data for aspect ratios greater than 5. Good agreement between analysis and experiment is found. The heat-transfer equations for vertical layers are generalized to include layers which are tilted up to 20° from the vertical, making the results useful for the design of solar collectors.

scholarly journals Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Heat Transfer ◽  
Haar Wavelet ◽  
Variable Thermal Conductivity ◽  
The Other ◽  
Wavelet Method ◽  
Combined Convection ◽  
Transfer Equations ◽  
Quasilinearization Technique ◽  
Good Agreement ◽  
Distribution Equation

We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i) temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii) cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

scholarly journals TWO APPROACHES TO THE COMPUTATION OF ELECTROTHERMAL PROCESSES AT INDUCTION HEATING OF MOVING INGOTS – BY FIELD THEORY AND THERMAL CIRCUIT THEORY

2021 ◽  
Vol 2021 (59) ◽  
pp. 5-10
Author(s):  
A.A. Shcherba ◽  
◽  
A.D. Podoltsev ◽  
I.M. Kucheriava ◽  
V.M. Zolotarev ◽  
...  
Keyword(s):  
Field Theory ◽  
Heat Transfer ◽  
Temperature Distribution ◽  
Induction Heating ◽  
Thermal Field ◽  
Circuit Theory ◽  
Thermal Processes ◽  
Computational Results ◽  
Thermal Circuit ◽  
Good Agreement

The model for the computation of thermal processes in induction heating installations with moving ingots is developed using equivalent thermal circuits. The controlled current sources as additional elements in the model are used to take into account the convective heat transfer along the moving ingot. The model is implemented in the program Matlab/Simulink and makes it possible to determine the temperature distribution along the ingot under steady-state heating conditions. The results are compared with data obtained by the alternative method which is based on the electromagnetic and thermal field theory and realized in the Comsol program. As shown the computational results by two methods concerning the temperature distribution along the ingot are in good agreement. The existing advantages and shortcomings of the used approaches are discussed. Ref. 8, fig. 3, table.

An implicit differential equation governing lumped capacitance, radiation dominated, unsteady, heat transfer

2012 ◽  
Vol 22 (7) ◽  
pp. 896-906
Author(s):  
Lawrence J. De Chant
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Simple Model ◽  
Differential Equations ◽  
Large Scale ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Implicit Differential Equation ◽  
Content Type ◽  
Integration Schemes

PurposeAlthough most physical problems in fluid mechanics and heat transfer are governed by nonlinear differential equations, it is less common to be confronted with a “so – called” implicit differential equation, i.e. a differential equation where the highest order derivative cannot be isolated. The purpose of this paper is to derive and analyze an implicit differential equation that arises from a simple model for radiation dominated heat transfer based upon an unsteady lumped capacitance approach.Design/methodology/approachHere we discuss an implicit differential equation that arises from a simple model for radiation dominated heat transfer based upon an unsteady lumped capacitance approach. Due to the implicit nature of this problem, standard integration schemes, e.g. Runge‐Kutta, are not conveniently applied to this problem. Moreover, numerical solutions do not provide the insight afforded by an analytical solution.FindingsA predictor predictor‐corrector scheme with secant iteration is presented which readily integrates differential equations where the derivative cannot be explicitly obtained. These solutions are compared to numerical integration of the equations and show good agreement.Originality/valueThe paper emphasizes that although large‐scale, multi‐dimensional time‐dependent heat transfer simulation tools are routinely available, there are instances where unsteady, engineering models such as the one discussed here are both adequate and appropriate.

scholarly journals A variational iteration method integral transform technique for handling heat transfer problems

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 55-61 ◽  
Author(s):  
Yuejin Zhou ◽  
Shun Pang ◽  
Guo Chong ◽  
Xiaojun Yang ◽  
Xiaoding Xu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Iteration Method ◽  
Integral Transform ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Excess Temperature ◽  
Variational Iteration ◽  
Transfer Equations ◽  
Transfer Problems ◽  
Integral Transform Technique

In this paper, we consider the heat transfer equations at the low excess temperature. The variational iteration method integral transform technique is used to find the approximate solutions for the problems. The used method is accurate and efficient.

scholarly journals Effect of temperature-dependency of surface emissivity on heat transfer using the parameterized perturbation method

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 123-125 ◽  
Author(s):  
Maziar Jalaal ◽  
Esmaiil Ghasemi ◽  
Domiri Ganji ◽  
Hasan Bararnia ◽  
Soheil Soleimani ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Perturbation Method ◽  
Industrial Processes ◽  
Effect Of Temperature ◽  
Temperature Dependency ◽  
Surface Emissivity ◽  
Runge Kutta Method ◽  
Transfer Equations ◽  
Parameterized Perturbation Method ◽  
Good Agreement

Knowledge of the temperature dependence of the physical properties such surface emissivity, which controls the radiative problem, is fundamental for determining the thermal balance of many scientific and industrial processes. The current work studies the ability of a strong analytical method called parameterized perturbation method (PPM), which unlike classic perturbation method do not need small parameter, for nonlinear heat transfer equations. The results are compared with the numerical Runge-Kutta method showed good Agreement.

Numerical Simulation of Hot Rolled Coil Temperature Field in Hot Coil Box

2011 ◽  
Vol 338 ◽  
pp. 572-575
Author(s):  
Gui Jie Zhang ◽  
Kang Li ◽  
Ying Zi Wang
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Coil Temperature ◽  
Hot Rolled ◽  
Strip Coil ◽  
Good Agreement

The heat transfer model was developed and the heat transfer of the strip coil stay in the hot coil box was analyzed. The temperature distribution of the strip coil was investigated use the model. The measured results are in good agreement with the calculated ones, has a guiding significance to further improve the technology.

scholarly journals A Generalized Analytical Model for Joule Heating of Segmented Wires

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Vivekananthan Balakrishnan ◽  
Toan Dinh ◽  
Hoang-Phuong Phan ◽  
Dzung Viet Dao ◽  
Nam-Trung Nguyen
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Experimental Studies ◽  
Governing Equations ◽  
Steady State Temperature ◽  
The One ◽  
Good Agreement

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

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