Q-conditional symmetry of a nonlinear two-dimensional heat-conduction equation

2000 ◽  
Vol 52 (6) ◽  
pp. 969-973
Author(s):  
M. I. Serov ◽  
L. O. Tulupova ◽  
N. V. Andreeva
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Two Dimensional ◽  
Conditional Symmetry

scholarly journals A Revised Tikhonov Regularization Method for a Cauchy Problem of Two-Dimensional Heat Conduction Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Songshu Liu ◽  
Lixin Feng
Keyword(s):  
Cauchy Problem ◽  
Heat Conduction ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Tikhonov Regularization Method ◽  
Two Dimensional ◽  
Convergence Estimate ◽  
Ill Posed

In this paper we investigate a Cauchy problem of two-dimensional (2D) heat conduction equation, which determines the internal surface temperature distribution from measured data at the fixed location. In general, this problem is ill-posed in the sense of Hadamard. We propose a revised Tikhonov regularization method to deal with this ill-posed problem and obtain the convergence estimate between the approximate solution and the exact one by choosing a suitable regularization parameter. A numerical example shows that the proposed method works well.

A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation

2015 ◽  
Vol 7 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Jingjun Zhao ◽  
Songshu Liu ◽  
Tao Liu
Keyword(s):  
Cauchy Problem ◽  
Exact Solution ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Kernel Method ◽  
Conduction Equation ◽  
Two Dimensional ◽  
Ill Posed ◽  
Well Posed ◽  
Regularized Solution

AbstractIn this paper, a Cauchy problem of two-dimensional heat conduction equation is investigated. This is a severely ill-posed problem. Based on the solution of Cauchy problem of two-dimensional heat conduction equation, we propose to solve this problem by modifying the kernel, which generates a well-posed problem. Error estimates between the exact solution and the regularized solution are given. We provide a numerical experiment to illustrate the main results.

Heat Conduction Equation Finite Volume Method to Achieve on MATLAB

2012 ◽  
Vol 195-196 ◽  
pp. 712-717
Author(s):  
Qiong Xue ◽  
Xiao Feng Xiao ◽  
Niang Zhi Fan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Two Dimensional ◽  
Partial Differential ◽  
Volume Method

Diffusion only, two dimensional heat conduction has been described on partial differential equation. Based on Finite Volume Method, Discretized algebraic Equation of partial differential equation have been deduced. different coefficients and source terms have been discussed under different boundary conditions, which include prescribed heat flux, prescribed temperature, convection and insulated. Transient heat conduction analysises of infinite plate with uniform thickness and two dimensional rectangle region have been realized by programming using MATLAB. It is useful to make the heat conduction equation more understandable by its solution with graphical expression, feasibility and stability of numerical method have been demonstrated by running result.

Heat transfer at small Grashof numbers

1957 ◽  
Vol 238 (1214) ◽  
pp. 412-423 ◽  
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Ambient Temperature ◽  
Heat Conduction Equation ◽  
Body Shape ◽  
The Body ◽  
Conduction Equation ◽  
Two Dimensional ◽  
Transfer Rates ◽  
Theory And Experiment

Rough physical arguments suggest that the heat transfer from a body, immersed in a fluid, should be determined by the heat-conduction equation alone whenever the Grashof number, G , associated with the problem is small. However, heat-transfer rates predicted in this fashion are not always in accordance with the experimentally determined values. It is shown that, while convection is negligible in comparison with conduction near the body, it becomes as important at distances from the body of the order ( G ) -n , where n varies between 1/3 and ½ with the body shape. Whenever this distance is large in comparison with all the dimensions of the body the use of the conduction equation yields correct heat-transfer rates. If, however, this distance is small in comparison with the body length, the heat transfer may be calculated from the two-dimensional convection solution. An examination of the solutions in these two extreme cases reveals that the heat loss is the same as that by conduction to a certain surrounding surface maintained at ambient temperature. This interpretation enables certain qualitative deductions to be made for the case when the ratio of the lengths is neither large nor small. The agreement between theory and experiment is satisfactory.

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