Exact and approximate solutions for two-dimensional temperature distribution induced by a moving Gaussian heat source

1998 ◽  
Author(s):  
J. Xie ◽  
A. Kar
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Approximate Solutions ◽  
Two Dimensional

Study on the Pendulum Characteristic of Nature Convection in Dimensional Enclosure

2012 ◽  
Vol 542-543 ◽  
pp. 1120-1123
Author(s):  
Chuan Zhi Mei ◽  
Lin Hua Piao ◽  
Quan Gang Yu ◽  
Bao Li Zhang ◽  
Xia Ding ◽  
...  
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Heat Source ◽  
Tilt Angle ◽  
Model Building ◽  
Two Dimensional ◽  
Point Heat Source ◽  
Equation Solving ◽  
Tilt Sensor ◽  
Characteristic 2

In this paper, the pendulum characteristic of nature convection gas in dimensional enclosure is analyzed by FEM. Using ANSYS-FLOTRAN CFD program, the stream field and the temperature field caused by the point heat source, when the two-dimensional enclosure is inclined, has been obtained by a series of procedure, such as model building, meshing, loads applying and equation solving. The results are as follow: (1)Under the buoyancy lift affecting, the direction of nature convection gas always keeps the vertical upward in two-dimensional enclosure, nature convection gas has the pendulum characteristic. (2)When the dimensional enclosure is inclined, temperature distribution at the several points in dimensional enclosure will change with the tilt angle. The pendulum characteristic can be utilized to measure the tilt angle by the gas pendulum tilt sensor.

Approximate solutions of nonlinear two‐dimensional Volterra integral equations

2021 ◽  
Author(s):  
Sumbal Ahsan ◽  
Rashid Nawaz ◽  
Muhammad Akbar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equations ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Two Dimensional

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

scholarly journals Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Jianhui Tian ◽  
Guoquan Jing ◽  
Xingben Han ◽  
Guangchu Hu ◽  
Shilin Huo
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Numerical Method ◽  
Functionally Graded ◽  
Thermal Problem ◽  
Linear Heat ◽  
Hybrid Numerical Method ◽  
Linear Heat Source ◽  
Gradient Parameter

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

A Simplified Numerical Approach for Finding the Temperature Distribution in Submerged arc Welding Process

2012 ◽  
Vol 622-623 ◽  
pp. 315-318
Author(s):  
Aparesh Datta ◽  
Subodh Debbarma ◽  
Subhash Chandra Saha
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Arc Welding ◽  
Welding Process ◽  
Numerical Approach ◽  
High Heat ◽  
Submerged Arc Welding ◽  
Fusion Welding ◽  
Arc Welding Process ◽  
Submerged Arc

The quality of joining has assumed a greater role in fabrication of metal in recent years, because of the development of new alloys with tremendously increased strength and toughness. Submerged arc welding is a high heat input fusion welding process in which weld is produced by moving localized heat source along the joint. The weld quality in turn affected by thermal cycle that the weldment experiences during the welding. In the present study a simple comprehensive mathematical model has been developed using a moving heat source and analyzing the temperature on one section and then the temperature distribution of other section are correlated with time delay with reference analyzed section.

scholarly journals A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

Temperature Distribution in Two-Dimensional Electron Gases under a Strong Magnetic Field

2010 ◽  
Vol 40 (5) ◽  
pp. 529-532 ◽  
Author(s):  
Naomi Hirayama ◽  
Akira Endo ◽  
Kazuhiro Fujita ◽  
Yasuhiro Hasegawa ◽  
Naomichi Hatano ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Temperature Distribution ◽  
Strong Magnetic Field ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Electron Gases

scholarly journals Numerical modeling of microwave heating

2010 ◽  
Vol 42 (1) ◽  
pp. 99-124 ◽  
Author(s):  
A.K. Shukla ◽  
A. Mondal ◽  
A. Upadhyaya
Keyword(s):  
Thermal Conductivity ◽  
Numerical Modeling ◽  
Temperature Distribution ◽  
Microwave Heating ◽  
Two Dimensional ◽  
Conventional Furnace ◽  
Microwave Furnace ◽  
Simulation Results ◽  
Heating Behavior ◽  
Cylindrical Samples

The present study compares the temperature distribution within cylindrical samples heated in microwave furnace with those achieved in radiatively-heated (conventional) furnace. Using a two-dimensional finite difference approach the thermal profiles were simulated for cylinders of varying radii (0.65, 6.5, and 65 cm) and physical properties. The influence of susceptor-assisted microwave heating was also modeled for the same. The simulation results reveal differences in the heating behavior of samples in microwaves. The efficacy of microwave heating depends on the sample size and its thermal conductivity.

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