Analytical Solution and Numerical Simulation for One-Dimensional Steady Nonlinear Heat Conduction in a Longitudinal Radial Fin with Various Profiles

2013 ◽  
Vol 44 (1) ◽  
pp. 20-38 ◽  
Author(s):  
R.J. Moitsheki ◽  
M.M. Rashidi ◽  
A. Basiriparsa ◽  
A. Mortezaei
Keyword(s):  
Numerical Simulation ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Nonlinear Heat Conduction ◽  
One Dimensional

Anharmonicity Dependent Heat Conduction in One-Dimensional Lattices

2013 ◽  
Vol 209 ◽  
pp. 129-132 ◽  
Author(s):  
Shreya Shah ◽  
Tejal N. Shah ◽  
P.N. Gajjar
Keyword(s):  
Thermal Conductivity ◽  
Numerical Simulation ◽  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Temperature Profile ◽  
Chain Length ◽  
Interparticle Interactions ◽  
One Dimensional ◽  
Harmonic Chain

The temperature profile, heat flux and thermal conductivity are investigated for the chain length of 67 one-dimensional (1-D) oscillators. FPU-β and FK models are used for interparticle interactions and substrate interactions, respectively. As harmonic chain does not produce temperature gradient along the chain, it is required to introduce anharmonicity in the numerical simulation. The anharmonicity dependent temperature profile, thermal conductivity and heat flux are simulated for different strength of anharmonicity β = 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1. It is concluded that heat flux obeys J = 0.3947 e0.553β with R2 = 0.9319 and thermal conductivity obeys κ = 0.0276 e0.5559β with R2 = 0.9319.

Simulation of Nonlinear Heat Conduction in Perforated Material by Improved Moving Particle Semi-Implicit Method

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Jianqiang Wang ◽  
Xiaobing Zhang
Keyword(s):  
Heat Conduction ◽  
Laplacian Operator ◽  
Nonlinear Heat Conduction ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Particle Distributions ◽  
Temperature Dependent Conductivity ◽  
Irregular Particle ◽  
Moving Particle ◽  
Temperature Dependent Thermal Conductivity

Abstract An improved moving particle semi-implicit (MPS) method is presented to simulate heat conduction with temperature-dependent thermal conductivity. Based on Taylor expansion, a modified Laplacian operator is proposed, and its accuracy in irregular particle distributions is verified. Two problems are considered: (1) heat conduction in a one-dimensional (1D) slab and (2) heat conduction in a perforated sector with different boundary conditions. Consistent results with a mesh-based method are obtained, and the feasibility of the proposed method for heat conduction simulation with temperature-dependent conductivity is demonstrated.

scholarly journals An Analytical Solution to the One-Dimensional Heat Conduction-Convection Equation in Soil

2012 ◽  
Vol 76 (6) ◽  
pp. 1978-1986 ◽  
Author(s):  
Linlin Wang ◽  
Zhiqiu Gao ◽  
Robert Horton ◽  
Donald H. Lenschow ◽  
Kai Meng ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
One Dimensional ◽  
Convection Equation ◽  
The One

scholarly journals ANALYTICAL SOLUTION OF A 2D TRANSIENT HEAT CONDUCTION PROBLEM USING GREEN´S FUNCTIONS

2020 ◽  
Vol 19 (1) ◽  
pp. 66
Author(s):  
J. R. F. Oliveira ◽  
J. A. dos Santos Jr. ◽  
J. G. do Nascimento ◽  
S. S. Ribeiro ◽  
G. C. Oliveira ◽  
...  
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
One Dimensional ◽  
Transient Heat Conduction Problem

Through the present work the authors determined the analytical solution of a transient two-dimensional heat conduction problem using Green’s Functions (GF). This method is very useful for solving cases where heat conduction is transient and whose boundary conditions vary with time. Boundary conditions of the problem in question, with rectangular geometry, are of the prescribed temperature type - prescribed flow in the direction x and prescribed flow - prescribed flow in the direction y, implying in the corresponding GF given by GX21Y22. The initial temperature of the space domain is assumed to be different from the prescribed temperature occurring at one of the boundaries along x. The temperature field solution of the two-dimensional problem was determined. The intrinsic verification of this solution was made by comparing the solution of a 1D problem. This was to consider the incident heat fluxes at y = 0 and y = 2b tending to zero, thus making the problem one-dimensional, with corresponding GF given by GX21. When comparing the results obtained in both cases, for a time of t = 1 s, it was seen that the temperature field of both was very similar, which validates the solution obtained for the 2D problem.

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