scholarly journals Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

2016 ◽  
Vol 63 (1) ◽  
pp. 129-144
Author(s):  
Mohammad Javad Noroozi ◽  
Seyfolah Saedodin ◽  
Davood Domiri Ganji
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Adomian Decomposition Method ◽  
Laser Source ◽  
Temperature Dependent ◽  
Conduction Model ◽  
Non Linear Equation ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Fourier Heat Conduction

Abstract The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

Nonlinear analysis of a non-Fourier heat conduction problem in a living tissue heated by laser source

2017 ◽  
Vol 10 (08) ◽  
pp. 1750107 ◽  
Author(s):  
Mohammad Javad Noroozi ◽  
Majid Goodarzi
Keyword(s):  
Heat Conduction ◽  
Nonlinear Analysis ◽  
Heat Conduction Problem ◽  
Adomian Decomposition Method ◽  
Experimental Result ◽  
Laser Source ◽  
Living Tissue ◽  
Conduction Model ◽  
Adomian Decomposition ◽  
Fourier Heat Conduction

The effect of laser, as a heat source, on a one-dimensional finite living tissue was studied in this paper. The dual phase lagging (DPL) non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method (ADM). It was concluded that the nonlinear analysis was important in non-Fourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.

scholarly journals A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 876 ◽  
Author(s):  
Stanisław Kukla ◽  
Urszula Siedlecka
Keyword(s):  
Heat Conduction ◽  
Hollow Cylinder ◽  
Single Phase ◽  
Heat Conduction Problem ◽  
Expansion Method ◽  
Maximum Temperature ◽  
Phase Lag ◽  
Conduction Model ◽  
Laplace Transform Technique ◽  
Finite Medium

In this paper, an investigation of the maximum temperature propagation in a finite medium is presented. The heat conduction in the medium was modelled by using a single-phase-lag equation with fractional Caputo derivatives. The formulation and solution of the problem concern the heat conduction in a slab, a hollow cylinder, and a hollow sphere, which are subjected to a heat source represented by the Robotnov function and a harmonically varying ambient temperature. The problem with time-dependent Robin and homogenous Neumann boundary conditions has been solved by using an eigenfunction expansion method and the Laplace transform technique. The solution of the heat conduction problem was used for determination of the maximum temperature trajectories. The trajectories and propagation speeds of the temperature maxima in the medium depend on the order of fractional derivatives occurring in the heat conduction model. These dependencies for the heat conduction in the hollow cylinder have been numerically investigated.

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