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 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.

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.

scholarly journals Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Jiawei Fu ◽  
Keqiang Hu ◽  
Linfang Qian ◽  
Zengtao Chen
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Intensity Factor ◽  
Functionally Graded ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Flux Intensity ◽  
Cylindrical Crack ◽  
Heat Flux Intensity ◽  
Fourier Heat Conduction

The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack.

Stoneley Wave Generation in Joined Materials With and Without Thermal Relaxation Due to Thermal Mismatch

2007 ◽  
Vol 74 (5) ◽  
pp. 1019-1025 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Relaxation Time ◽  
Heat Conduction ◽  
Thermal Relaxation ◽  
Interface Temperature ◽  
Stoneley Wave ◽  
Asymptotic Results ◽  
Time Step ◽  
Conduction Model ◽  
Special Cases ◽  
Fourier Heat Conduction

Two perfectly bonded, thermoelastic half-spaces differ only in their thermal parameters. Their governing equations include as special cases the Fourier heat conduction model and models with either one or two thermal relaxation times. An exact solution in transform space for the problem of line loads applied to the interface is obtained. Even though the elastic properties of the half-spaces are identical, a Stoneley function arises, and conditions for the existence of roots are more restrictive than for the isothermal case of two elastically dissimilar half-spaces. Moreover, roots may be either real or imaginary. An exact expression for the time transform of the Stoneley residue contribution to interface temperature change is derived. Asymptotic results for the inverse that, valid for either very short or very long times after load application, is obtained and show that, for long times, residue contributions for all three special cases obey Fourier heat conduction. Short-time results are sensitive to case differences. In particular, a time step load produces a propagating step in temperature for the Fourier and double-relaxation time models, but a propagating impulse for the single-relaxation time model.

Thermoelastic Actuation: Solution for Circular Composite Plates With Application in MEMS

2002 ◽  
Author(s):  
Venkataraman Chandrasekaran ◽  
Mark Sheplak ◽  
Louis N. Cattafesta ◽  
Bhavani V. Sankar
Keyword(s):  
Heat Conduction ◽  
Joule Heating ◽  
Plate Theory ◽  
Composite Plates ◽  
Mechanical Analysis ◽  
Conduction Model ◽  
Time Harmonic ◽  
Out Of Plane ◽  
Fourier Heat Conduction ◽  
Analytical Expressions

This paper presents the dynamic analysis of a thermoelastically actuated circular composite diaphragm, for MEMS applications. The diaphragm is used as an acoustic transmitter, actuated at ultrasonic frequencies via a diffused surface heater at its center. The principle of operation of the thermal actuator is the generation of an oscillating temperature gradient across the diaphragm cross-section due to Joule heating of the diffused heater, creating a thermal moment that results in out-of-plane bending of the diaphragm. The mechanical analysis of the diaphragm, modeled as a composite plate, is based on the classical laminated plate theory. The time harmonic heat conduction resulting from the Joule heating of the diffused surface heater, modeled as a surface heat flux input, is analyzed using the Fourier heat conduction model. Analytical expressions have been obtained for the temperature distribution, and the resulting thermal moment, and plate deflection.

scholarly journals Exact Solution of Space-Time Fractional Partial Differential Equations by Adomian Decomposition Method

2021 ◽  
pp. 75-87
Author(s):  
Vidya N. Bhadgaonkar ◽  
Bhausaheb R. Sontakke
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Adomian Decomposition Method ◽  
Physical Models ◽  
Partial Differential ◽  
Conduction Model ◽  
Adomian Decomposition ◽  
Present Technique

The intention behind this paper is to achieve exact solution of one dimensional nonlinear fractional partial differential equation(NFPDE) by using Adomian decomposition method(ADM) with suitable initial value. These equations arise in gas dynamic model and heat conduction model. The results show that ADM is powerful, straightforward and relevant to solve NFPDE. To represent usefulness of present technique, solutions of some differential equations in physical models and their graphical representation are done by MATLAB software.

Thermal Stress Associated With Non-Fourier Heat Conduction in Femtosecond Laser Heating of Multilayer Metallic Films

2018 ◽  
Author(s):  
Swarup Bag ◽  
M. Ruhul Amin
Keyword(s):  
Thin Film ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Temperature Distribution ◽  
Pulse Laser ◽  
Laser Heating ◽  
Laser Source ◽  
Phase Lag ◽  
Dual Phase ◽  
Fourier Heat Conduction

In the present work, the deformation behavior in metallic film subjected to ultra-short laser heating is investigated. Static thermo-elastic behavior is predicted for 100 nm thin film of either single layer or multiple layers. The temperature distribution is estimated from dual-phase lag non-Fourier heat conduction model. The maximum temperature after single pulse is achieved 730 K. The temperature profile for this pulse laser is used to compute elastic stress and distortion field following the minimization of potential energy of the system. In the present work, the simulation has been proposed by developing 3D finite element based coupled thermo-elastic model using dual phase lag effect. The experimental basis of transient temperature distribution in ultra-short pulse laser is extremely difficult or nearly impossible, the model results have been validated with literature reported thermal results. Since the temperature distribution due to pulse laser source varies with time, the stress analysis is performed in incremental mode. Hence, a sequentially coupled thermo-mechanical model is developed that is synchronized between thermal and mechanical analysis in each time steps of transient problem. The maximum equivalent stress is achieved 0.3 GPa. Numerical results show that the predicted thermal stress may exceeds the tensile strength of the material and may lead to crack or damage the thin film.

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