Boubaker Polynomials Expansion Scheme Solution to the Heat Transfer Equation Inside Laser Heated Biological Tissues

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. A. Aweda ◽  
M. Agida ◽  
M. Dada ◽  
O. B. Awojoyogbe ◽  
K. Isah ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Numerical Simulations ◽  
Laser Heating ◽  
Transfer Equation ◽  
Biological Tissues ◽  
Heat Transfer Equation ◽  
Boubaker Polynomials ◽  
Laser Heated ◽  
Expansion Scheme

In this study, an analytical solution to the heat transfer equation in biological tissues during laser heating is presented. The results were compared to recently published numerical simulations.

Systems Actuated by Shape Memory Alloys: Identification and Modeling

2021 ◽  
Vol 1 (2) ◽  
pp. 12-20
Author(s):  
Najmeh Keshtkar ◽  
Johannes Mersch ◽  
Konrad Katzer ◽  
Felix Lohse ◽  
Lars Natkowski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Transfer Equation ◽  
Mechanical Parameters ◽  
Heat Transfer Equation ◽  
The Mathematical Model

This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.

scholarly journals Assessment of Hyperbolic Heat Transfer Equation in Theoretical Modeling for Radiofrequency Heating Techniques

2008 ◽  
Vol 2 (1) ◽  
pp. 22-27 ◽  
Author(s):  
Juan A López-Molina ◽  
Maria J Rivera ◽  
Macarena Trujillo ◽  
Fernando Burdío ◽  
Juan L Lequerica ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Transfer Equation ◽  
Cardiac Tissue ◽  
Thermal Relaxation ◽  
Propagation Speed ◽  
Biological Tissues ◽  
Heating Time ◽  
Theoretical Modeling ◽  
Rf Heating ◽  
Heat Transfer Equation

Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier’s theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode surface. Our results therefore suggest that HHTE should be considered for RF heating of the cornea (which requires very small electrodes and a heating time of 0.6 s), and for rapid ablations in cardiac tissue (less than 30 s).

scholarly journals Analytical solution for the 1-D heat transfer equations with radiative loss

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 47-53
Author(s):  
You-Chang Lv ◽  
Man Wang ◽  
Ying-Wei Wang
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Transfer Equation ◽  
Integral Transform ◽  
Radiative Loss ◽  
Heat Transfer Equation ◽  
Transfer Equations ◽  
Type Integral ◽  
Transfer Problems

In this paper, we consider the 1-D heat transfer equation with radiative loss. The variational iterative Sumudu type integral transform is used to obtain the analytical solution for the heat transfer problems. The presented method is efficient and accurate.

Boubaker Polynomials Weak Solutions to a Robin Boundary Conditioned Dynamic-State Heat Transfer Problem

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
K. ben Mahmoud Boubaker
Keyword(s):  
Heat Transfer ◽  
Weak Solutions ◽  
Transfer Equation ◽  
Transfer Problem ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Dynamic State ◽  
Heat Transfer Equation ◽  
Boubaker Polynomials ◽  
Robin Boundary

In this paper we are concerned with the solution of a Robin boundary conditioned problem associated with the local heat transfer equation. The results are obtained using both symmetrical system features and expansions of a Boubaker polynomial subsequence. The yielded profile is compared with some recently proposed models.

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