scholarly journals FREEZING OF BIOLOGICAL TISSUES DURING CRYOSURGERY USING HYPERBOLIC HEAT CONDUCTION MODEL

2015 ◽  
Vol 20 (4) ◽  
pp. 443-456 ◽  
Author(s):  
Sonalika Singh ◽  
Sushil Kumar
Keyword(s):  
Mathematical Model ◽  
Heat Conduction ◽  
Blood Perfusion ◽  
Biological Tissues ◽  
Freezing Process ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Ideal Property

This paper considers hyperbolic heat conduction model for biological tissue freezing during cryosurgery with non ideal property of tissue, metabolism and blood perfusion. Mathematical model is solved numerically using finite difference method to obtain temperature distribution and phase change interfaces in tissue during freezing. The effects of phase lag of heat flux in hyperbolic bio-heat model on freezing process are studied. Comparative study of parabolic and hyperbolic bio-heat models is also made here.

Overshooting Phenomenon in the Hyperbolic Heat Conduction Model

2003 ◽  
Vol 42 (Part 1, No. 8) ◽  
pp. 5383-5386 ◽  
Author(s):  
Mohammad Al-Nimr ◽  
Malak Naji ◽  
Salem Al-Wardat
Keyword(s):  
Heat Conduction ◽  
Hyperbolic Heat Conduction ◽  
Conduction Model ◽  
Heat Conduction Model

A smoothing spline-based regularization of the initial inverse problem in a two-dimensional heat equation

2008 ◽  
Vol 223 (2) ◽  
pp. 439-449 ◽  
Author(s):  
K Masood ◽  
M T Mustafa
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Smoothing Splines ◽  
Smoothing Spline ◽  
Hyperbolic Heat Conduction ◽  
Parabolic Model ◽  
Initial Profile ◽  
Conduction Model ◽  
Heat Conduction Model

A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.

Some theorems on linear theory of thermoelasticity for an anisotropic medium under an exact heat conduction model with a delay

2016 ◽  
Vol 22 (5) ◽  
pp. 1177-1189 ◽  
Author(s):  
Bharti Kumari ◽  
Santwana Mukhopadhyay
Keyword(s):  
Heat Conduction ◽  
Anisotropic Body ◽  
Spatial Behavior ◽  
Inhomogeneous Material ◽  
Phase Lag ◽  
Conduction Model ◽  
Delay Term ◽  
Heat Conduction Model ◽  
Thermoelasticity Theory ◽  
Equation Of Heat Conduction

The present work is concerned with a very recently proposed heat conduction model—an exact heat conduction model with a delay term for an anisotropic and inhomogeneous material—and some important theorems within this theory. A generalized thermoelasticity theory was proposed based on the heat conduction law with three phase-lag effects for the purpose of considering the delayed responses in time due to the micro-structural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in the Hadamard sense. Subsequently, a proposal was made to reformulate this constitutive equation of heat conduction theory with a single delay term and the spatial behavior of the solutions for this theory have been investigated. A Phragmen–Lindelof type alternative was obtained and it has been shown that the solutions either decay in an exponential way or blow-up at infinity in an exponential way. The obtained results are extended to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction to the delay term and a Phragmen–Lindelof type alternative was obtained for the forward and backward in time equations. In the present work, we consider the basic equations concerning this new theory of thermoelasticity for an anisotropic and inhomogeneous material and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for an anisotropic body. An alternative characterization of the mixed initial-boundary value problem is formulated and a variational principle as well as a reciprocity principle is established.

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