The Thermal Behavior Analysis of a Human Eye Subjected to Laser Radiation Under the Non-Fourier Law of Heat Conduction

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Najat A. Alghamdi ◽  
Hamdy M. Youssef
Keyword(s):  
Heat Conduction ◽  
Laser Irradiation ◽  
Power Density ◽  
Evaporation Rate ◽  
Relaxation Times ◽  
Blood Perfusion ◽  
Absolute Temperature ◽  
Ambient Temperatures ◽  
Human Eye ◽  
Fourier Heat Conduction

Abstract Purpose: The physiological conditions and environment have vital roles in the heat transfer in the human tissues, such as the multilayered human-eye. In this paper, a mathematical model of the human eye subjected to an exponential laser beam concerning the change in blood perfusion, porosity, evaporation rate, and ambient temperatures has been constructed based on non-Fourier heat conduction law. Methods: The human eye has been divided into six layers. Appropriate boundary and interface conditions have been considered. A separable function has been assumed, and the twelve equations have been formulated in matrix form. The solutions have been calculated by using maple 17 software. Results: The results have been shown in figures with different cases. The absolute temperature distribution based on various values of the power density of laser irradiation and relaxation times parameters have been discussed first. The effect of the blood perfusion, porosity, evaporation rate, time, and ambient temperatures have also been discussed. Conclusions: The power density of laser irradiation, blood perfusion, porosity, evaporation rate, time, and ambient temperatures significantly affects the value of the temperature passing through the human eye layers.

Analysis of the Thermal Response in Micromachine under the Thermal Shock

2011 ◽  
Vol 464 ◽  
pp. 583-587
Author(s):  
Ying Ze Wang ◽  
Xin Nan Song
Keyword(s):  
Heat Conduction ◽  
Relaxation Times ◽  
Boundary Surface ◽  
Thermal Relaxation ◽  
Thermal Response ◽  
Heat Propagation ◽  
Hyperbolic Heat Conduction ◽  
Thermal Relaxation Times ◽  
Fourier Heat Conduction ◽  
Sudden Temperature Change

The thermal response for given micromachine with the boundary surface exposed to sudden temperature change is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at the outer surface and interior of the micro beam are evaluated for various thermal relaxation times. The behaviors of hyperbolic heat propagation in micro beam are analyzed and possible anomalies are discussed by comparing the thermal behaviors of Fourier heat conduction.

Nonclassical Heat Transfer Models for Laser-Induced Thermal Damage in Biological Tissues

2011 ◽  
Author(s):  
Jianhua Zhou ◽  
J. K. Chen ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Thermal Wave ◽  
Thermal Damage ◽  
Blood Perfusion ◽  
Biological Tissues ◽  
Phase Lag ◽  
Fourier Heat Conduction

To ensure personal safety and improve treatment efficiency in laser medical applications, one of the most important issues is to understand and accurately assess laser-induced thermal damage to biological tissues. Biological tissues generally consist of nonhomogeneous inner structures, in which heat flux equilibrates to the imposed temperature gradient via a thermal relaxation mechanism which cannot be explained by the traditional parabolic heat conduction model based on Fourier’s law. In this article, two non-Fourier heat conduction models, hyperbolic thermal wave model and dual-phase-lag (DPL) model, are formulated to describe the heat transfer in living biological tissues with blood perfusion and metabolic heat generation. It is shown that the non-Fourier bioheat conduction models could predict significantly different temperature and thermal damage in tissues from the traditional parabolic model. It is also found that the DPL bioheat conduction equations can be reduced to the Fourier heat conduction equations only if both phase lag times of the temperature gradient (τT) and the heat flux (τq) are zero. Effects of laser parameters and blood perfusion on the thermal damage simulated in tissues are also studied. The result shows that the overall effects of the blood flow on the thermal response and damage are similar to those of the time delay τT. The two-dimensional numerical results indicate that for a local heating with the heated spot being smaller than the tissue bulk, the variations of the non-uniform distributions of temperature suggest that the multi-dimensional effects of thermal wave and diffusion not be negligible.

The Model of Non-Fourier Heat Conduction in a Kind of Two-Phase Medium With Great Different Heat Conductivity

2008 ◽  
Author(s):  
Wen-Qiang Lu ◽  
Junfeng Lu
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Conduction ◽  
Heat Conductivity ◽  
Rapid Heating ◽  
Relaxation Times ◽  
High Heat Flux ◽  
Phase Lag ◽  
Two Phase ◽  
Fourier Heat Conduction

The model of non-Fourier heat conduction in a kind of two-phase mediums with great different heat conductivity is deduced by the idea and mathematics of dual phase lag. It is pointed out that the relaxation times to establish heat flux and temperature gradient include both kinds in this model: the relaxation time appeared under the conditions of applied high heat flux and rapid heating, the relaxation time introduced by the non-equilibrium heat exchange between the two-phase mediums. It is very important to distinguish the both kinds of relaxation times for analyzing and explaining the experimental phenomena of non-Fourier heat conduction in this kind of two-phase mediums.

Mathematical model of thermal effects of blinking in human eye

2015 ◽  
Vol 09 (01) ◽  
pp. 1650006 ◽  
Author(s):  
D. B. Gurung ◽  
K. C. Gokul ◽  
P. R. Adhikary
Keyword(s):  
Thermal Effects ◽  
Extreme Values ◽  
Choroidal Melanoma ◽  
Transient State ◽  
Blood Perfusion ◽  
Heat Transfer Process ◽  
Eyelid Closure ◽  
Ambient Temperatures ◽  
Human Eye ◽  
Palpebral Conjunctiva

Blinking is regarded as the continuous interrupted eyelid closure or opening and its thermal effect will compromise between these two. During a blink, the heat loss via convection, radiation and tear evaporation from cornea is prevented, warm tear is layered across corneal surface and the vessels of the palpebral conjunctiva provide heat to anterior eye. In most of the thermal models in human eye that are found in literatures, effect of blinking is not included, simulation is carried out only in open eye. Thus, in this paper, thermal effects of blinking are investigated using one-dimensional finite element method in transient state case. The bio-heat transfer process is simulated during different blinking rates, lid closure and opening. The simulation is carried out using normal and extreme values of ambient temperatures, blood temperatures, evaporation rates, blood perfusion rates, and lens thermal conductivities. Blinking is found to increase corneal and lens temperature by 1.29°C and 0.78°C respectively when compared to open eye. The results obtained from this model are useful in predicting temperature distribution in different laser eye surgeries, hyperthermia and cryosurgery treatment of eyelid carcinoma, choroidal melanoma and can be used for diagnosing temperature-related diseases.

Fourier and Non-Fourier Heat Conduction Effects in Biological Tissue under Laser Irradiation

2009 ◽  
Vol 36 (10) ◽  
pp. 2582-2586 ◽  
Author(s):  
杨洪钦 Yang Hongqin ◽  
陈建玲 Chen Jianling ◽  
王瑜华 Wang Yuhua ◽  
谢树森 Xie Shusen ◽  
李晖 Li Hui
Keyword(s):  
Heat Conduction ◽  
Laser Irradiation ◽  
Biological Tissue ◽  
Fourier Heat Conduction

Bio-Heat Transfer Model of Human Eye Subjected to Retinal Laser Irradiation

2010 ◽  
Author(s):  
Arunn Narasimhan ◽  
Kaushal Kumar Jha
Keyword(s):  
Heat Transfer ◽  
Laser Radiation ◽  
Numerical Model ◽  
Laser Irradiation ◽  
Laser Power ◽  
Blood Perfusion ◽  
Transient Temperature ◽  
Transfer Model ◽  
Two Dimensional ◽  
Human Eye

Retinopathy is a surgical process in which maladies of the human eye are treated by laser irradiation. A two-dimensional numerical model of the human eye geometry has been developed to investigate steady and transient thermal effects due to laser radiation. In particular, the influence of choroidal pigmentations and choroidal blood convection — parameterized as a function of choroidal blood perfusion are investigated in detail. The Pennes bio-heat transfer equation is invoked as the governing equation and a finite volume formulation is employed in the numerical method. The numerical model is validated with available experimental and two-dimensional numerical results. For a 500 μm diameter spot size, laser power of 0.2 W, with 100% absorption of laser radiation in the Retinal Pigmented Epithelium (RPE) region, the peak RPE temperature is observed to be 175 °C at steady state, with no blood perfusion in choroid. It reduces to 168.5 °C when the choroidal blood perfusion rate is increased to 23.3 kgm−3s−1. However, under transient simulations, the peak RPE temperature is observed to remain constant at 104 °C after 100 ms of the laser surgery period. A truncated three-dimensional model incorporating multiple laser irradiation spots is also developed to observe the spatial effect of choroidal blood perfusion. For a circular array of seven uniformly distributed spots of identical diameter and laser power of 0.2 W, steady and transient temperature evolution are presented with analysis.

Dynamic Crack Extension Along the Interface of Materials That Differ in Thermal Properties: Convection and Thermal Relaxation

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Crack Extension ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Crack Edge ◽  
Dynamic Crack ◽  
Solution Behavior ◽  
Special Cases ◽  
Fourier Heat Conduction

Moving surface loads cause crack extension at a constant subcritical speed between perfectly bonded materials. The materials differ only in thermal properties and are governed by coupled thermoelastic equations that admit as special cases Fourier heat conduction and thermal relaxation with one or two relaxation times. Convection from the crack surfaces is allowed and for the latter two models is itself influenced by thermal relaxation. A dynamic steady state of plane strain is assumed. Fourier heat conduction is shown to dominate away from the crack edge at low speeds; solution behavior at the crack edge at high speeds depends upon the particular thermal model. Thermal mismatch is seen to cause solution behavior similar to that for the isothermal bimaterial, and so insight into the case of general material mismatch is provided.

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