scholarly journals Thermo-vibrational analyses of skin tissue subjected to laser heating source in thermal therapy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mina Ghanbari ◽  
Ghader Rezazadeh
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Mechanical Response ◽  
Thermal Therapy ◽  
Skin Tissue ◽  
Transient Temperature ◽  
Hyperbolic Heat Conduction ◽  
Two Dimensional ◽  
Thermomechanical Response

AbstractLaser-induced thermal therapy, due to its applications in various clinical treatments, has become an efficient alternative, especially for skin ablation. In this work, the two-dimensional thermomechanical response of skin tissue subjected to different types of thermal loading is investigated. Considering the thermoelastic coupling term, the two-dimensional differential equation of heat conduction in the skin tissue based on the Cattaneo–Vernotte heat conduction law is presented. The two-dimensional differential equation of the tissue displacement coupled with the two-dimensional hyperbolic heat conduction equation in the tissue is solved simultaneously to analyze the thermal and mechanical response of the skin tissue. The existence of mixed complicated boundary conditions makes the problem so complex and intricate. The Galerkin-based reduced-order model has been utilized to solve the two-sided coupled differential equations of vibration and heat transfer in the tissue with accompanying complicated boundary conditions. The effect of various types of heating sources such as thermal shock, single and repetitive pulses, repeating sequence stairs, ramp-type, and harmonic-type heating, on the thermomechanical response of the tissue is investigated. The temperature distribution in the tissue along depth and radial direction is also presented. The transient temperature and displacement response of tissue considering different relaxation times are studied, and the results are discussed in detail.

Two-Dimensional Vibrating And Thermal Response of Skin Tissue To Different Types of Heat Sources Considering The Hyperbolic Heat Transfer Equation

2021 ◽  
Author(s):  
Mina Ghanbari ◽  
Ghader Rezazadeh
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Skin Tissue ◽  
Transient Temperature ◽  
Hyperbolic Heat Conduction ◽  
Two Dimensional ◽  
Thermomechanical Response ◽  
Different Types

Abstract Laser-induced thermal therapy, due to its applications in various clinical treatments, has become an efficient alternative, especially for skin ablation. In this work, the two-dimensional thermomechanical response of skin tissue subjected to different types of thermal loading is investigated. Considering the thermoelastic coupling term, the two-dimensional differential equation of heat conduction in the skin tissue based on the Cattaneo–Vernotte heat conduction law is presented. The two-dimensional differential equation of the tissue displacement coupled with the two-dimensional hyperbolic heat conduction equation of tissue is solved simultaneously to analyze the thermal and mechanical response of the skin tissue. The existence of mixed complicated boundary conditions makes the problem so complex and intricate. The Galerkin-based reduced-order model has been utilized to solve the two-sided coupled differential equations of skin displacement and heat transfer with accompanying complicated boundary conditions. The effect of various types of heating sources such as thermal shock, single and repetitive pulses, repeating sequence stairs, ramp-type, and harmonic-type heating, on the thermomechanical response of the tissue is investigated. The temperature distribution in the tissue along the depth and radial direction is also presented. The transient temperature and displacement response of tissue considering different relaxation times are studied, and the results are discussed in detail.

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

2020 ◽  
Vol 234 (20) ◽  
pp. 3951-3966
Author(s):  
Jaideep Dutta ◽  
Balaram Kundu
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Cancer Treatment ◽  
Thermal Response ◽  
Skin Tissue ◽  
Hyperbolic Heat Conduction ◽  
Two Dimensional ◽  
Regional Hyperthermia ◽  
Hyperthermia Therapy ◽  
The Impact

The formation of the present work is based on the development of the exact analytical solution of two-dimensional temperature response by employing the hyperbolic heat conduction bioheat model in a single-layered human skin tissue subjected to the regional hyperthermia therapy (RHT) for cancer treatment. The mathematical approach has been utilized as a hybrid form of ‘separation of variables’ and ‘finite integral transform’ method. Three kinds of surface heat fluxes (constant, sinusoidal and cosine) have been employed as an external heat source on the therapeutic surface of the square-shaped skin tissue of 100 mm × 100 mm. An innovative form of initial condition (spatially dependent) has been implemented in the present mathematical formulation as skin tissues are highly non-homogeneous and non-uniform in structure. The present research outcome indicates that cosine heat flux would be a suitable alternative for the sinusoidal heat flux. The impact of the relaxation time lag has been clearly noted in the thermal response with the waveform-like behaviour and it justifies the postulate of hyperbolic heat conduction. The two-dimensional temperature of the skin tissue has been observed in the range of 48.1 ℃–40 ℃ (in decreasing order). Estimated peak temperatures are in the proposed spectrum of hyperthermia therapy for an exposure time of 100 s, and this fact is true in an agreement with the medical protocol of the cancer treatment. The accuracy of the mathematical modelling and in-house computer codes are justified with the published numerical models and the maximum deviation of the thermal response has been noticed in order of 1.5–3%. The two-dimensional surface thermal contours have provided a glimpse of heat flow in the physical domain of skin tissue under different heating conditions and this research output may be beneficial to establish the theoretical standard of the regional hyperthermia treatment for cancer eradication.

Exact Solution of Two-Dimensional Hyperbolic Heat Conduction Equation With Combined Boundary Conditions and Arbitrary Initial Conditions

2009 ◽  
Author(s):  
Seyed Reza Mahmoudi ◽  
Nikola Toljic
Keyword(s):  
Exact Solution ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Equation ◽  
Initial Conditions ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Application Range

Analytical solution of hyperbolic heat conduction equation has so far been limited only to one-dimensional frameworks. With the expanding of the application range for the fast heat sources in microelectronic industries, the two-dimensional solution of non-Fourier heat conduction becomes increasingly important. This paper presents an exact solution of hyperbolic heat conduction equation for a finite plane with sides subjected to combined boundary conditions. In the mathematical model, the heating on boundaries is treated as an apparent heat source whereas sides of the plane with the second kind boundaries are assumed to be insulated. The important characteristic of the proposed solution is its simplicity.

Transient Heat Transfer in Microscale Porous Materials Heated by Microsecond Laser Pulse of High Power Density

2002 ◽  
Author(s):  
Fangming Jiang ◽  
Dengying Liu ◽  
Jim S.-J. Chen ◽  
Richard S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Laser Pulse ◽  
Power Density ◽  
High Power ◽  
Hyperbolic Model ◽  
Transient Temperature ◽  
Hyperbolic Heat Conduction ◽  
High Power Density ◽  
High Heat Transfer

A novel experimental method was developed to measure the rapid transient temperature variations (heating rate > 107 K/s) of porous samples heated by high surface heat fluxes. With a thin film (0.1 μm thick) resistance thermometer of platinum as the temperature sensor and a super-high speed digital oscilloscope (up to 100 MHz) as the data recorder, rapid transient temperature variation in a porous material heated by a microsecond laser pulse of high power density is measured. Experimental results indicate that for high heat transfer cases (q′ > 109 W/m2) with short durations (5 – 20 μs) of heating, non-Fourier heat conduction behaviors appear. The non-Fourier hyperbolic heat conduction model and the traditional Fourier parabolic model are employed to simulate this thermal case respectively and the FDM is used to perform the numerical analysis. The hyperbolic model predicts thermal wave behavior in qualitative agreement with the experimental data.

scholarly journals Simplified Grinding Temperature Model Study

2019 ◽  
Vol 6 (2) ◽  
pp. a1-a7
Author(s):  
N. V. Lishchenko ◽  
V. P. Larshin ◽  
H. Krachunov
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Heat Source ◽  
Boundary Conditions ◽  
Grinding Temperature ◽  
Temperature Model ◽  
One Dimensional ◽  
Heating And Cooling ◽  
Equation Of Heat Conduction ◽  
The One

A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth. Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.

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