In the present paper, the new concept of “memory dependent derivative” in the Pennes’ bioheat transfer and heat-induced mechanical response in human living tissue with variable…
Abstract
Purpose
In the present paper, the new concept of “memory dependent derivative” in the Pennes’ bioheat transfer and heat-induced mechanical response in human living tissue with variable thermal conductivity and rheological properties of the volume is considered.
Design/methodology/approach
A problem of cancerous layered with arbitrary thickness is considered and solved analytically by Kirchhoff and Laplace transformation. The analytical expressions for temperature, displacement and stress are obtained in the Laplace transform domain. The inversion technique for Laplace transforms is carried out using a numerical technique based on Fourier series expansions.
Findings
Comparisons are made with the results anticipated through the coupled and generalized theories. The influence of variable thermal, volume materials properties and time-delay parameters for all the regarded fields for different forms of kernel functions is examined.
Originality/value
The results indicate that the thermal conductivity and volume relaxation parameters and MDD parameter play a major role in all considered distributions. This dissertation is an attempt to provide a theoretical thermo-viscoelastic structure to help researchers understand the complex thermo-mechanical processes present in thermal therapies.
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Magdy A. Ezzat, Shereen M. Ezzat and Modhi Y. Alkharraz
The purpose of this study is to develop a comprehensive size-dependent piezoelectric thermo-viscoelastic coupling model that accounts for two fundamentally distinct size-dependent…
Abstract
Purpose
The purpose of this study is to develop a comprehensive size-dependent piezoelectric thermo-viscoelastic coupling model that accounts for two fundamentally distinct size-dependent models that govern fractional dual-phase lag heat transfer and viscoelastic deformation, respectively.
Design/methodology/approach
The fractional calculus has recently been shown to capture precisely the experimental effects of viscoelastic materials. The governing equations are combined into a unified system, from which certain theorems results on linear coupled and generalized theories of thermo-viscoelasticity may be easily established. Laplace transforms and state–space approach will be used to determine the generic solution when any set of boundary conditions exists. The derived formulation is used to two concrete different problems for a piezoelectric rod. The numerical technique for inverting the transfer functions is used to generate observable numerical results.
Findings
Some analogies of impacts of nonlocal thermal conduction, nonlocal elasticity and DPL parameters as well as fractional order on thermal spreads and thermo-viscoelastic response are illustrated in the figures.
Originality/value
The results in all figures indicate that the nonlocal thermal and viscoelastic parameters have a considerable influence on all field values. This discovery might help with the design and analysis of thermal-mechanical aspects of nanoscale devices.
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Magdy A. Ezzat and Roland W. Lewis
The system of equations for fractional thermo-viscoelasticity is used to investigate two-dimensional bioheat transfer and heat-induced mechanical response in human skin tissue…
Abstract
Purpose
The system of equations for fractional thermo-viscoelasticity is used to investigate two-dimensional bioheat transfer and heat-induced mechanical response in human skin tissue with rheological properties.
Design/methodology/approach
Laplace and Fourier’s transformations are used. The resulting formulation is applied to human skin tissue subjected to regional hyperthermia therapy for cancer treatment. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions.
Findings
Comparisons are made with the results anticipated through the coupled and generalized theories. The influences of volume materials properties and fractional order parameters for all the regarded fields are examined. The results indicate that volume relaxation parameters, as well as fractional order parameters, play a major role in all considered distributions.
Originality/value
Bio-thermo-mechanics includes bioheat transfer, biomechanics, burn injury and physiology. In clinical applications, knowledge of bio-thermo-mechanics in living tissues is very important. One can infer from the numerical results that, with a finite distance, the thermo-mechanical waves spread to skin tissue, removing the unrealistic predictions of the Pennes’ model.
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Mohamed M. Hendy and Magdy A. Ezzat
Whereas, the classical Green-Naghdi Type II (GN-II) model struggles to accurately represent the thermo-mechanical behavior of thermoelectric MHD due to its inability to account…
Abstract
Purpose
Whereas, the classical Green-Naghdi Type II (GN-II) model struggles to accurately represent the thermo-mechanical behavior of thermoelectric MHD due to its inability to account for the memory effect. A new mathematical model of the GN-II theory incorporates a fractional order of heat transport to address this issue.
Design/methodology/approach
The employment of the matrix exponential method, which forms the basis of the state-space approach in contemporary theory, is central to this strategy. The resulting formulation, together with the Laplace transform techniques, is applied to a variety of problems. Solutions to a thermal shock problem and to a problem of a layer media both without heat sources are obtained. Also, a problem with the distribution of heat sources is considered. The numerical technique is used to achieve the Laplace transform inversion.
Findings
According to the numerical results and its graphs, the influences of the fractional order parameters, figure-of-merit factor, thermoelectric power and Peltier coefficient on the behavior of the field quantities are investigated in the new theory.
Originality/value
The new modeling of thermoelectric MHD has advanced significantly as a result of this work, providing a more thorough and precise tool for forecasting the behavior of these materials under a range of thermal and magnetic conditions.
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The purpose of this paper is to deal with the propagation of Love waves in inhomogeneous viscoelastic layer overlying a gravitational half-space. It has been observed velocity of…
Abstract
Purpose
The purpose of this paper is to deal with the propagation of Love waves in inhomogeneous viscoelastic layer overlying a gravitational half-space. It has been observed velocity of Love waves depends on viscosity, gravity, inhomogeneity and initial stress of the layer.
Design/methodology/approach
The dispersion relation for the Love wave in closed form is obtained with Whitaker’s function.
Findings
The effect of various non-dimensional inhomogeneity factors, gravity factor and internal friction on the non-dimensional Love wave velocity has been shown graphically. The authors observed that the dispersion curve of Love wave increases as the inhomogeneity factor increases. It is seen that increment in gravity, inhomogeneity and internal friction decreases the damping phase velocity of Love waves but it is more prominent in case of internal friction.
Originality/value
Surface plot of Love wave reveals that the velocity ratio increases with the increase of non-dimensional phase velocity and non-dimensional wave number. The above results may attract seismologists and geologists.