In this paper, generalized dual-phase-lag (DPL) model has been studied for the numerical analysis of spatial variation of temperature within living biological tissues during thermal therapy applications. A new hybrid ...In this paper, generalized dual-phase-lag (DPL) model has been studied for the numerical analysis of spatial variation of temperature within living biological tissues during thermal therapy applications. A new hybrid numerical scheme based on finite difference scheme and Chebyshev wavelet Galerkin method are used to solve the generalized DPL model with constant heat flux boundary condition. Multi-resolution and multi-scale computational property of Chebyshev wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. Our study demonstrates that due to presence of coupling factor (convection–perfusion), generalized DPL model predicts lower temperature than classical DPL and Pennes model at the tumor position. Higher values of phase lag times results in lower temperature at the tumor position. But, in case of variation of phase lag time due to temperature gradient, the nature of temperature profile also depends on the spatial coordinate. The effect of the blood temperature, porosity and interfacial convective heat transfer on temperature distribution has been investigated. It is found that larger values of porosity and interfacial convective heat transfer results in lower temperature at the tumor position. Also, both porosity and interfacial convective heat transfer are pronounced more at higher values. The whole analysis is presented in dimensionless form.展开更多
The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation ef...The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.展开更多
The introduced method in this paper consists of reducing a system of integro-differential equations into a system of algebraic equations, by expanding the unknown functions, as a series in terms of Chebyshev wavelets ...The introduced method in this paper consists of reducing a system of integro-differential equations into a system of algebraic equations, by expanding the unknown functions, as a series in terms of Chebyshev wavelets with unknown coefficients. Extension of Chebyshev wavelets method for solving these systems is the novelty of this paper. Some examples to illustrate the simplicity and the effectiveness of the proposed method have been presented.展开更多
文摘In this paper, generalized dual-phase-lag (DPL) model has been studied for the numerical analysis of spatial variation of temperature within living biological tissues during thermal therapy applications. A new hybrid numerical scheme based on finite difference scheme and Chebyshev wavelet Galerkin method are used to solve the generalized DPL model with constant heat flux boundary condition. Multi-resolution and multi-scale computational property of Chebyshev wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. Our study demonstrates that due to presence of coupling factor (convection–perfusion), generalized DPL model predicts lower temperature than classical DPL and Pennes model at the tumor position. Higher values of phase lag times results in lower temperature at the tumor position. But, in case of variation of phase lag time due to temperature gradient, the nature of temperature profile also depends on the spatial coordinate. The effect of the blood temperature, porosity and interfacial convective heat transfer on temperature distribution has been investigated. It is found that larger values of porosity and interfacial convective heat transfer results in lower temperature at the tumor position. Also, both porosity and interfacial convective heat transfer are pronounced more at higher values. The whole analysis is presented in dimensionless form.
基金Project supported by the National Natural Science Foundation of China(Nos.51709191,51706149,and 51606130)the Key Laboratory of Advanced Reactor Engineering and Safety,Ministry of Education of China(No.ARES-2018-10)the State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University of China(No.Skhl1803)
文摘The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.
文摘The introduced method in this paper consists of reducing a system of integro-differential equations into a system of algebraic equations, by expanding the unknown functions, as a series in terms of Chebyshev wavelets with unknown coefficients. Extension of Chebyshev wavelets method for solving these systems is the novelty of this paper. Some examples to illustrate the simplicity and the effectiveness of the proposed method have been presented.
基金Supported by the National Natural Science Foundation of China(11601076)the Science and Technology Project of Jiangxi Provincial Education Department(GJJ170473)
