Browsing by Author "Surjan Singh"

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Analysis of classical Fourier, SPL and DPL heat transfer model in biological tissues in presence of metabolic and external heat source
(Springer Verlag, 2016) Dinesh Kumar; Surjan Singh; K.N. Rai
In this paper, the temperature distribution in a finite biological tissue in presence of metabolic and external heat source when the surface subjected to different type of boundary conditions is studied. Classical Fourier, single-phase-lag (SPL) and dual-phase-lag (DPL) models were developed for bio-heat transfer in biological tissues. The analytical solution obtained for all the three models using Laplace transform technique and results are compared. The effect of the variability of different parameters such as relaxation time, metabolic heat source, spatial heat source, different type boundary conditions on temperature distribution in different type of the tissues like muscle, tumor, fat, dermis and subcutaneous based on three models are analyzed and discussed in detail. The result obtained in three models is compared with experimental observation of Stolwijk and Hardy (Pflug Arch 291:129–162, 1966). It has been observe that the DPL bio-heat transfer model provides better result in comparison of other two models. The value of metabolic and spatial heat source in boundary condition of first, second and third kind for different type of thermal therapies are evaluated. © 2015, Springer-Verlag Berlin Heidelberg.
Analytical solution of Fourier and non-Fourier heat transfer in longitudinal fin with internal heat generation and periodic boundary condition
(Elsevier Masson SAS, 2018) Surjan Singh; Dinesh Kumar; K.N. Rai
In this paper, the analytical solution of Fourier and non-Fourier model of heat transfer in longitudinal fin in presence of internal heat generation has been studied under periodic boundary condition. The whole analysis is given in dimensionless form. These two mathematical models have been solved analytically, using Laplace transform technique. Temperature distribution in longitudinal fin is measured using residual theorem in complex plane for the inverse Laplace transform technique. Thermal wave nature is appeared for small value of Fo. The longitudinal fin temperature is evaluated for different value of parameters with respect to space coordinate. The effect of variability of different parameters on temperature distribution in fin is studied in detailed. It has been observed that the cooling process is faster in non-Fourier model in comparison to Fourier model. © 2017 Elsevier Masson SAS
Convective-radiative fin with temperature dependent thermal conductivity, heat transfer coefficient and wavelength dependent surface emissivity
(Elsevier Ltd, 2014) Surjan Singh; Dinesh Kumar; K.N. Rai
In this paper, we have studied heat transfer process in a continuously moving fin whose thermal conductivity, heat transfer coefficient varies with temperature and surface emissivity varies with temperature and wavelength. Heat transfer coefficient is assumed to be a power law type form where exponent represent different types of convection, nucleate boiling, condensation, radiation etc. The thermal conductivity is assumed to be a linear and quadratic function of temperature. Exact solution obtained in case of temperature independent thermal conductivity and in absence of radiation conduction parameter is compared with those obtained by present method and is same up to ten decimal places. The whole analysis is presented in dimensionless form and the effect of variability of several parameters namely convection-conduction, radiation-conduction, thermal conductivity, emissivity, convection sink temperature, radiation sink temperature and exponent on the temperature distribution in fin and surface heat loss are studied and discussed in detail. © 2014 National Laboratory for Aeronautics and Astronautics
Exact and wavelet collocation solution of fin problem with temperature dependent internal heat generation
(Begell House Inc., 2014) Surjan Singh; Dinesh Kumar; K.N. Rai
In this paper, we studied heat transfer in longitudinal fin with temperature dependent internal heat generation and temperature dependent thermal conductivity. It has been observed that solution exists and unique. We consider three particular cases when the thermal conductivity is (1) constant (2) linear and (3) exponential function of temperature. We obtained exact solution in case I and exact solution in explicit integral form is case II and III. The wavelet collocation method has been used in this nonlinear problem. In case I, exact solution is compared with those obtained by wavelet collocation solution and optimal linearization solution. It has been observed that the wavelet collocation solution and exact solution is the same while optimal linearization solutions are having error. In case II, we have compared our results with those obtained by optimal linearization solution and observed that optimal linearization method having similar error as in case I. In case III, the wavelet collocation solution is provided. The whole analysis is provided in dimensionless form. The effect of variability of different parameters on dimensionless fin temperature and on fin efficiency are studied and discussed in detailed. © 2014, Begell House Inc. All rights reserved.
Legendre Wavelet Collocation Solution for System of Linear and Nonlinear Delay Differential Equations
(Springer, 2017) Dinesh Kumar; S. Upadhyay; Surjan Singh; K.N. Rai
The proposed article is to describe the study of the system of linear and nonlinear delay differential equations subjected to initial-interval conditions. The existence and uniqueness theorem for solution of the proposed problem has been provided. The Legendre wavelet collocation method has been used in solution. We are presenting certain powerful tools as wavelet concepts, properties and description of this method. The main objective of the proposed method is to achieve high accuracy in minimum computation. The convergence analysis of Legendre wavelet collocation method is also presented. Some numerical examples of linear and non-linear system of delay differential equations are discussed in detail. The comparative study of Legendre wavelet collocation method, Exact, Runge–Kutta fourth order, dde23 (MATLAB solver) and Taylor’s series method solutions are also provided. © 2017, Springer India Pvt. Ltd.
Mathematical modelling and simulation of three phase lag bio-heat transfer model during cancer treatment
(Elsevier Masson s.r.l., 2023) Mukesh Kumar; Harpreet kaur; Subrahamanyam Upadhyay; Surjan Singh; K.N. Rai
We have developed a two-dimensional mathematical model that described the study of bio-heat transfer. Our model is an initial boundary value problem of partial differential equation. The solution consists of the three step procedure- (i) transformation of problem in dimensionless form (ii) by using finite differences, the problem converted into ordinary matrix differential equation (iii) applying Legendre wavelet Galerkin method, the problem is transferred into the generalised system of Sylvester equations which are solved by applying Bartels-Stewart Algorithm of generalised inverse. We have used this method to determine the temperature profile in three different boundary conditions. The consequence of boundary conditions on temperature profile are discussed in detail. The effect of phase lag due to heat flux, phase lag due to temperature gradient and phase lag due to thermal displacement have been observed. And, we have seen that temperature profile increases when the phase lags decreases. We have also observed the effect of blood perfusion rate and metabolic heat generation in specific. Results are validated with exact results in particular case. © 2022 Elsevier Masson SAS