Browsing by Author "Rajneesh Kumar Chaudhary"

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A numerical study of a moving boundary problem with variable thermal conductivity and temperature-dependent moving PCM under periodic boundary condition
(Springer Science and Business Media Deutschland GmbH, 2022) Vikas Chaurasiya; Rajneesh Kumar Chaudhary; Mohamed M. Awad; Jitendra Singh
The work in this paper concerns the study of a one-phase moving boundary problem with size-dependent thermal conductivity and moving phase change material. We have considered a time-dependent boundary condition at the surface y= 0 and a temperature-dependent moving phase change material which later both assumed in periodic nature. A quadratic profile for temperature distribution is assumed to solve the problem numerically via heat balance integral method. In a particular case, we compared our results with exact solution and found to be closed. The effect of various parameters either on temperature profile or on tracking of melting front are also discussed in detail. The parameters physically interpret that transition process becomes fast for a higher value of Stefan number or/and Peclet number while there is a small delay in the propagation of melting interface for larger value of either amplitude of moving phase change material or amplitude of periodic boundary condition. Furthermore, we discuss a comparative study on temperature profile as well as on moving melting front in case of standard problem, moving boundary problem with constant thermal conductivity and presence of convection, and moving boundary problem with variable thermal conductivity and presence of convection and obtained result shows that the transition process is faster in case of moving boundary problem with constant thermal conductivity and presence of convection and is slower in case of moving boundary problem with variable thermal conductivity and presence of convection while it is between them in case of standard problem. © 2022, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
A numerical study on the thermal response in multi-layer of skin tissue subjected to heating and cooling procedures
(Springer Science and Business Media Deutschland GmbH, 2022) Rajneesh Kumar Chaudhary; Vikas Chaurasiya; Mohamed M. Awad; Jitendra Singh
This article deals with studies for the behavior of the temperature distribution in multi-layer skin during thermal injuries and its first aid treatment under generalized boundary condition. The finite difference scheme is used to estimate the temperature profile over time and distance. The skin is damaged by heating via generalized boundary condition, after that first aid treatment is applied by cooling phenomenon via the different cold temperature of liquids, the stability of numerical scheme has been discussed, and are also validated the numerical code accuracy by comparison the obtained results with the previous reference results. In the first aid treatment by cooling, the temperature at DS interface is increased constantly over time for a few seconds, then after that, the temperature goes down. The temperature rises along with distance as long as the heat effect is present in the skin, when the heat effect has vanished, the temperature in the skin starts to decrease. During cooling, the heat effect is decreasing faster for the second kind boundary condition in comparison to the first and third kind boundary conditions. It is observed that with a higher blood perfusion rate, skin transfers more heat into the blood due to a convection process, and for this reason, a large amount of heat can be carried away from the skin. The skin burns with 100 oC for 15 s and then we applied first aid treatment by cooling with 0 oC water. Then, it was observed from the mathematical results that 41 s of time is sufficient for cooling to save the rest of the living part of the subcutaneous tissue. The effect of blood perfusion rate, heating and cooling procedures, and generalized boundary conditions are discussed in detail and the results are presented graphically for the analysis of the behavior of the temperature response in multi-layer skin. © 2022, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
A one-phase Stefan problem with size-dependent thermal conductivity and moving phase change material under the most generalized boundary condition
(Taylor and Francis Ltd., 2022) Vikas Chaurasiya; Rajneesh Kumar Chaudhary; Abderrahim Wakif; Jitendra Singh
In the current paper, we analyzed a one-phase moving boundary problem that includes a size-dependent thermal conductivity and a moving phase change material under the most generalized boundary condition. A numerical solution to the problem is obtained via heat balance integral method (HBIM) with an approximation of the quadratic temperature profile. In particular, numerical results are compared against the exact solution and previous work and found to be closed. The effect of dimensionless problem parameters on temperature profile and moving melting interface are shown in figures. The physical behavior of these parameters shows that the melting interface enhanced growing for a large value of either Stefan number, Péclet number or Kirpichev number while it deterred with increasing the Nusselt number. A comparative study between moving boundary problem with size-dependent thermal conductivity and moving PCM, moving boundary problem with constant thermal conductivity and moving PCM, and standard problem is presented in each kind of boundary conditions. We also found that the second kind flux boundary condition is physically more realistic for the melting process than the first and third kind temperature boundary condition for a moving boundary problem with size-no independent thermal conductivity and moving PCM. For limiting value of the Nusselt number ((Formula presented.)), we found a unique λ with the Stefan number and Péclet number. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
A study for multi-layer skin burn injuries based on DPL bioheat model
(Springer Science and Business Media B.V., 2021) Rajneesh Kumar Chaudhary; Kabindra Nath Rai; Jitendra Singh
In this paper, multi-layer skin burn injuries are studied using the DPL bioheat model when skin surface is subjected to different non-Fourier boundary conditions. A skin made of three layers known as epidermis, dermis, and subcutaneous layer. These layers assumed to be homogeneous and each layer studied separately. The metabolic heat varies linearly with temperature. The diffusion and evaporation of water in the multi-layer of skin increases heat loss in the skin layer. To solve the BVP of hyperbolic PDE, the FELWG method has been used. The whole analysis presented in a non-dimensional form and the results are shown graphically. In a particular case, the result obtained is compared with the exact solution and is in good agreement. The effects of relaxation time, layer thickness, different temperature, and non-Fourier boundary condition are analyzed at the temperature of the tissue related to the burning of the skin, and the three layers are discussed in detail. © 2020, Akadémiai Kiadó, Budapest, Hungary.
A study of thermal injuries when skin surface subjected under most generalized boundary condition
(Begell House Inc., 2020) Rajneesh Kumar Chaudhary; Kabindra Nath Rai; Jitendra Singh
In this paper, we studied a mathematical model describing the process of heat transfer in multi-layer of skin when the skin surface is subjected to the most generalized boundary conditions (B.C.): a multi-layer skin made of three different layers known as the epidermis, dermis, and subcutaneous layer, and each layer was studied separately. We considered time lagging heat transfer model with different physical parameters. Metabolic heat varies linearly with temperature. The mathematical model has been solved using the Finite Element Legendre Wavelet Galerkin Method (FELWGM). In the epidermis layer, we analyzed the effect of diffusion and vaporization of water which increases heat loss in a skin layer. The obtained results are shown graphically and found close to the exact solution in a special case. The effect of lagging time, perfusion of blood, vaporization, and diffusion of water on temperature related to the burning of skin layer are analyzed and discussed in detail for the three layers. © 2020 by Begell House, Inc. www.begellhouse.com.
Analysis of thermal injuries using classical Fourier and DPL models for multi-layer of skin under different boundary conditions
(World Scientific, 2021) Rajneesh Kumar Chaudhary; Dinesh Kumar; Kabindra Nath Rai; Jitendra Singh
In this paper, the temperature distribution in the multi-layer of the skin is studied when the skin surface is subjected to most generalized boundary condition. Our skin model consists of three layers known as the epidermis, dermis, and subcutaneous layers. All layers of skin are assumed to be connected with point of interface condition and taking the barrier in between each of the two layers by symmetric flux condition and analyzing each layer separately. The classical Fourier and non-Fourier (DPL) models are extended to analyze the behavior of heat transfer in the multi-layer of the skin. The Laplace transform technique is used to derive analytical solutions for the multi-layer of skin models. The effects of the variability of different parameters such as relaxation time, layer thickness, and different types of boundary conditions on the behavior of temperature distribution in the multi-layer of skin are analyzed and discussed in detail. All the effects are shown graphically. It has been observed that during temperature distribution in the multi-layer of skin, the measurement of skin damage is less on the DPL model (τq ≥ τt) in comparison to the classical Fourier model. © 2021 World Scientific Publishing Company.
Correction to: A study for multi-layer skin burn injuries based on DPL bioheat model (Journal of Thermal Analysis and Calorimetry, (2021), 146, 3, (1171-1189), 10.1007/s10973-020-09967-3)
(Springer Science and Business Media B.V., 2021) Rajneesh Kumar Chaudhary; Kabindra Nath Rai; Jitendra Singh
In the original publication of the article, the following equations has been incorrectly published. The corrected equations are given. © 2020, Akadémiai Kiadó, Budapest, Hungary.
Numerical analysis of DPL bioheat transfer model with nonlocal impact on skin tissue during hyperthermia
(Elsevier Ltd, 2023) Rajneesh Kumar Chaudhary; Jitendra Singh
This article discussed a numerical study of dual-phase-lag (DPL) bioheat transfer model with nonlocal impact on skin tissue during hyperthermia therapy when Gaussian type heat device is applied to the skin's outer surface. With the aid of a sufficient value of the parameters η,Qro and rp for a heating device of the Gaussian type, the temperature distribution at the targeted location is controlled and maintained. These parameters are employed to destroy a significant number of cancer cells in the targeted location while protecting the surrounding healthy tissue. The temperature profile at the targeted location decreases as lagging time τq and τT increases, and increases as spatial lagging λq increases. The blood perfusion effect can be shown when the value of α increases or when blood temperature decreases then it is seen that the temperature profile decreases. The numerical results obtained by the Finite element Legendre wavelet Galerkin (FELWG) approach are compared with the analytical results obtained in the specific situation to evaluate the precision. The obtained numerical results logically relate to the analytical results when we utilized the operational matrix of order M−1 (where M=100). All impacts of problem parameters are graphically represented during hyperthermia treatment. © 2023 Elsevier Ltd
Numerical analysis of thermal response on a non-linear model of multi-layer skin under heating and cooling processes
(Elsevier Ltd, 2022) Rajneesh Kumar Chaudhary; Jitendra Singh
Based on the non-linear model of multi-layer skin, the present study is performed under heating and cooling processes with linear and non-linear generalized boundary conditions. The numerical outcome is obtained utilizing Runge Kutta (4,5) along with the finite difference scheme and the accuracy of this scheme is shown graphically by comparing it with an accurate analytical outcome in a special case. When the value of γ increases, the skin temperature is gradually higher in the case of a linear boundary condition and gradually lower in the case of a non-linear boundary condition with respect to linear boundary condition at epidermis-dermis (ED) interface. During cooling, the heat effect has slightly quick vanished in a non-linear boundary condition than in a linear boundary condition. The effect of a non-linear boundary condition gradually decreases as the value of heat transfer coefficient rises, then it reflecting the nature of the first kind of linear boundary condition. The exponential blood perfusion rate has a slightly quick vanishes of heat effect in comparison to constant and linear blood perfusion rate. To investigate the conduct of the temperature distribution in multi-layer skin, all the impacts are depicted graphically. © 2022 Elsevier Ltd
Numerical estimation of temperature response with step heating of a multi-layer skin under the generalized boundary condition
(Elsevier Ltd, 2022) Rajneesh Kumar Chaudhary; Vikas Chaurasiya; Jitendra Singh
In this article, we discussed a one-dimensional bioheat transfer mathematical model that describes the process of temperature distribution in tissue for the multi-layer skin under the step heating generalized boundary condition. The finite difference scheme is used to estimate the temperature profile along with time and distance. We discussed the stability of the numerical scheme and also validated the accuracy of the numerical code by comparing the present results with the previous reference results. To remove heat from the skin is considered by the surface temperature, heat flux, and ambient temperature to be zero with the help of the unit step like function. Then, we observed that the skin temperature in the second kind boundary condition was slowly decreasing over time as compared to the first and third kind boundary conditions. The temperature or heat flux at the skin surface is assumed to be high then there is negligible effect of the blood perfusion rate on the temperature response over a short time period and the effect of blood perfusion rate is visible when the time duration is long. Effect of blood perfusion rate, heating and after removal of heating, water diffusion, and generalized boundary condition for the analysis of the behavior of temperature response in multi-layer skin are discussed in detail and the results obtained are presented graphically. © 2022 Elsevier Ltd
Numerical simulation of burn injuries with temperature-dependent thermal conductivity and metabolism under different surface heat sources
(Elsevier Ltd, 2023) Faishal Ansari; Rajneesh Kumar Chaudhary; Jitendra Singh
In the present paper, the phenomena of heat transport inside human forearm tissue are studied through a one-dimensional nonlinear bioheat transfer model under the influence of various boundary and interface conditions. In this study, we considered temperature-dependent thermal conductivity and metabolic heat to predict temperature distribution inside the forearm tissue. We have studied the temperature distribution inside inner tissue and bone because it has been found that burn injuries are mostly affected by layer thickness. The temperature distribution inside human forearm tissue is analyzed using the finite difference and bvp4c numerical techniques. To examine the accuracy of present numerical code, we compare the obtained numerical result with the exact analytical result in a specific case and find an excellent agreement with the exact results. We also validated our present numerical code with a hybrid scheme based on Runge-Kutta (4,5) and finite difference technique and found it in good compliance. From the obtained results, we observed that the homogeneous heat flux has a greater impact on the temperature at the outer surface of the skin, but the sinusoidal heat flux has a greater impact on the temperature of the subcutaneous layer and inner tissue. It is found that there is no burn injury in the first type of heat source (Tw=44°C), but it may occur in the second and third types of heat sources. It has been observed that by raising the blood perfusion rate and reducing the values of reference metabolic heat, coefficient of thermal conductivity, and heat fluxes, we can manage and reduce burn injuries and achieve hyperthermia temperature. © 2023 Elsevier Ltd
Numerical simulation of non–linear skin model with energy dissipation during hyperthermia and its validation with experimental data
(Taylor and Francis Ltd., 2024) Rajneesh Kumar Chaudhary; Jitendra Singh
This work deals with a non–linear skin model with energy dissipation exposed to hyperthermia therapy based on a Gaussian–type external heat source and also consider that the blood perfusion rate relies linearly on temperature. Since skin tissue is very sensitive to temperature, it is crucial to predict the temperature response with energy dissipation to ensure hyperthermia efficacy and minimize adverse effects. The present model, which is supported by experimental data, indicates that the temperature profile of skin tissue increases less in comparison to the non–linear Pennes model due to energy dissipation. A hybrid strategy is utilized to get computed outcomes for the present problem and obtained outcome is compared to the analytical outcome in a specific situation and is confirmed with high precision through table and graph. To damage a significant number of cancerous cells width, we have to manage or reduce enough value of the antenna constant accordingly, and the length of the probe region may be changed according to the position of the tumor or cancer cells in skin tissue. The temperature profile at the targeted area reduces when the values of rate of thermal conductivity, rate of blood perfusion per unit volume and blood perfusion constant increase. © 2023 Taylor & Francis Group, LLC.
Numerical simulation of the skin tissue subjected to hyperthermia treatment using a nonlinear DPL model
(Elsevier Ltd, 2022) Rajneesh Kumar Chaudhary; Dinesh Kumar; Kabindra Nath Rai; Jitendra Singh
This article deals with the study of simulation-based mathematical modeling of tissue using the non-linear dual-phase-lag bioheat transfer (DPLBHT) model for hyperthermia treatment of tumor or cancer cells with Gaussian distribution type heat source. The metabolic heat source as an exponential variation, blood perfusion rate as a linear variation and thermal conductivity as a linear variation are considered to be temperature-dependent, resulted in a more accurate prediction of the non-linear DPLBHT model. At initial time, τq is more effective than τt in the targeted region. When the infected or cancerous cells increases in width then for effective treatment the value of the antenna constant could be decreased and the value of probe region can be changed according to the tumor location in the skin tissue. When the value of γ, Wbo, a1 and a2 increases, the temperature profile in the target region decreases. The numerical solution is obtained by hybrid scheme using Runge Kutta (4,5) and finite difference technique. This technique is compared for accuracy with an exact analytical result in a particular case as shown in figures and table and found in good compliance. The effect of lagging, metabolic heat source, blood perfusion rate, coefficient of thermal conductivity, external heat source parameter and the other associated parameter are studied in detail and the results are presented graphically. © 2022 Elsevier Ltd
Numerical simulation of thermal response for non-linear multi-layer skin model subjected to heating and cooling
(Elsevier Ltd, 2023) Rajneesh Kumar Chaudhary; Ibrahim A. Abbas; Jitendra Singh
In this article, a non-linear model of multi-layer skin has been studied to analyze the temperature distribution within the skin tissue under the heating and cooling processes. A hybrid scheme based on the finite-difference and Runge Kutta (4,5) schemes is used to compute the numerical results. The numerical result is compared to the precise analytical result in a particular case and found in excellent compliance. The damage of skin layer thickness is affected by the variation of non-linear parameters and we observed that the thickness of skin layer is less damaged by adding the effect of blood perfusion (α) and damage of skin thickness is slightly increased by adding the impact of metabolic heat generation (β). The mathematical results are obtained and it is observed that 80 s and 173 s of time is sufficient for cooling when skin is cooled by cold water and Newton's cooling law, respectively under the practical situation that the present non-linear multi-layer skin model defines. Furthermore, the temperature difference of skin between Newton's cooling law and cold water can be reduced as the value of the heat transfer coefficient rises. The impact of the coefficient of blood perfusion rate, coefficient of metabolic heat generation, heating and cooling procedures, and Newton's cooling law are described in detail and their effects are shown graphically to explore the behavior of the temperature distribution in multi-layer skin. © 2023 Elsevier Ltd
Numerical study of a dual-phase-lag bioheat transfer model via finite element Runge-Kutta (4,5) in spherical tissue with temperature-dependent blood perfusion during magnetic hyperthermia
(Taylor and Francis Ltd., 2025) Faishal Ansari; Rajneesh Kumar Chaudhary; Jitendra Singh
The present article involves a dual-phase-lag nonlinear bioheat model for living spherical tissue during magnetic hyperthermia. In this study, we considered temperature-dependent blood perfusion to forecast accurate hyperthermia temperature for the treatment of tumor cells. Due to the nonlinearity, this problem is handled by a finite element Runge-Kutta (4,5) technique, which is a combination of Runge-Kutta (4,5) and finite difference approaches. In this technique, we discretize the partial derivatives of space variables by using the central difference scheme. After the discretization, the current problem turns out as a system of second-order ODEs with initial conditions. Again, we convert the system of second-order ODEs into the system of first-order coupled ODEs. Then, we employed the RK (4,5) scheme to resolve the problem completely for time interval. The result obtained by the present numerical scheme is validated through an exact analytical result in a special situation, and it is noticed that both results are very close to each other. After analyzing the results, we found that when tumor cells are treated by magnetic hyperthermia, temperature-dependent blood perfusion significantly affects the hyperthermia temperature. It is seen that the impact of quadratically temperature-dependent blood perfusion is more effective than the linearly temperature-dependent types of blood perfusion. The convection effect due to the quadratically temperature-dependent term in the blood perfusion is greater than the other terms. The magnetic heat source is crucial in regulating the temperature inside the living tissue for determining hyperthermia temperature. By rising the ratio of lagging time due to heat flux ((Formula presented.)) and temperature gradient ((Formula presented.)), the temperature profile drops, and these effects are observed initially for a few seconds. © 2025 Taylor & Francis Group, LLC.