Browsing by Author "Vikas Chaurasiya"

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A computational solution of a phase-change material in the presence of convection under the most generalized boundary condition
(Elsevier Ltd, 2020) Vikas Chaurasiya; Dinesh Kumar; K.N. Rai; Jitendra Singh
This article presents a mathematical model describing inward melting process of a phase change material in the presence of convection under the most generalized boundary condition. It is assumed that the material within a container have different geometrical configuration like circular cylinder or sphere. All thermophysical properties of the solid and liquid regions are assumed to be homogeneous. Initially, we convert the mathematical model into an initial value problem in the form of vector matrix representation using a finite difference technique. Two numerical methods; the operational matrix of integration for Bessel functions and finite element Legendre wavelet Galerkin method, are applied to solve the initial value problem. Thus, the obtained results from both methods analyzed for constant (or time depending) temperature or constant (or time depending) heat flux. The whole study is presented in dimensionless form. The effect of Stefan number, Peclet number, Kirpichev number and Biot number on dimensionless temperature profile and dimensionless moving front are illustrated graphically. © 2020 Elsevier Ltd
A computational study of binary eutectic system with convection under volumetric freezing: A Moving Boundary Problem
(Elsevier Ltd, 2024) Susheel Kumar; Vikas Chaurasiya; Jitendra Singh
A reduction in the operating time during the solidification of an eutectic alloy is one of the prime demands in front of the investigators. The classical theory of solidification was not able to offer rapid solidification of an alloy due to not account the structural property of the material. To account convection and external heat sink effect, an external volumetric heat sink is considered and it depends on the distance and time. The thermal conductivity, density, and specific heat of the mushy zone are assumed to be the linear combination of solid and liquid regions properties with a solid fraction distribution. The mathematical model accounts for the solid fraction distribution, which has a linear relationship with the temperature of the mushy zone. The analytical solution of the problem has been determined via similarity transformation. To explore the current study, numerical data of the Copper-Aluminum alloy with 5% Copper is presented. It has been found that with a volumetric heat sink, the rate of solidification becomes faster than usual. Further, the rate of heat removal from the surface accelerates. Convection enhances the rate of freezing of the eutectic alloy. The temperature of the mushy region is going up for the increasing value of the solid fraction in mushy zone, which is lying in [0,1] and when we increase the strength of volumetric heat, then the temperature profile decreases and, the first-interface and second-interface increase gradually in the whole medium. We compared the current result with Tien and Geiger's result, and it is found in good compliance. It is expected that the current study will improve the fundamental understanding of the solidification of an eutectic alloy and reduce the time for freezing, which is useful to design industrial freezing devices for alloys. © 2024 Elsevier Ltd
A new look in heat balance integral method to a two-dimensional Stefan problem with convection
(Taylor and Francis Ltd., 2022) Vikas Chaurasiya; Subrahamanyam Upadhyay; Kabindra Nath Rai; Jitendra Singh
In the current work, we developed a new approximation function for temperature profile with the help of Legendre wavelet in heat-balance integral method (HBIM) to solve a two-dimensional moving boundary problem with moving phase change material (PCM). It is assumed that PCM moves with induced velocity u along x and y direction. In heat transfer mechanism conduction and convection driven by fluid flow in liquid region is considered. To validate the current approximate method, we compared our numerical results with a previous work and found in strong acceptance. In particular, to show the accuracy of the present approximate method, we compared our numerical results against exact solution by converting present problem into a one-dimensional standard melting problem and found in good acceptance. The effect of Péclet number on temperature profile and moving melting front are analyzed in detail. Furthermore, it is shown that with a moving phase change material (PCM) the liquid/solid interface get accelerated and hence, the melting process becomes fast. This study may be applicable in thermal management and energy storage system. © 2022 Taylor & Francis Group, LLC.
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 of solidification on binary eutectic system with moving phase change material
(Elsevier Ltd, 2021) Vikas Chaurasiya; K.N. Rai; Jitendra Singh
A one-dimensional moving boundary problem describing solidification of a eutectic system under imposed material movement occupying a semi-infinite medium is solved for two different cases of solid fraction distribution within the mushy zone. In the first case it is assumed that the solid fraction distribution has a linear relationship with temperature and in the second case solid fraction distribution is varying linearly with distance within the mushy zone. An exact solution of the problem is obtained with the help of a similarity technique. To demonstrate the current study experimental data of Al-Cu solidification are presented. All the thermal-physical properties of each part are discussed in detail for both models. The temperature profile in each region and moving interfaces are calculated for different Peclet number Pe. In the present study it is shown that the moving interfaces are enhanced, growing relatively faster and assisting in the process of phase-transition when material moves in the direction of freeze but transition is delayed when material moves in the reverse direction. It is also shown that mushy zone becomes thinner when surface temperature is lower than the solidus temperature for different Peclet numbers. In addition, the heat removal Q at the surface ξ=0 is shown with respect to time for different Peclet numbers. To validate our study, we compare our results with a previous published work and they are found to be close. © 2021 Elsevier Ltd
A study on cylindrical moving boundary problem with variable thermal conductivity and convection under the most realistic boundary conditions
(Elsevier Ltd, 2022) Vikas Chaurasiya; Abderrahim Wakif; Nehad Ali Shah; Jitendra Singh
The melting of a phase change material is the most applicable process in thermal energy storage system to capture heat transfer phenomena arising in a class of moving boundary problem. Demand of present technology motivates researchers to develop new theories and techniques for thermal management of a material. Experimental work on melting of a material may be difficult and development of robust theoretical formulation in cylindrical geometry with convection is critical. While there is already available study on cylindrical moving boundary problem, but still insufficient modeling of a size-dependent thermal conductivity and convection effect is not addressed properly, which is being considered in this paper and is expected to improve the previous understanding. In this work, a one-dimensional moving boundary problem with size-dependent heat conductivity and convection effect is analyzed in cylindrical geometry. In the mathematical model, we have considered a time-dependent temperature boundary condition which later assumed in periodic form, and a convective boundary condition at the outer surface of the body. The numerical result of the problem is obtained successfully via heat-balance integral method. Our numerical result is compared with a previous work and found in good acceptance. From mathematical framework, it is found that convection delayed melting process. With a size-no independent thermal conductivity, the rate of moving front decreases more in comparison to the fixed thermal conductivity. © 2022 Elsevier Ltd
An analytical study of coupled convective heat and mass transfer with volumetric heating describing sublimation of a porous body under most sensitive temperature inputs: Application of freeze-drying
(Elsevier Ltd, 2023) Vikas Chaurasiya; Jitendra Singh
Sublimation heat-mass transfer has great applications in the pharmaceutical and food industries, such as the preservation of biological products, accelerated freeze-drying (AFD), energy storage systems, microwave freeze-drying, and enabling long-time active covid like vaccines. The current technological demand encourages investigators to provide new knowledge for freeze-drying so that it reduces the high economic cost, prevents materials from being denatured, and remains stable for a long time. In connection with this, it is of key interest to analyze the impact of convective heat and mass transfer, the rate of water vaporization, and the volumetric heating source under the most realistic temperature inputs. Despite the available works on sublimation, there is still a lack of mathematical modeling that accounts for these informations together and is presently being considered. This paper presents a heat and mass transfer problem describing sublimation in a half-porous space. The mathematical model accounts for convective heat/mass transfer and a volumetric heat source within dried and frozen regions. In addition, convection driven by the mass transfer of ice crystals within the dried region is also considered. Three different types of temperature input are placed at the surface x=0 to obtain the rapid sublimation process without harming the material properties. The exact solution to the problem is obtained successfully by using similarity transformation. The impact of various problem parameters on sublimation is comprehensively studied. In this study, it is found that with a volumetric heating source term G0, material sublimates faster than without one. Furthermore, convective heat transfer in terms of Pe1 and Pe2, enhances the temperature within the porous medium, and as a result, material sublimates faster than usual. As the value of the convective term β goes up, a reduction in the temperature field is observed. The temperature of the medium rises as the value of the Kirpichev-like number Ki increases. Similar observation is found in the case of Biot like number Bi. The concentration profile decreases as the value of the Luikov number Lu increases. It is also found that Newton-type temperature input offers a faster sublimation rate in comparison to constant and flux-type temperature input. The analytical results obtained in this study show excellent agreement with previous available results. These results provide a comprehensive theoretical and mathematical understanding of sublimation heat/mass transfer and are expected to be useful in energy storage systems, food technology, and accelerated freeze drying. © 2023 Elsevier Ltd
An analytical study of coupled heat and mass transfer freeze-drying with convection in a porous half body: A moving boundary problem
(Elsevier Ltd, 2022) Vikas Chaurasiya; Jitendra Singh
The freeze-drying of a porous body is the most commonly used process in food technology to capture the coupled heat and mass transfer phenomena which appears in a class of moving boundary problem. The modern technology demand encourages investigators to provide techniques for accelerated food drying (AFD) and preservation of material to be denatured. Experimental study of freeze-drying of a porous body may be difficult and exploration of robust theoretical models with convection is critical. Further, the problem concerning in coupled heat and mass transfer, there is lack of mathematical analysis in the previous literatures which does not accounts the convective heat and mass transfer, convective term due to water vapour and condition for the limitation of sublimation and desorption. It is therefore, essential to develop mathematical formulation to discuss these type of freeze-drying phase change processes. In the current paper, the mathematical work is devoted to study a coupled heat and mass transfer problem describing freeze-drying of a material in a porous half-space. The problem accounts convection in porous frozen, sublimated and desorbed regions and a convective term due to moisture flow of the water vapour in the sublimated region. The exact solution of the proposed problem is obtained via similarity transformation. Condition for the limitation of sublimation and desorption is obtained and illustrated graphically. The effect of various parameters on thermal properties is discussed in detailed. The range values of governing problem parameters are taken as: 0 to 2 for Pe, 0.01 to 1.0 for β, 0.1 to 0.9 for α21, 0.1 to 2.1 for γ1, 0.5 to 2.0 for γ3, 0.2 to 0.8 for ω, 0.01 to 0.85 for (ϵ ‐ ω), 0 to 50 for v and 0.21 to 1.65 for ϵ. In current work, it is shown that the freeze-drying process becomes faster in the presence of convection rather than in the absence of convection. Furthermore, the rate of water vaporization from the surface of the porous body enhanced, as a result freeze-drying process deterred. The current work may be expected aid in accelerated freeze drying (AFD) technology. © 2022 Elsevier Ltd
Analytical study of a moving boundary problem describing sublimation process of a humid porous body with convective heat and mass transfer
(Springer Science and Business Media B.V., 2023) Vikas Chaurasiya; Ankur Jain; Jitendra Singh
Sublimation of a humid porous body occurs commonly in food technology and thermal energy storage system. Especially, in accelerated freeze-drying, preservation of biological materials to be denatured is the prime interest. Despite the available literature on sublimation, there is a general lack of mathematical analysis of the effect of convection in the frozen and vapour regions, and rate of evaporation of water vapour in the vapour region. Therefore, it is essential to explore a mathematical model which accounts for these physical processes. This paper attempts to address these gaps in the modeling of sublimation of a humid porous body. For a specific form of the velocity profile, an exact solution of the current problem is obtained via similarity technique. Particularly, results from the current work are shown to be in strong agreement with the results of a previous work. The impact of various dimensionless problem parameters on the sublimation process is discussed extensively. Condition for sublimation limit is discussed. It is obtained that sublimation can take place only under limit of sublimation curve. It is found that, in the presence of convection, sublimation process becomes fast and the material requires less time than usual to sublimate. Furthermore, higher rate of evaporation of water vapour produces a lower temperature field and slower propagation rate of sublimation interface. © 2023, Akadémiai Kiadó, Budapest, Hungary.
Heat transfer analysis describing freezing of a eutectic system by a line heat sink with convection effect in cylindrical geometry
(De Gruyter Open Ltd, 2022) Vikas Chaurasiya; Dinesh Kumar; Kabindra Nath Rai; Jitendra Singh
The current article devoted to study a moving boundary problem describing freezing of a eutectic system in a semi-infinite medium in cylindrical symmetry. The solidification of the material is considered by a line heat sink of strength Q place at r = 0. The heat transfer is considered due to both mechanism, conduction and convection driven by fluid motion in the liquid region, mushy region and possibly in porous solid phase. The analysis is concerned with extended freezing temperature range between solidus and liquidus temperatures respectively. The solid fraction is considered to have a linear relationship with temperature within the mushy zone. A direct integration method is used to solve the mathematical model, resulting an exact solution of the problem is obtained. To illustrate the application of current study and validity of mathematical model, a numerical example of freezing of an Al-Cu alloy with 5% Cu is presented. In addition, the temperature distribution in each region and position of moving interfaces is shown for different Peclet number. In this work, we obtained that the process of freezing becomes fast in the presence of convection. Moreover, it is shown that for a large value of Q, strength of line heat sink, the freezing of a eutectic alloy increases rapidly. Both eutectic and solid solution alloys come under the application of current study. © 2022 Walter de Gruyter GmbH, Berlin/Boston.
Heat transfer analysis for the solidification of a binary eutectic system under imposed movement of the material
(Springer Science and Business Media B.V., 2022) Vikas Chaurasiya; K.N. Rai; Jitendra Singh
The current article deals with a moving boundary problem describing solidification of a eutectic alloy in a semi-infinite medium. The process of solidification of a eutectic alloy is considered under imposed movement of material in the mushy zone in place of liquidus zone due to imposing an insulated boundary condition at liquidus front. It is assumed that solid fraction fs has a linear, quadratic and cubic relationship with distance within the mushy zone between the solidus and liquidus. An exact solution of the problem is obtained with the help of similarity transformation. A numerical example of the solidification of Al–Cu alloy is presented to demonstrate the application of the current analysis. Solidification of eutectic system is discussed in the absence of material movement and in the presence of material movement in each case of solid fraction distribution. Thus, the temperature profile and moving interfaces in each region are shown for different Peclet numbers Pe. In addition, heat extraction Q from the surface x= 0 is shown with respect to the time for different Pe. The novelty of the current study is transition process becomes fast when material moves in the direction of freeze and hence time for complete freezing of the alloy reduces. Moreover, mushy zone becomes thinner when material moves in the direction of freeze. A comparative study and error analysis between the present work and Tien and Geiger (ASME J Heat Transf 89:230–233, 1967)[9] in linear case of solid fraction are presented in figure and tables. The application of the present analysis is useful for both eutectic and solid solution alloys. © 2021, Akadémiai Kiadó, Budapest, Hungary.
Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties
(De Gruyter Open Ltd, 2022) Jitendra; Vikas Chaurasiya; Kabindra Nath Rai; Jitendra Singh
The main aim of the current article is to describe an uni-dimensional moving boundary problem with conduction and convection effect when thermal conductivity and specific heat varying linearly with temperature and time. The Mathematical model has nonlinearity due to presence of variable thermal conductivity and specific heat. A Legendre wavelet residual approach is introduced to get the solution of the problem with high accuracy. The surface heat flux is taken as an exponent function of time while latent heat is presented as an exponent function of position. Galerkin technique is used to obtain the numerical solution in case of constant physical properties while collocation technique is used for variable thermal physical properties. When it is considered that thermal physical properties are constant then obtained numerical solution was compared with exact solution and found in good acceptance. The effect of convection and variable thermal conductivity with time and temperature on the location of the moving layer thickness is analyzed. Further the effect of Peclet number and other physical parameters on the location of moving layer thickness are discussed in detail. © 2022 Walter de Gruyter GmbH, Berlin/Boston.
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 investigation of a non-linear moving boundary problem describing solidification of a phase change material with temperature dependent thermal conductivity and convection
(Taylor and Francis Ltd., 2023) Vikas Chaurasiya; Jitendra Singh
Problems related to the change in state of a PCM offer a great contribution in the field of heat transfer, describing melting, freezing, and sublimation. While most articles already exist on the mathematical aspects of this type of problem that account for constant thermal conductivity, there is still insufficient modeling and solutions involving convection driven by heated fluid and temperature-dependent thermal conductivity, which are presently being considered. In connection with this, the moving boundary problems become highly non-linear and their exact treatments are restricted. To deal with non-linearity, the numerical solution of the problem is obtained via the LWC technique. Convergence analysis of the non-linear model is extensively presented. Numerical codes are validated against analytical results and found to be in strong agreement. Numerical data of the solidification of the (Formula presented.) alloy is presented for the validation of the current model. It is found that the rate of freezing increases as the value of the dimensionless parameter b increases. The impact of other parameters on freezing is discussed in detail. Furthermore, in the Stefan problem with convection and temperature-dependent thermal conductivity, the rate of freezing is faster than the standard problem, and in the Stefan problem with convection and fixed thermal conductivity. © 2023 Taylor & Francis Group, LLC.
Numerical simulation of a non-classical moving boundary problem with control function and generalized latent heat as a function of moving interface
(Walter de Gruyter GmbH, 2023) Jitendra; Vikas Chaurasiya; Kabindra Nath Rai; Jitendra Singh
In this paper, the work is concerned with the study of moving boundary based on non-classical heat equation that includes a time dependent heat flux and convection. The latent heat is represented as a function of the moving interface. Mathematical model accounts for a control function varying with heat flux. We have obtained the explicit solution of the given mathematical model in the presence of convection and a control function. The Legendre wavelet Galerkin approach (LWGA) is used to solve the mathematical problem. In a particular case, our numerical results were compared with previous results and found to be in excellent agreement. Moreover, the current numerical technique is more efficient and accurate in comparison to the previous available method. An extensive analysis of the problem parameters is presented. It is found that the control function offers a significant contribution during the melting or freezing of a PCM. A greater value of the heat flux accelerates the rate of propagation of interface. Convection heat transfer increases the speed of the interface. Results obtained from the current study are expected to improve the fundamental understanding of heat transfer and aid in sublimation and desorption like physical phenomena. © 2023 Walter de Gruyter GmbH, Berlin/Boston.
Numerical Study of a Non-Linear Porous Sublimation Problem With Temperature-Dependent Thermal Conductivity and Concentration-Dependent Mass Diffusivity
(American Society of Mechanical Engineers (ASME), 2023) Vikas Chaurasiya; Ankur Jain; Jitendra Singh
Sublimation heat transfer occurs in a wide range of engineering processes, such as accelerated freeze drying (AFD), energy storage, and food technology. Particularly in the microwave AFD process, preservation of material with the least possible energy consumption is desirable. In connection with this, it is of interest to analyze the effect of temperature/concentration dependent heat/mass transfer properties. Given the limited literature available on sublimation, there is a general lack of physical understanding of this particular problem. The present work analyzes the nonlinear sublimation process driven by convective heat/mass transfer and evaporation of water vapor using the Legendre wavelet collocation method (LWCM). Results from the present work are shown to be in excellent agreement with the exact solution of the special case of a linear problem. Further, the present numerical technique shows good agreement with finite difference method in case of a completely nonlinear model. The model is used for a comprehensive investigation of the impact of the problem parameters, on the rate of sublimation. It is found that the sublimation rate increases with increasing values of b1 and decreasing values of b2. The impact of other dimensionless problem parameters such as P_eclet numbers Pe1 and Pem, convection due to mass transfer of water vapor b, latent heat of sublimation l0 and Luikov number Lu on sublimation process is also discussed in detail. These observations offer a comprehensive theoretical and mathematical understanding of sublimation heat/mass transfer for improving the performance and efficiency of freeze-drying and related engineering processes. © 2023 by ASME.
Taylor–Galerkin–Legendre-wavelet approach to the analysis of a moving fin with size-dependent thermal conductivity and temperature-dependent internal heat generation
(Springer Science and Business Media B.V., 2023) Vikas Chaurasiya; Subrahamanyam Upadhyay; K.N. Rai; Jitendra Singh
In heat transfer, fins are commonly used to enhance the heat transfer rate from surfaces and are widely applicable in heat exchangers and thermal energy storage systems. The material used for fins typically has a high heat conductivity. While the study of temperature-dependent heat conductivity for fins is already available, an insufficient mathematical description is observed in the case of size-dependent heat conductivity and convective heat transfer. In the current work, a heat transfer study is presented to estimate the temperature field in a moving fin that accounts for size-dependent heat conductivity and internal heat generation that depends on temperature under periodic boundary conditions. To observe the temperature field, we have developed a hybrid numerical method based on Taylor–Galerkin and Legendre wavelets. The stability analysis of the developed method is discussed in detail. Our numerical method shows excellent agreement with the analytical solution obtained in a special case. The impact of problem parameters is extensively discussed. This study shows that fin temperature decreases periodically with a space-dependent heat conductivity. In addition, for a problem which accounts for constant heat conductivity and movable fin, have greater temperature response, and standard problem which accounts for constant heat conductivity have weaker temperature response while it is between them for a problem that includes size-dependent heat conductivity and moving fin. It is shown that fin efficiency can be improved by lowering the value of the Knudsen number. Moreover, fin problem with fixed thermal conductivity offer greater efficiency in comparison with size-dependent thermal conductivity. © 2023, Akadémiai Kiadó, Budapest, Hungary.
Thermal analysis of freeze-drying process with mass transfer of water vapor: Volumetric heating approach
(Elsevier Ltd, 2025) Vikas Chaurasiya; Jitendra Singh
The current work deals with a heat and mass transfer problem describing the freeze-drying process of a phase-change material in a one-dimensional semi-infinite porous medium, which is divided into three regions: prefreezing, primary drying, and secondary drying. The effect of convection on drying rate, induced by residual mass transfer of the water vapor within the desorbed region, followed by the convective term driven by mass transfer of the water vapor within the sublimated region, is considered. An internal heat generation in terms of a volumetric heat source is also accounted for. In addition, fixed and time-dependent boundary conditions are the driving functions at the surface x=0 that cause freeze-drying to occur. The exact treatment of the mathematical model is carried out via similarity transformation. The present analytical work shows excellent agreement with previous available works. It is found that after the end of the sublimation of the material through a porous medium, only a small amount of water is available for desorption. Moreover, a volumetric heat source produces a faster desorption rate than usual. With the heat flux condition, the Kirpichev number shows a pronounced impact on the temperature field and evolution rate of the sublimation and desorption interfaces. © 2025 Elsevier Ltd