Temperature Dependent Internal Heat Research Articles

Bernstein operational matrix of differentiation to analyze the conductive, convective, and radiative non-linear sublimation model with temperature-dependent internal heat generation

Theoretical modeling of solid-vapor phase change process, known as sublimation, is of much interest in the pharmaceutical industry and freeze-drying technology. While past theoretical studies on sublimation assume that the phase change material (PCM) remains in direct contact with the heat source or sink with no heat loss due to the surrounding temperature, in most practical scenarios, PCM experiences less heat on its surface due to the loss of some amount of heat in the surrounding environment. Considering the impact of heat radiation on the porous surface is essential for ensuring the precision of the phase change process. The present study reports a theoretical model of a sublimation problem where heat generation is in proportion to the local temperature and loss of heat due to thermal radiation occurs in the porous medium. In connection with thermal radiation, a convective boundary condition is assumed at the surface of the porous body. The solution of the non-linear mathematical model is determined numerically via the Bernstein operational matrix of differentiation method. It is found that temperature-dependent heat generation enhances the temperature within the porous medium and thus, the rate of sublimation increases, while it is delayed due to heat loss through the radiation.

Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Analysis of heat and mass transfer of a non-linear convective heat generating fluid flow in a porous medium with variable viscosity

The present study addresses the significance of analyzing the heat and mass transfer characteristics of a non-linear convective fluid flow featuring variable viscosity within a porous medium. Our focus lies on understanding the impact of varying viscosity on the hydromagnetic coupling stress, particularly in the presence of internal heat generation. The fluid is confined within a porous medium, and convection cooling takes place at both wall of the fluid. A key assumption in our investigation is the nonlinearity nature of the buoyancy force, specifically when there is a substantial difference in temperature and concentration within the fluid and its surroundings, the buoyancy force becomes quadratic. The exploration of couple stress fluids, alongside considerations of temperature-dependent internal heat generation and mass transfer, contributes to advancing our understanding of thermal system performance. By accounting for nonlinearity in density, temperature, and concentration, the research aims to provide more accurate results than previous linear models, crucial for optimizing energy consumption in practical applications such as nuclear reactors and heat exchangers. Dealing with this type of problem often pose significant challenges, as they often lack analytical solutions, necessitating the use of more advanced numerical methods or approximation techniques. We employ Spectral Quasilinearisation Method (SQLM) to solve the coupled non-linear boundary value problems (PDE) arising from the model, momentum equation, energy equation, concentration equation, and entropy generation. The obtained results are then validated using the Runge–Kutta method and a good agreement is achieved. The findings for the dimensionless velocity, temperature, mass concentration and entropy generation are presented in graphics and in table manner, and effects of controlling parameters are extensively explained. The results highlight that an increase in variable viscosity leads to an enhancement in the velocity profile, while simultaneously reducing the temperature in the system. Furthermore, increments in the non-linear convection parameter and coupling stress parameter result in an appreciation of the velocity profile, temperature profile, and entropy generation rate.

Taylor–Galerkin–Legendre-wavelet approach to the analysis of a moving fin with size-dependent thermal conductivity and temperature-dependent internal heat generation

Taylor–Galerkin–Legendre-wavelet approach to the analysis of a moving fin with size-dependent thermal conductivity and temperature-dependent internal heat generation

A comparative analysis of dovetail and rectangular fins with insulated tips wetted with ZnO-SAE 50 nanolubricant for energy transfer process

This study focuses on exploring innovative methods of energy conservation specifically through the nonlinear fin equation. To improve the heat transfer efficiency in cooling systems, the research suggests utilizing nano lubricants that possess superior thermo-physical properties. Unlike other nanofluids, the use of nanolubricants can decrease corrosion and abrasion in operational parts such as the bore-piston, gasket, and valve mechanisms. The study concentrates on the temperature distribution in both rectangular and longitudinal dovetail fins utilized in double-pipe heat exchanger applications. The energy equation is formulated to consider radiation, temperature-dependent internal heat generation, and wetted conditions, and is subsequently transformed into a dimensionless form. Numerical solutions to the resulting differential equation are obtained through the utilization of the collocation method. The study explores the use of a specific heat transfer liquid (ZnO-SAE 50) nanolubricant to analyze thermal dispersion in both straight rectangular and dovetail fins. Additionally, it investigates how temperature-dependent internal heat generation impacts convection-conduction heat transfer. The study finds that an increase in surface emissivity results in greater heat transfer through the fin's surface in the presence of nanolubricant.

Effect of temperature-dependent internal heat generation over exponential and dovetail convective-radiative porous fin wetted in hybrid nanofluid

The main objective of this research is to conduct a comparative study of the thermal variations in a dovetail and exponential fin, considering fully wet conditions, ternary nanofluid, and internal heat generation in the form of both linear and non-linear functions. Additionally, the influence of a magnetic field as a driving force for heat transfer systems is taken into account. The mathematical modelling involves the use of dimensionless transformations to convert the energy equation into an ordinary differential equation, which is then analytically solved using the Differential transformation method (DTM). The study focuses on exploring the effects of significant thermal parameters such as radiation conduction, wet factor, heat generation, and ambient temperature on the temperature profile. Graphical analysis is employed to investigate the thermal performance. The main findings indicate that ternary nanoliquid exhibits a higher thermal response compared to nano and hybrid nanoliquid. Moreover, the nonlinear forms of internal heat generation and ternary nanofluids demonstrate a higher rate of heat transfer.

Assessment of transient thermal distribution in a moving porous plate with temperature-dependent internal heat generation using Levenberg–Marquardt backpropagation neural network

ABSTRACT In the present paper, the transient temperature distribution within a moving porous plate is scrutinized by considering the internal heat generation, convection and radiation condition. Furthermore, an effective artificial intelligence technique is proposed for discussing the transient thermal behavior in a moving plate by employing the Levenberg-Marquardt backpropagation network. Using suitable non-dimensional terms, the governing partial differential equation (PDE) is transformed into its non-dimensional form. The transformed equation is then solved using the finite difference method (FDM) and the obtained thermal values (datasets) are used as target values in the process of neural network mapping. This network uses the training, testing, and validation processes to determine the solution of several scenarios established at various process times. The behavior of dimensionless transient temperature profile has been inspected for diverse values of non-dimensional parameters such as heat generation number, radiative parameter, porosity parameter, and conductive parameter with the assistance of graphs. The significant outcomes elucidate that, the transient temperature profile of the porous plate increases with the change in time. Further, it enriches for rise in the magnitude of Peclet number and heat generation number while it drops for enhanced values of porosity parameter.

Exploring the Effect of Peclet Number on the Transient Thermal Response of a Convective-Radiative Moving Porous Fin

In the thermal analysis of moving fins, there have been conflicting results as well as discussion on the effects of Peclet number on the thermal responses of fins. While some authors agreed the increase in Peclet number, increases the fin temperature, the other class of researchers is of the opinion that when the Peclet number increases, the fin temperature decreases. It could be said that many of these divergence views arose from the physics of the problem as well as the mathematical model governing the heat transfer problem. Therefore, in this work, through modeling from the first principle, the effect of Peclet number on the thermal behaviour of convective-radiative moving porous fin is explored. First, a transient thermal model of a convective-radiative rectangular moving porous fin with temperature-dependent internal heat generation is developed. The developed thermal model is nondimensionalized to bring up the needed Peclet number in the dimensional governing equation of the heat transfer process. Thereafter, the model is solved analytically using the Laplace transform method and the effect of Peclet number on the thermal behaviour of the fin is investigated and discussed. It is hoped that the present study will help for better understanding of the thermal problems in extended surfaces.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Computational Investigations of an Internally Heated Convective-Radiative Porous Fin subjected to Magnetic Field: Comparative Methods and Parametric Studies

The concern of this paper is to compare the computational efficiencies and accuracies of three approximate analytical methods; namely, homotopy analysis method (HAM), optimal homotopy asymptotic method (OHAM) and differential transform method (DTM) for the nonlinear thermal performance analysis of a convective-radiative porous fin with temperature-dependent internal heat generation under the influence of magnetic field. To establish the computational accuracies of the three methods, the results of the three series solutions are compared with the results of the developed exact analytical and numerical methods. Also, the symbolic solutions developed in this work are used to explore the impacts of the controlling parameters on the performance of the passive device. It is established that as the coductive-convective, conductive-radiative and magnetic field parameters increase, the fin temperature distribution decreases and hence, the fin thermal efficiency is improved. An increase in temperature distribution in the fin is noticed as the nonlinear thermal conductivity parameter increases. It is envisaged that the present study will give a good insight into the nonlinear analysis of extended surfaces which will aid proper design in thermal systems.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Nonlinear Thermal Response Analysis of an Internally Heated Radiative-Convective Porous Fin subjected to Magnetic Fields using Method of Lines

This paper demonstrated the computational efficiency and accuracy of method of lines for the nonlinear transient thermal response analysis of a radiative-radiative porous fin with temperature-dependent internal heat generation under the influence of magnetic fields. To establish the computational accuracy of the method, the results of the solution are compared with the results of the developed exact analytical method. Also, the numerical solutions through the method of lines are adopted to explore the impacts of the model parameters on the performance of the passive device. It is found that as the conductive-convective, conductive-radiative, and magnetic field parameters increase, the fin temperature distribution in the fin decreases. The temperature distribution in the fin increases through the ?n as the nonlinear thermal conductivity parameter increases. It is hoped that the present study gives a good insight into the nonlinear analysis of the extended surface which will aid the proper design of the extended surfaces in thermal systems.

A Very Simple Procedure for Constructing the Solution of Nonlinear Elliptic PDEs (with Nonlinear Boundary Conditions) Arising from Heat Transfer Problems in Solids

This work presents a procedure for constructing the solution of a second order nonlinear partial differential equation subjected to nonlinear boundary conditions in a very simple and systematic way. The class of equations to be considered here includes, but is not limited to, the partial differential equations which govern the steady-state heat transfer process in bodies with temperature-dependent thermal conductivity and temperature-dependent internal heat source. In addition, it will be considered a large class of nonlinear boundary conditions, especially those arising from the description of the heat exchange process from/to bodies at high temperature levels. Proofs of the solution’s existence and uniqueness are presented.

Effect of Non-Linear Thermal Radiation and Partial slip on Unsteady MHD Flow of a Nanofluid Past a Permeable Stretching Sheet through a Porous Medium with Suction/Injection, convective Heat Transfer

We discuss the effect of non-linear thermal radiation on the boundary layer flow of a thermophoretic magnetohydrodynamics dissipative nanofluid over an unsteady stretching sheet in a porous medium with space and temperature dependent internal heat source/sink. The governing equations are transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using the Shooting Technique. The effects of non-dimensional governing parameters on the velocity, temperature, concentration profiles, friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. We observed that the Radiation parameter (Rd) to enhance the velocity, temperature profiles, heat and mass transfer rates of the fluid and reduce the concentration profiles. An increase in slip parameter (A11), reduces the velocity, enhances the temperature and nano-concentration., Nu and Sh reduce with increasing Rd & A11 on =0. Accuracy of the results compared with the existing ones. Excellent agreement is found with earlier studies.

Dynamics of hybrid nanofluid through a semi spherical porous fin with internal heat generation

Semi-spherical fins are widely considered to be one of the best thermal exchangers available. It is widely employed, including aero planes, chemicals and electronic kits and porous medium is an extensive application that includes drying efficiency enhancement, filtering insulations, hydraulic oils, reactor temperature control and solar collectors. With these applications in perspective, the current study uses Darcy’s model to examine the performance of hybrid nanofluids flowing over a semi-spherical porous fin. Additionally, temperature dependent internal heat generating condition, natural convection and radiation effects are also taken into account. The nonlinear form of an ordinary differential equation (ODE) along with boundary conditions is resolved using RKF 45 method. The numerical results are obtained for various physical constraints and the impact of these constraints on fin surface temperature is discussed via graphs. The results show that increasing an internal heat generation parameter raises temperature, whereas the opposite is true for radiation and convective parameters. Furthermore, the temperature of the hybrid nanofluid is consistently higher than the temperature of the nanofluid.

FRACTAL MODEL OF POROUS FIN WITH TEMPERATURE-DEPENDENT HEAT GENERATION AND ITS NOVEL SOLUTION

Porous fins with temperature-dependent internal heat generation are frequently used to improve performance in a wide range of heat transfer and porous media applications. Thermal analysis of the porous fin fractal model with temperature-dependent heat generation is generated using fractal derivatives and investigated analytically using a novel Maclaurin series method (MSM). Nonlinear temperature distribution in a porous longitudinal fin is produced by the MSM. The porous fin solution is demonstrated using the Sierpinski fractal, which is based on time-dependent heat generation. The effects of the convection parameter, porosity, internal heat production, and generation number parameter on the dimensionless temperature distribution are discussed. MSM results are graphically and tabularly compared to existing solution methods such as HPM, CM, CSCM, LWCM, and GWRM. A comparison study reveals that MSM is a very reliable, accurate, and effective addition in the field of differential equations.

Analysis of Transient Thermal Distribution in a Convective–Radiative Moving Rod Using Two-Dimensional Differential Transform Method with Multivariate Pade Approximant

The transient temperature distribution through a convective-radiative moving rod with temperature-dependent internal heat generation and non-linearly varying temperature-dependent thermal conductivity is elaborated in this investigation. Symmetries are intrinsic and fundamental features of the differential equations of mathematical physics. The governing energy equation subjected to corresponding initial and boundary conditions is non-dimensionalized into a non-linear partial differential equation (PDE) with the assistance of relevant non-dimensional terms. Then the resultant non-dimensionalized PDE is solved analytically using the two-dimensional differential transform method (2D DTM) and multivariate Pade approximant. The consequential impact of non-dimensional parameters such as heat generation, radiative, temperature ratio, and conductive parameters on dimensionless transient temperature profiles has been scrutinized through graphical elucidation. Furthermore, these graphs indicate the deviations in transient thermal profile for both finite difference method (FDM) and 2D DTM-multivariate Pade approximant by considering the forced convective and nucleate boiling heat transfer mode. The results reveal that the transient temperature profile of the moving rod upsurges with the change in time, and it improves for heat generation parameter. It enriches for the rise in the magnitude of Peclet number but drops significantly for greater values of the convective-radiative and convective-conductive parameters.

Melting heat transfer assessment on magnetic nanofluid flow past a porous stretching cylinder

The assessment of melting heat transfer and non-uniform heat source on magnetic Cu–H2O nanofluid flow through a porous cylinder was studied. The transformed differential equations describing the motion of Cu–H2O fluid together with pertinent boundary conditions were handled numerically with the assistance of Keller box method. The ranges of volume fraction of copper particles were taken as 0–25%. The impacts of various governing parameters on the physical measures such as Nusselt number, surface drag force, temperature and velocity were analyzed by representing through graphs and tables. It was noted that the flow was influenced accordingly with the governing parameters. The outcomes showed that the rate of heat exchange improved with elevated Reynolds number, space and temperature-dependent internal heat source and melting parameters. The comparison of our data in relation to those of previous works has been shown.

MHD and Slip Effect in Micropolar Hybrid Nanofluid and Heat Transfer over a Stretching Sheet with Thermal Radiation and Non-uniform Heat Source/Sink

In the presence of slips, non-uniform heat source/sink, thermal radiation and magnetohydrodynamic (MHD), micropolar hybrid nanofluid and heat transfer over a stretching sheet has been studied. The problem is modelled as a mathematical formulation that involves a system of the partial differential equation. The similarity approach is adopted, and self-similar ordinary differential equations are obtained and then those are solved numerically using the shooting method. The flow field is affected by the presence of physical parameters such as micropolar parameter, magnetic field parameter, suction parameter and slip parameter whereas the temperature field is affected by thermal radiation parameter, space-dependent parameter, temperature-dependent internal heat generation/absorption parameter, Prantl number and Biot number. The skin friction coefficient, couple stress and local Nusselt number are tabulated and analysed. The effects of the governing parameters on the velocity profiles, angular velocity profiles and temperature profiles are illustrated graphically. The results of velocity profiles, angular velocity profiles and temperature profiles are also obtained for several values of each parameters involved.

A Study on Thermal Performance of Palladium as Material for Passive Heat Transfer Enhancement Devices in Thermal and Electronics Systems

In this work, the thermal behavior of fin made of palladium material under the influences of thermal radiation and internal heat generation is investigated. The thermal model for the extended surface made of palladium as the fin material is first developed and solved numerically using finite difference method. The influences of the thermal model parameters on the heat transfer behaviour of the extended surface are investigated. The results show that the rate of heat transfer through the fin and the thermal efficiency of the fin increase as the thermal conductivity of the fin material increases. This shows that fin is more efficient and effective for a larger value of thermal conductivity. However, the thermal conductivity of the fin with palladium material is low and constant at the value of approximately 75 W/mK in a wider temperature range of -100℃ and 227℃ . Also, it is shown that the thermal efficiencies of potential materials (except for stainless steel and brass) for fins decrease as the fin temperatures increase. This is because the thermal conductivities of most of the materials used for fins decreases as temperature increases.However, keeping other fin properties and the external conditions constant, the thermal efficiency of the palladium is constant as the temperature of the fin increases within the temperature range of -100℃ and 227℃. And outside the given range of temperature, the thermal conductivity of the material increases which increases the efficiency of the fin. The study will assist in the selection of proper material for the fin and in the design of passive heat enhancement devices under different applications and conditions.

Application of an Integral Numerical Technique for a Temperature-Dependent Thermal Conductivity Fin with Internal Heat Generation

A numerical study of convective heat transfer in a longitudinal fin with temperature-dependent thermal conductivity and internal heat generation is undertaken. Integral calculations are implemented on each generic element of the discretized problem domain. The resulting systems of nonlinear equations are solved efficiently because of the coefficient matrix sparsity to yield both the dependent variable and its flux. In order to validate the formulation, the effects of the thermogeometric parameter, nonlinearity due to the temperature-dependent thermal conductivity, and of the heat transfer coefficient on the fin temperature distribution are investigated. The results are found to be in agreement with those for similar problems described in the literature and with the physics of the problem.