Temperature Dependent Internal Heat Generation Research Articles

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.

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.

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.

Transient Response of Longitudinal Fins under Step Changes in Base Temperature and Heat Flux using Lattice Boltzmann Method

The present article reports the transient response of longitudinal fins having linear and non-linear temperature dependent thermal conductivity, convection coefficient and internal heat generation under two cases of base boundary condition, (i) step change in base temperature and (ii) step change in base heat flux. The fin tip is assumed to be adiabatic. Both, linear and non-linear, temperature dependency of thermo-physical properties is addressed in the mathematical formulation and the solution for the above cases is obtained using Lattice Boltzmann method (LBM) implemented in an in-house source code. LBM, being a dynamic method, simulates the macroscopic behavior by using a simple mesoscopic model and offers enormous advantages in terms of simple algorithm to handle even the most typical of boundary conditions that are easy and compact to program even in case of complicated geometries too. Although the transient response of longitudinal fins has been reported earlier, however power law variation of thermo physical properties for the above two base condition has not been reported till date. The present article first establishes the validity of LBM code with existing result and then extends the code for solving the transient response of the longitudinal fin under different sets of application-wise relevant conditions that have not been treated before. Results are reported for several combination of thermal parameter and are depicted in form of graphs.

Thermal exploration of radial porous fin fully wetted with SWCNTs and MWCNTs along with temperature-dependent internal heat generation

The numerical examination of radiation and natural convection in a porous radial fin along with varying internal heat generation with respect to temperature is carried out in the current study. The aim of this study is to scrutinize the heat transfer phenomenon in fin wetted with water-based carbon nanotubes like single-walled carbon nanotubes and multiwalled carbon nanotubes. In the proposed work, the Darcy’s model is employed for the analysis. The modeled equations are nondimensionalized and solved by utilizing Runge–Kutta–Fehlberg method. The impact of relevant parameters on the heat transfer rate is comprehensively explored with an aid of graphs. Here, multiwalled carbon nanotube–water shows better heat transfer from surface of fin compared to single-walled carbon nanotube–water.

Investigation of Ti6Al4V and AA7075 alloy embedded nanofluid flow over longitudinal porous fin in the presence of internal heat generation and convective condition

The thermal attributes of porous fin due to radiation and natural convection have been carried out in the presence of nanofluid flow. The geometry of the fin taken for the analysis is rectangular profiled longitudinal fin. The temperature-dependent internal heat generation condition is also considered along with Darcy’s model. The two types of nanofluid containing titanium alloy () and aluminium alloy (AA7075) immersed in water is considered for the investigation. The modelled nonlinear ordinary differential equation is numerically solved by the Runge–Kutta–Fehlberg technique. The impact of geometric parameter on the heat transfer analysis of the fin due to the flow of both nanofluids is plotted and consequences are physically interpreted. It is observed that the presence of the water-based titanium alloy better enhances the fin heat transfer rate.

Design of computational intelligent procedure for thermal analysis of porous fin model

The importance of rectangular porous fins for the transformation of heat through the system is well-recognized to analyze the physical characteristics of material in practical applications. In this study, a neuro-computing based stochastic numerical paradigm has been designed to study the dynamics of temperature distribution in porous fin model by exploiting the strength of artificial neural network (ANN) modeling integrated with global search exploration with genetic algorithms (GAs) and efficient local search with interior-point technique (IPT). The governing porous fin equation is transformed into an equivalent nonlinear second order ordinary differential equation. Effect of heat on rectangular type fin with thermal conductivity and temperature dependent internal heat generation is measured through stochastic solver based on ANN optimized with GA-IPT in case of two different materials, Silicon nitride Si3N4 and Aluminium Al. The proposed technique ANN-GA-IPT has been applied on transformed equation for multi-times and the accuracy, convergence and robustness of designed model has been validated by analysis of variance test.

Stochastic technique for solutions of non-linear fin equation arising in thermal equilibrium model

In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature dependent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, and genetic algorithm - sequential quadratic programming with different selections of weights. The governing fin equation is transformed into an equivalent non-linear second order ODE. For this transformed ODE model we have performed several simulations to provide the justification of better convergence of results. Moreover, the effectiveness of the designed models is validated through a complete statistical analysis. This study reveals the importance of rectangular fins during the heat transformation through the system.

ANALYTICAL DECOMPOSITION SOLUTIONS FOR HEAT TRANSFER ON STRAIGHT FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY AND INTERNAL HEAT GENERATION

This paper analyses heat transfer across straight convecting fins with temperature dependent thermal conductivity and internal heat generation using the Adomian decomposition method (ADM). The ADM is the preferred analytical scheme adopted to provide approximate solutions to nonlinear equations arising from the dependence of thermal conductivity and heat transfer coefficient on temperature distribution. The effect of parameters such as internal heat generation, thermo geometric and thermal conductivity on the temperature profile and heat flux is studied. Where results reveal that thermo geometric parameter and thermal conductivity causes a significant increase in heat transfer across fin base. This study provides useful insight to fins operational performance in applications such as radiators, boilers, refrigeration devices, oil pipelines amongst others. Comparison of solutions with existing works in literature forms good agreement.

Heat Transfer in Plane with Temperature Dependent Thermal Variables

In this paper we consider heat transfer in a wall with temperature dependent heat conductivity and internal heat generation. It turns out the model considered is non-linear. We employ the classical Lie point symmetry analysis to determine the exact solutions. A number of cases for thermal conductivity and internal heat generation are considered. In some cases the exact solutions are not possible to construct. However, we first use the obtained exact solution as a bench mark for the quasilinear method. Since confidence is established, we then use the quasilinear method to solve some other applicable problem.

An optimization study to investigate non-linearity in thermal behaviour of porous fin having temperature dependent internal heat generation with and without tip loss

This work is devoted to study the temperature distribution, efficiency and optimization of rectangular porous fins for insulated and convective tip conditions. The governing differential equations obtained in the analysis of porous fins are highly non linear in kind. Two approximate analytical techniques, Adomian Decomposition method (ADM) and Differential transformation method (DTM) are adopted to predict the temperature distribution in the porous fin with temperature dependent heat generation, and temperature dependent thermal conductivities of fin material and fluid passing through fin pores. A numerical scheme using finite difference method has been applied to validate the analytical results. The analytical results obtained have been found in accordance with the numerical results. The role of different important parameters have been discussed to understand their importance in the heat transfer through porous fins. Also, a comparison has been presented between solid and porous fins and the results indicate that by selecting an appropriate value of porosity higher heat transfer rate can be achieved.

Surface deformation on thermocapillary convection in a binary fluid with internal heat generation and temperature dependent viscosity

The effects of temperature dependent viscosity and internal heat generation on the onset of steady Bénard-Marangoni convection in a horizontal binary fluid layer heated from below is investigated theoretically. The upper free surface is assumed to be deformable and the lower boundary is considered to be rigid and perfectly insulated to temperature perturbations. The asymptotic solution of the long wavelength is obtained using regular perturbation method with wave number as a perturbation parameter. It is found that the surface deformation of a binary fluid layer enhances the onset of thermocapillary convection while increasing the value of internal heat generation and temperature dependent viscosity will destabilize the binary fluid layer system.