Thermo-geometric Parameter Research Articles

Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM‐PA)

AbstractTemperature distribution, and efficiency of a rectangular profiled longitudinal fin are examined in this investigation with the impact of the magnetic field. By exploiting appropriate non‐dimensional terms, the heat transfer equation incorporating temperature‐dependent thermal conductivity, heat transfer coefficient, and Maxwell expression for the effect of the magnetic field yield a dimensionless nonlinear ordinary differential equation (ODE) with corresponding boundary conditions (BCs). Sumudu transform method with Pade approximant (STM‐PA) has been employed to obtain an analytical solution for the temperature profile of a longitudinal rectangular fin subjected to a uniform magnetic field under multi‐boiling heat transfer. The STM‐PA results are compared to the Runge‐Kutta Fehlberg's fourth‐fifth (RKF‐45) order technique for computational verification and are observed to be in good accordance. The behavior of dimensionless temperature profile has been explicated graphically for diverse values of non‐dimensional parameters such as thermal conductivity parameter, Hartmann number, and thermogeometric parameter. The results of this study show that as the thermal conductivity parameter enriches, the temperature profile of the longitudinal fin improves, whereas it declines for the Hartmann number and thermogeometric parameter. Under multi‐boiling heat transference, fin efficiency varies significantly depending on the impact of pertinent variables.

Thermal and multi-boiling analysis of a rectangular porous fin: A spectral approach

Abstract Fins are commonly utilized to enhance (dissipate) heat in various engineering systems that include heat exchangers. In the present investigation, the impact of multi-boiling and thermo-geometric factors on a convective–radiative rectangular porous fin subjected to the temperature-dependent thermal conductivity of linear and non-linear variations is discussed extensively. The governing equations describing the problem were formulated with the aid of Darcy law. Similarity variables were employed to reduce the models to non-dimensional form. The solution of the governing dimensionless equation is approximated using the RK4 and spectral local linearization methods. Before parametric analysis, the agreement between the two numerical methods was established. Findings reveal that the non-linear variation of thermal conductivity shows better thermal efficiency than the linear variation. An improvement in the multi-boiling heat transfer parameter retards the temperature distribution of the fin. Furthermore, increasing the thermo-geometric parameter will result in a progressive decrease in the temperature of the fin. The results obtained in this work will aid in the design of heat exchangers and other heat transfer equipments.

Numerical investigation of efficiency of fully wet porous convective-radiative moving radial fin in the presence of shape-dependent hybrid nanofluid

The main focus of the study is a fully wet porous fin of radial profile exposed to convective-radiative heat exchange with the hybrid nanofluid flowing past it with a constant velocity of U. In the analysis, spherical-spherical, spherical-cylindrical, and spherical-platelet shape combinations of two nanoparticles are considered. The mixture model is employed to assess all the thermophysical attributes of the hybrid nanofluid except thermal conductivity and dynamic viscosity, which are estimated by applying the nanoparticle volume fraction-based interpolation method. The fin model with the applied conditions results in an ordinary differential equation which is made dimensionless and then numerically resolved by applying the Runge Kutta Fehlberg (RKF) 4-5th ordered technique. The effect of Peclet number, wet fin parameter, thermogeometric parameter, nanoparticle volume fraction, convective parameter, radiative parameter, exponential index, empirical shape factor and ambient temperature (dimensionless) on the energy field and thermal gradient profiles of the radial fin subjected to shape-dependent hybrid nanofluid flow has been graphically analysed. Furthermore, the thermal fin efficiency has been modelled and its variation with the significant parameters has been examined. One of the major outcomes was that efficiency increases with nanoparticle volume fraction. Further, it is significantly affected by the shape factor of the nanoparticles and achieves the highest value for spherical-platelet combination. The results obtained motivate further study of nanotechnology assisted extended surface technology.

Exploration of Temperature Distribution through a Longitudinal Rectangular Fin with Linear and Exponential Temperature-Dependent Thermal Conductivity Using DTM-Pade Approximant

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, the thermal distribution of a fin is comparatively studied for both exponentially varying temperature-dependent thermal conductivity and linearly varying temperature-dependent thermal conductivity. Further, the thermal distribution of a longitudinal fin is examined by using ANSYS software with different fin materials. Many physical mechanisms can be explained by ordinary differential equations (ODEs) with symmetrical behavior, the significance of which varies based on the perspective. The governing equation of the considered problem is reduced to a non-linear ODE with the assistance of dimensionless terms. The resultant equation is solved analytically using the DTM-Pade approximant and is also solved numerically using Runge-Kutta Fehlberg’s fourth-fifth (RKF-45) order method. The features of dimensionless parameters influencing the fin efficiency and temperature profile are discussed through graphical representation for exponentially and linearly varying temperature-dependent thermal conductivity. This study ensures that the temperature field enhances for the higher magnitude of thermal conductivity parameter, whereas it diminishes for diverse values of the thermo-geometric parameter. Also, greater values of heat generation and heat transfer parameters enhance the temperature profile. Highlight: Thermal distribution through a rectangular profiled straight fin is examined. Linear and non-linear thermal properties are considered. The combined impact of conduction, convection, and internal heat generation is taken for modeling the energy equation of the fin. Thermal simulation is performed for Aluminum Alloy 6061 (AA 6061) and Cast Iron using ANSYS.

Thermal stress and temperature distribution of an annular fin with variable temperature-dependent thermal properties and magnetic field using DTM-Pade approximant

The thermal distribution within a rectangular profiled annular fin in the presence of a magnetic field and internal heat generation is examined in the present inspection. Furthermore, the linear and nonlinear temperature-dependent thermal conductivity and heat transfer coefficient are considered. The heat transfer equation is nondimensionalized using dimensionless terms, which results in a nonlinear ordinary differential equation (ODE) with related boundary conditions, which is then solved analytically and numerically using the DTM-Pade approximant and Runge–Kutta Fehlberg’s fourth-fifth order (RKF-45) approach respectively. Moreover, the effect of several non-dimensional parameters on temperature gradient, radial, and tangential thermal stresses is explained with the assistance of graphs. The significant outcomes of the investigation reveal that enhancing the heat generation parameter strengthens temperature distribution significantly, but increasing the magnitude of the thermo-geometric parameter and magnetic field parameter leads to the lessening of thermal distribution through the fin.

RETRACTED: Thermal analysis of an annular fin under multi-boiling heat transfer coefficient using differential transform method with Pade approximant (DTM-Pade)

The convective heat transfer between the object and surrounding environment can be improved by increasing the surface area. This can be done by mounting an annular/radial fin to a cylindrical surface and thus enormous heat is transferred by the annular fin. Motivated by this fact, the temperature distribution and thermal stresses of an annular fin with internal heat generation under multi-boiling heat transfer are examined using the differential transform method (DTM)-Pade approximant. The governing equation and corresponding boundary conditions are transformed into a highly nonlinear ordinary differential equation (ODE) by introducing suitable non-dimensional terms. The resultant transformed ODE is solved analytically using DTM-Pade approximant. The results achieved from DTM-Pade and Runge-Kutta Fehlberg fourth-fifth (RKF-45) technique are compared for numerical validation and are found to be close to each other. The performance of the fin and aspects of dimensionless temperature profile has been elucidated graphically with the impact of dimensionless parameters. Furthermore, the results of this scrutiny manifest that the temperature profile of the fin increases with the impact of thermal conductivity parameter and heat generation parameter whereas it decreases for thermo-geometric parameter. Fin efficiency varies significantly with the impact of prescribed parameters under multi boiling heat transfer cases. The radial and tangential stress distribution are more in the case of radiation heat transfer compared to other cases.

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.

Heat transfer analysis of an inclined porous fin using Differential Transform Method

ABSTRACT The thermal attribute of an inclined porous fin of a longitudinal profile has been determined in the presence of convection and radiation effect. The Darcy’s model is utilised here. The governing equation, nonlinear second-order ordinary differential equation, has been derived. An effective analytical method, Differential Transform Method, has been implemented to find the solution of the dimensionless problem. The obtained outcome has been compared with that of the Adomian Decomposition Method as well as Runge–Kutta–Fehlberg method. The efficiency of the fin for different values of dimensionless parameters has been investigated. The influence of significant parameters has been illustrated with graphical interpretation. The thermo-geometric parameter and radiative parameter support in heat transfer rate from fin surface.

A new analytical solution of longitudinal fin with variable heat generation and thermal conductivity using DRA

In this paper, nonlinear differential equation for a longitudinal fin (LF) heat transfer with thermal conductivity and heat generation that depends on temperature is solved numerically by employing Runge–Kutta technique of fourth-order (RK4) featuring shooting technique and analytically via a new modified analytical technique called Duan–Rach method. The physical model of the heat transfer was utilized to examine the influences of the thermogeometric parameters, heat transfer rate and variable thermal conductivity on the temperature profile and efficiency of LF. The obtained outcomes show that the temperature profile of fin, heat transfer and the efficiency of the fin are considerably impacted by the fin factor of thermogeometric. The analytical outcomes by a new efficient algorithm are compared with the numerical computations of the RK4 featuring shooting techniques and various available literature outcomes to achieve the precision of the proposed technique. Obtained results show obviously the fidelity of the suggested approach. Flow model of longitudinal fin and the effect of thermogeometric parameter on dimensionless temperature distribution.

Effects of particle fouling and magnetic field on porous fin for improved cooling of consumer electronics

AbstractThe combined effect of particulate fouling and magnetic field on the efficiency of a convective–radiative porous fin heatsink with temperature‐dependent thermal conductivity is presented. The developed thermal models are solved using differential transformation method. The effects of thermal conductivity, porosity, convection, radiation parameter, and thermal fouling number on the fin thermal efficiency are investigated. The presence of thermal fouling on the surface of the fin is shown to increase the temperature distribution. The presence of particle deposition on the fin surface significantly decreases the rate of heat transfer as additional thermal resistance of the fouling layer decreases the thermal performance of porous fin heatsink. Moreover, the fin efficiency decreases as the value of fouled Biot, Darcy, radiation number, and thermogeometric parameter increases. It is established that Mf < Mc, which indicates that the efficiency of the fouled fin is greater than the efficiency of the clean fin. Furthermore, the result of the present study is validated with the established results of Chebyshev spectral collocation method and fourth‐order Runge–Kutta with shooting method and an error margin of 0.000000023 is established.

Exact solution of a nonlinear fin problem of temperature-dependent thermal conductivity and heat transfer coefficient

This paper studies a class of nonlinear problems of convective longitudinal fins with temperature-dependent thermal conductivity and heat transfer coefficient. For thermal conductivity and heat transfer coefficient dominated by power-law nonlinearity, the exact temperature distribution is obtained analytically in an implicit form. In particular, the explicit expressions of the fin temperature distribution are derived explicitly for some special cases. An analytical expression for fin efficiency is given as a function of a thermogeometric parameter. The influences of the nonlinearity and the thermogeometric parameter on the temperature and thermal performance are analyzed. The temperature distribution and the fin efficiency exhibit completely different behaviors when the power-law exponent of the heat transfer coefficient is more or less than negative unity.

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.

Optimum Design and Performance Analyses of Convective-Radiative Cooling Fin under the Influence of Magnetic Field Using Finite Element Method

In this study, the optimum design dimensions and performance analyses of convective-radiative cooling fin subjected to magnetic field are presented using finite element method. The numerical solutions are verified by the exact analytical solution for the linearized models using Laplace transform. The optimum dimensions for the optimum performance of the convection-radiative fin with variable thermal conductivity are investigated and presented graphically. Also, the effects of convective, radiative, and magnetic parameters as well as Biot number on the thermal performance of the cooling fin are analyzed using the numerical solutions. From the results, it is established that the optimum length of the fin and the thermogeometric parameter increases as the nonlinear thermal conductivity term increases. Further analyses also reveal that as the Biot number, convective, radiative, and magnetic parameters, increases, the rate of heat transfer from the fin increases and consequently improves the efficiency of the fin. Additionally, effects of the thermal stability values for the various multiboiling heat transfer modes are established. It is established that, in order to ensure stability and avoid numerical diffusion of the solution by the Galerkin finite element method, the thermogeometric parameter must not exceed some certain values for the different multiboiling heat transfer modes. It is hope that the present study will enhance the understanding of thermal response of solid fin under various factors and fin design considerations.

Investigation of Simultaneous Effects of Surface Roughness, Porosity, and Magnetic Field of Rough Porous Microfin Under a Convective–Radiative Heat Transfer for Improved Microprocessor Cooling of Consumer Electronics

The ever-increasing demand for high-processing compact electronic systems has unequivocally called for improved microprocessor performance. However, increasing microprocessor performance requires increasing power and on-chip power density, both of which are associated with increased heat dissipation. Electronic cooling using fin has been identified as a reliable cooling approach in miniaturized electronic systems. However, an investigation into the thermal behavior of fin would help in the design of miniaturized, effective heatsinks for reliable microprocessor cooling. The aim of this paper is to investigate the simultaneous effects of surface roughness, porosity, and magnetic field on the performance of a porous microfin under a convective-radiative heat transfer mechanism. The developed thermal model considers variable thermal properties according to linear, exponential, and power laws, and is solved using the Chebychev spectral collocation method. A parametric study is carried out using the numerical solutions to establish the influences of porosity, surface roughness, and the magnetic field on the microfin thermal behavior. The results of the simulation establish that thermal efficiency of the microfin is significantly affected by the porosity, magnetic field, geometric ratio, nonlinear thermal conductivity parameter, thermogeometric parameter, and the surface roughness of the microfin. Furthermore, the study establishes that the fin efficiency ratio which is the ratio of efficiency of the rough fin to the efficiency of the smooth fin is found to be greater than unity when the rough and smooth fins of equal geometrical, physical, thermal, and material properties are subjected to the same operating condition.

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.

Corrected quasi one-dimensional heat conduction equation for the analysis of straight fins of uniform profile

Justification of the quasi one-dimensionality assumption in the analysis of fins of various shapes has been traditionally based on the criterion that fins have large slenderness ratios, i.e., large length and small thickness. This simplistic approach is based on a mere geometric consideration that obviates the implications of the two-dimensional heat paths in the axial and transversal directions that occurs in fins. Beginning with the formal differential formulation of the two-dimensional heat conduction equation for straight fins of uniform profile and the appropriate boundary conditions, the central objective of the present paper is to develop a systematic mathematical procedure that revolves around a new corrected quasi one-dimensional heat conduction equation that is more physically sound. The step-by-step mathematical development depends on two controlling parameters: (1) a thermo-geometric parameter, i.e., the transverse Biot number based on the half-thickness, and (2) a geometric parameter, i.e., the slenderness ratio. The computed two-dimensional heat transfer rates clearly demonstrate that the corrected quasi one-dimensional heat conduction equation captures the two-dimensional heat paths flawlessly and as a direct result is better than the standard quasi one-dimensional heat conduction equation. The discrepancy between the corrected quasi one-dimensional and the standard quasi one-dimensional heat transfer rates is of the order of 10%.

Performance of convective-radiative porous fin heat sink under the influence of particle deposition and adhesion for thermal enhancement of electronic components

This work presents an investigation on the effect of particle deposition and adhesion on the thermal behaviour of convective-radiative porous fin heat sink using Differential Transform method (DTM). The numerical solutions of the developed thermal models are also used to study the influence of thermal conductivity, porosity, convection and radiation factors on the thermal distribution and efficiency of the fin. The analysis reveals the impact of particles or thermal fouling on the surface of the fin, which causes a rise in the temperature uniformity and distribution in the fin while reducing the rate of heat transfer from the fin. Moreover, the study also establishes that the heat transfer rate decreases due to particle deposition on the fin which depends on the particle size, particle density and cooling air flow rate. The fin efficiency decreases with increasing value of the fouled Biot, Darcy and radiation numbers, and thermo-geometric parameter. Furthermore, the analysis shows that the efficiency of the fouled porous fin is always greater than the efficiency of the clean porous fin. The result of this study shows an excellent agreement with the established results of Runge-Kutta with shooting method.

Improved thermal management of computer microprocessors using cylindrical-coordinate micro-fin heat sink with artificial surface roughness

In this work, numerical study on the thermal behaviour and subsequent heat transfer enhancement of cylindrical micro-fin heat sink with artificial surface roughness is analyzed using Chebychev spectral collocation method. The developed thermal models consider variable thermal properties in accordance with linear, exponential and power laws. The numerical solutions are used to carry out parametric studies and to establish the thermal performance enhancement of the rough fins over the existing smooth fins. Following the results obtained from simulations, it is established that the thermal efficiency of the micro-fin is significantly affected by the geometric ratio, nonlinear thermal conductivity parameter, thermo-geometric parameter and the surface roughness of the micro-fin. In addition, the results show that geometric ratio and the surface roughness of the fin enhance its thermal performance. The fin efficiency ratio which is the ratio of the efficiency of the rough fin to the efficiency of the smooth fin is found to be greater than unity when the rough and the smooth fins are subjected to the same operations with the same geometrical, physical, thermal and material properties. From the investigation, it is established that improved thermal management of electronic and thermal systems can be achieved through the use of artificial rough surface fins or heat sink.

Variation of Parameters Method for Thermal Analysis of Straight Convective- Radiative Fins with Temperature Dependent Thermal Conductivity

In this study, thermal performance across straight convecting- radiating fin with temperature dependent thermal conductivity is considered. The variation of parameters (VPM) is adopted to analyze the nonlinear higher order differential equations arising due to thermal conductivity and heat transfer coefficient on temperature distribution. Pertinent parameters such as thermo geometric and radiation parameters effect on temperature profile are investigated. Result obtained illustrates that quantitative increase of thermo geometric parameter causes a significant increase in temperature distribution due to increase in ratio of convective to conduction heat transfer which influence is significant toward fin base while increasing radiation parameter leads to decrease in temperature distribution due to increasing heat transfer from fins surface to ambient environment . Comparative analysis of result obtained in study against literature proves to be in satisfactory agreement. Therefore study provides useful insight to fins operational performance in applications such as radiators, boilers, refrigeration devices, oil pipelines amongst others.

Prediction of Temperature distribution in Straight Fin with variable Thermal Conductivity and Internal Heat Generation using Legendre Wavelet Collocation Method

Due to increasing applications of extended surfaces as passive methods of cooling, study of thermal behaviors and development of mathematical solutions to nonlinear thermal models of extended surfaces have been the subjects of research in cooling technology over the years. In the thermal analysis of fin, various methods have been applied to solve the nonlinear thermal models. This paper focuses on the application of Legendre wavelet collocation method to the prediction of temperature distribution in longitudinal rectangular fin with temperature-dependent thermal conductivity and internal heat generation. The numerical approximations by the method are used to carry out parametric studies of the effects of the model parameters on the temperature distribution in the fin. The results show that the thermal performance of the fin is favoured at low values of thermogeometric parameter and internal heat generation decreases the performance of the fin. The results can serve as verification of the solutions of other methods of analysis of the component.