Predicting the Temperature Distribution in Longitudinal Fins of Various Profiles with Power Law Thermal Properties Using the Variational Iteration Method

In this chapter we provide the review and a narrative of some obtained results for steady and transient heat transfer though extended surfaces (fins). A particular attention is given to exact and approximate analytical solutions of models describing heat transfer under various conditions, for example, when thermal conductivity and heat transfer are temperature dependent. We also consider fins of different profiles and shapes. The dependence of thermal properties render the considered models nonlinear, and this adds a complication and difficulty to solve these model exactly. However, the nonlinear problems are more realistic and physically sound. The approximate analytical solutions give insight into heat transfer in fins and as such assist in the designs for better efficiencies and effectiveness.

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“…Biot number E Aspect ratio A temperature distribution in a rectangular fin for varying values of n, M ¼ 1:7. (see also [36]).…”

Section: Conflict Of Interestmentioning

confidence: 85%

Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces

Moitsheki¹,

Ndlovu²,

Ntsime³

2021

Heat Transfer - Design, Experimentation and Applications

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“…An assumption has been made in this inspection that the power exponent of * ( ) k T is greater than zero since most practical problems assume positive thermal conductivity. The heat transmission characteristics are examined in many investigations using non-linearly temperature-dependent * ( ) k T [9,21,22]. The transformed equation derived using Equations ( 5) and ( 7) is given as:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Kader et al [21] inspected the heat transfer and efficiency of a longitudinal fin with power-law temperature dependent thermal conductivity. Ndlovu and Moitsheki [22] employed the variational iteration technique (VIM) to analyze the heat transference through an extended surface with varied profiles, taking into account power-law temperature dependent thermal conductivity.…”

Section: Introductionmentioning

confidence: 99%

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

Sowmya¹,

Sarris

Vishalakshi³

et al. 2021

Symmetry

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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.

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“…Furthermore, the exploration for an analytical solution to the extremely complicated non-linear differential equation of the fluid flow and fin subjected to convection and radiation is a major scientific and engineering priority. Thus, the approximate analytical expression for temperature profile of the fin and boundary layer flow of liquid was addressed by several authors using various methodologies, including the variational iteration method (VIM) (see, Ndlovu and Moitsheki [21]), homotopy perturbation method (HPM) (see, Ranjan et al [22]), and homotopy analysis method (HAM) (see, Zeeshan et al [23]). One such technique is the differential transform method (DTM), which yields an analytical solution in the form of a polynomial.…”

Section: Introductionmentioning

confidence: 99%

Performance analysis of a longitudinal fin under the influence of magnetic field using differential transform method with Pade approximant

Sowmya

Kumar²,

Srilatha

et al. 2022

Z Angew Math Mech

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The temperature distribution in a longitudinal fin with magnetic field due to conductive-convective-radiative heat transfer is debriefed in this research article. Thermal properties of the fin material, such as thermal conductivity and heat transfer coefficient, have been considered to vary non-linearly with local temperature whereas surface emissivity has been taken to be constant. The main governing equation of the current model is developed with the aid of Fourier's law of heat conduction, exponentially temperature-dependent thermal conductivity, Maxwell expression for the effect of the magnetic field, and powerlaw temperature-dependent heat transfer coefficient. This equation is converted into a non-dimensional form using dimensionless variables and then traced out numerically with the assist of Runge-Kutta Fehlberg's fourth-fifth method. Also, the transformed nonlinear energy equation is solved using a DTM-Pade approximant, yielding an approximate closed-form solution. The findings of the analytical and numerical investigation are depicted graphically. The outcomes have divulged that the convective and radiative parameters significantly decrease the temperature distribution and improve convective cooling from the fin surface. The rise in the Hartmann number is responsible for the decreasing of the temperature distribution and it aids in accelerating heat transfer.

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Predicting the Temperature Distribution in Longitudinal Fins of Various Profiles with Power Law Thermal Properties Using the Variational Iteration Method

Cited by 13 publications

References 20 publications

Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces

Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces

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

Performance analysis of a longitudinal fin under the influence of magnetic field using differential transform method with Pade approximant

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