Exact, analytic temperature distributions of pin fins with constant thermal conductivity and power‐law type heat transfer coefficient

Shivanian, Elyas; Campo, Antônio

doi:10.1002/htj.21289

Cited by 2 publications

(3 citation statements)

References 25 publications

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“…When the energy balance equation is applied for the differential section depicted in Figure 1, it yields the following equation: 42

q false(x false) - q false(x + △ x false) = \overset{m}{true} c_{p} false(T - T_{a} false) + h P △ x false(1 - ξ false) false(T - T_{a} false),

where q represents the heat flux,

\overset{m}{true}

represents the mass flow rate of the fluid passing through the porous material, and

\overset{m}{true} = ρ ν △ x P

. c p represents the specific heat capacity of the fluid, h represents the convective heat transfer coefficient, T represents the fin temperature, and T a represents the ambient temperature.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Considering these expressions, the one‐dimensional energy equation of a straight porous pin fin can be formulated by Fourier's law of heat conduction as 42

\frac{d^{2} T}{d x^{2}} - \frac{4 ρ c_{p} g K β {((), T - T_{a})}^{2}}{γ d k_{e f f}} - \frac{4 h false(1 - ξ false) false(T - T_{a} false)}{d k_{e f f}} = 0 .

…”

Section: Problem Formulationmentioning

confidence: 99%

“…When the energy balance equation is applied for the differential section depicted in Figure 1, it yields the following equation: 42 q(x)…”

Section: Problem Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Numerical solution for a porous fin thermal performance problem by application of Sinc collocation method

Nabati

Salehi

Taherifar

2021

Math Methods in App Sciences

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Heat transfer can be enhanced in various equipment by utilizing fins that have pores in their media. Efforts have been made to solve the porous fins problem by numerical, semianalytical, and analytical methods. In this paper, after the extraction of equations and the expression of boundary conditions, the Sinc collocation method is employed for problem solving the first time. By using the properties of the Sinc collocation method, the nonlinear problem is discritized into a nonlinear system of equations. The results support the accuracy and speed of the solution. The effects of effective physical parameters such as fins porosity, thermal conductivity of fin, Raley's number, and Darcy parameter have been considered in solving the problem. Also, the variations in temperature distribution, efficiency, and performance of fins are investigated. Therefore, changes in the parameters of the solving method indicate the convergence of the problem in the domain of many issues. In general, the results show that the proposed method can be considered as a powerful method for solving different types of fines.

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“…When the energy balance equation is applied for the differential section depicted in Figure 1, it yields the following equation: 42

q false(x false) - q false(x + △ x false) = \overset{m}{true} c_{p} false(T - T_{a} false) + h P △ x false(1 - ξ false) false(T - T_{a} false),

where q represents the heat flux,

\overset{m}{true}

represents the mass flow rate of the fluid passing through the porous material, and

\overset{m}{true} = ρ ν △ x P

. c p represents the specific heat capacity of the fluid, h represents the convective heat transfer coefficient, T represents the fin temperature, and T a represents the ambient temperature.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Considering these expressions, the one‐dimensional energy equation of a straight porous pin fin can be formulated by Fourier's law of heat conduction as 42

\frac{d^{2} T}{d x^{2}} - \frac{4 ρ c_{p} g K β {((), T - T_{a})}^{2}}{γ d k_{e f f}} - \frac{4 h false(1 - ξ false) false(T - T_{a} false)}{d k_{e f f}} = 0 .

…”

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Numerical solution for a porous fin thermal performance problem by application of Sinc collocation method

Nabati

Salehi

Taherifar

2021

Math Methods in App Sciences

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Results for the heat transfer of a fin with exponential-law temperature-dependent thermal conductivity and power-law temperature-dependent heat transfer coefficients

Shivanian

AhmadSoltani

Sohrabi

2022

Nonlinear Engineering

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In this article, thermal behavior analysis of nonlinear fin problem with power-law heat transfer coefficient is studied to determine temperature distribution. This new supposition for the thermal conductivity, exponential-law temperature dependent, makes it to be nonlinear that is a general case in some sense. It is shown that the governing fin equation, that is, a nonlinear second-order differential equation, is exactly solvable with proper boundary conditions. To this purpose, the order of differential equation is reduced and then is converted into a total differential equation by multiplying a proper integration operant. An exact analytical solution is given to advance physical meaning, and the existence of unique solution for some specific values of the parameters of the model is demonstrated. The results are shown graphically. It is observed that fin efficiency is decreasing with respect to the power-law mode for heat transfer.

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Exact, analytic temperature distributions of pin fins with constant thermal conductivity and power‐law type heat transfer coefficient

Cited by 2 publications

References 25 publications

Numerical solution for a porous fin thermal performance problem by application of Sinc collocation method

Numerical solution for a porous fin thermal performance problem by application of Sinc collocation method

Results for the heat transfer of a fin with exponential-law temperature-dependent thermal conductivity and power-law temperature-dependent heat transfer coefficients

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