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Transient Conjugate Heat Transfer Analysis of a Cylindrical Pin Fin Made by Functionally Graded Material Embedded in the Turbulent Flow

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Abstract

In this study, a transient conjugate heat transfer analysis of a wall-mounted finite-height cylindrical pin fin with H/D = 3 made by functionally graded material (FGM) embedded in the turbulent flow is numerically presented by means of the finite volume approach. Considerations are carried out for a constant Reynolds number of 30,000 based on the fin diameter and free-stream velocity. For the FGM fin, two linearly inward and outward conductivity variations under two various inhomogeneity indices of 0.4 and 0.8 are tested and the obtained results are validated against the available data for the fin with homogeneous material (H.M). It was found that the FGM fin with inward conductivity variation and β = 0.8 develops minimum and maximum temperature at the fin-base and fin tip, respectively. On the other hand, the minimum and maximum temperature gradients along the fin axis occur for FGM fin with inward conductivity variation having β = 0.8 and H.M fins, respectively. Finally, it is revealed that the FGM fin with inward conductivity variation and β = 0.8 and H.M fin provide maximum and minimum heat transfer rates with approaching turbulent flow, respectively.

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Abbreviations

\(A\) :

Area

\(C_{{\text{D}}}\) :

Drag coefficient

\(c_{{\text{p}}}\) :

Specific heat

\(C_{{\text{p}}}\) :

Pressure coefficient

\(D\) :

Diameter of cylindrical pin fin

\(F_{{\text{D}}}\) :

Drag force

\(H\) :

Height of cylindrical pin fin

\(k\) :

Conductivity

\(k_{0}\) :

Conductivity of homogeneous material

\(n\) :

Normal vector

\(p\) :

Pressure

\(p_{\infty }\) :

Free-stream pressure

\(q^{\prime\prime}\) :

Heat flux

\({\text{Re}}\) :

Reynolds number

\(t\) :

Time

\(\Delta t\) :

Time step

\(T\) :

Temperature

\(T_{\infty }\) :

Free-stream temperature

\(T^{*}\) :

Non-dimensional flow time

u :

Streamwise velocity

\(U_{\infty }\) :

Free-stream velocity

\(v\) :

Lateral velocity

\(w\) :

Spanwise velocity

\(x\) :

Streamwise coordinate

\(y\) :

Lateral coordinate

\(z\) :

Spanwise coordinate

\(\alpha\) :

Angular location

\(\beta\) :

Inhomogeneity index

\(\theta\) :

Non-dimensional temperature

\(\rho\) :

Density

\(\tau\) :

Non-dimensional time step

\(\nu\) :

Dynamic viscosity

\(f\) :

Fluid

\(s\) :

Solid

\(w\) :

Wall

\(-\) :

Time-averaged

\({\text{FGM}}\) :

Functionally graded material

\({\text{H}}.{\text{M}}\) :

Homogeneous material

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran

    Mousa Kafili Kurdkandi & Rahim Hassanzadeh

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  1. Mousa Kafili Kurdkandi
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  2. Rahim Hassanzadeh
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Correspondence to Rahim Hassanzadeh.

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Kafili Kurdkandi, M., Hassanzadeh, R. Transient Conjugate Heat Transfer Analysis of a Cylindrical Pin Fin Made by Functionally Graded Material Embedded in the Turbulent Flow. Arab J Sci Eng 48, 12625–12643 (2023). https://doi.org/10.1007/s13369-022-07374-4

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