Thermal Optimization of an Array of Needle-Shaped using Constructal Theory

Subject Areas : optimization and simulation

Maryam  Hoseinzadeh ¹ (Department of Mechanical Engineering, Shahrekord University, Iran)
Afshin  Ahmadi Nadooshan ² (Department of Mechanical Engineering, Shahrekord University, Iran)
Morteza  Bayareh ³ (Department of Mechanical Engineering, Shahrekord University, Iran)

Received: 2018-04-27 Accepted : 2018-08-20 Published : 2018-09-01

Keywords: Needle-Shaped Fins, Constructal Theory, Forced Convection, Reynolds Number, Optimization,

Abstract :

In the present paper, the constructal theory is employed to determine the optimal configuration of three rows of needle-shaped fins. The heat transfer across the fins is due to laminar forced convection. Second order upwind scheme is used for discretization of the diffusion terms of governing equations. The pressure–velocity coupling is performed using the SIMPLE algorithm. The heat transfer is optimized subject to constant fin volume. The effect of Reynolds number and thermal conductivity on the optimal configuration is investigated. The results obtained from the present simulations are in good agreement with the numerical results. The results show that pin–fins flow structure leads to the best performance when the pin–fin diameters and heights are non-uniform. At Re = 100 and 200, the optimal value of is 1.3. It is revealed that at Re = 50, the optimal value for is approximately 1.1. The results demonstrate that heat transfer rate is an increasing function of the Reynolds number.

References:

[1]     Incropera, F. P., DeWitt D. P. Introduction to Heat Transfer. J. Wiley & Sons, 1990.

[2]     Almogbel, M., Bejan, A., Cylindrical Trees of Pin Fins, International Journal of Heat and Mass Transfer, Vol. 43, No. 23, 2000, pp. 4285-4297.

[3]     Bello-Ochende, T., Meyer, J. P., and Bejan, A., Constructal Multi-Scale Pin–Fins, International Journal of Heat and Mass Transfer, Vol. 53, No. 13, 2010, pp. 2773-2779.

[4]     Yang, A., Chen, L., Xie, Z., Feng, H., and Sun, F., Constructal Heat Transfer Rate Maximization for Cylindrical Pin-Fin Heat Sinks, Applied Thermal Engineering, Vol. 108, 2016, pp. 427-425.

[5]     Bello-Ochende, T., Bejan, A., Constructal Multi-Scale Cylinders in Cross-Flow, International Journal of Heat and Mass Transfer, Vol. 48, No. 7, 2005, pp. 1373-1383.

[6]     Page, L. G., Bello-Ochende, T., and Meyer, J. P., Constructal Multi Scale Cylinders with Rotation Cooled by Natural Convection, International Journal of Heat and Mass Transfer, Vol. 57, No. 1, 2013, pp. 345-355.

[7]     Olakoyejo, O. T., Meyer, J. P., Numerical Optimization of Square Pin-Fins for Minimum Thermal Resistance with Non-Uniform Design Dimensions, International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, 14–16 July, 2014.

[8]     Goshayeshi, H. R., Vafa Toroghi, R., An Experimental Investigation of Heat Transfer of Free Convection on Triangular Fins in Order to Optimize the Arrangement of Fins, International Journal of Science, Technology and Society, Vol. 2, No. 5, 2014, pp. 152-160.

[9]     Goodarzian, H., Sahebi, S. A., Shobi, M. O., and Safaee, J., A Collocation Solution on the Optimization of Straight Fin with Combined Heat and Mass Transfer, International Journal of Physical Sciences, Vol. 6, No. 9, 2011, pp. 2268-2275.

[10]  Rubio-Jimenez, C. A., Kandlikar, S. G., and Hernandez-Guerrero, A., Numerical Analysis of Novel Micro Pin Fin Heat Sink with Variable Fin Density, IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 2, No.5, 2012, pp. 825-833.

[11]  Salimpour, M. R., Sharifhasan, M., and Shirani, E., Constructal Optimization of Microchannel Heat Sinks with Noncircular Cross Sections, Heat Transfer Engineering, Vol. 34, No. 10, 2013, pp. 863-874.

[12]  Jadhav, R. S., Balaji, C., Fluid Flow and Heat Transfer Characteristics of a Vertical Channel with Detached Pin-Fin Arrays Arranged in Staggered Manner on Two Opposite Endwalls, International Journal of Thermal Sciences, Vol. 105, 2016, pp. 57-74.