On Numerical Investigation of Semi-empirical Relations Representing Local Nusselt Number at Lower Nozzle-target Spacing’s

Authors

1 MPSTME – NMIMS University, India

2 Veermata Jijabai Technological Institute, Mumbai, India

3 Qassim University, Saudi

4 Mechanical Engineering Department, Faculty of Engg., IIUM, Kuala Lumpur, Malaysia

Abstract

Examining the cooling rate using impingement of air jet finds a wide application in electronic packaging and micro-scale fluid heat interaction systems, While the prediction of Nusselt profile at low nozzle-target spacing is a big issue. The plot of area average Nusselt number magnitude against the nozzle-target spacing (Z/d) shows a gradual decrement in the profile upto Z/d = 1 and beyond that is steady. The present work aims in anticipating the profile of Nusselt number using semi-empirical relations. These semi-empirical relations are derived using using regression analysis which is carried out between Re, Z/d and local Nusselt number.The data required for regression are obtained through computation. Numerical simulations are accomplished for different impinging and geometric parameters. The semi-empirical power law relations are correlated between Z/d and Re. These are predicted differently for four distinct region of heat sink (stagnant point, near jet region, far jet region, near wall region). The developed correlations are found to bear negative exponent with Z/d and positive exponent with Re. The negative power of r/d and Z/d varies from 0.23 – 0.64 and 0.0025 – 0.38, respectively, While the exponents of Re varies in the positive range of 0.4-0.76.

Keywords


1.     Katti, V. and Prabhu, S., "Experimental study and theoretical analysis of local heat transfer distribution between smooth flat surface and impinging air jet from a circular straight pipe nozzle", International Journal of Heat and Mass Transfer,  Vol. 51, No. 17-18, (2008), 4480-4495.

2.     Alimohammadi, S., Murray, D.B. and Persoons, T., "Experimental validation of a computational fluid dynamics methodology for transitional flow heat transfer characteristics of a steady impinging jet", Journal of Heat Transfer,  Vol. 136, No. 9, (2014), 091703.

3.     Gorji, S., Seddighi, M., Ariyaratne, C., Vardy, A., O’Donoghue, T., Pokrajac, D. and He, S., "A comparative study of turbulence models in a transient channel flow", Computers & Fluids,  Vol. 89, (2014), 111-123.

4.     Langtry, R.B. and Menter, F.R., "Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes", AIAA Journal,  Vol. 47, No. 12, (2009), 2894-2906.

5.     Malan, P., Suluksna, K. and Juntasaro, E., "Calibrating the),-reo transition model for commercial cfd", in Proceedings of the 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition., (2009), 1-20.

6.     Angioletti, M., Nino, E. and Ruocco, G., "Cfd turbulent modelling of jet impingement and its validation by particle image velocimetry and mass transfer measurements", International Journal of Thermal Sciences,  Vol. 44, No. 4, (2005), 349-356.

7.     Li, H.-Y., Chao, S.-M. and Tsai, G.-L., "Thermal performance measurement of heat sinks with confined impinging jet by infrared thermography", International Journal of Heat and Mass Transfer,  Vol. 48, No. 25-26, (2005), 5386-5394.

8.     El-Sheikh, H.A. and Garimella, S.V., "Heat transfer from pin-fin heat sinks under multiple impinging jets", IEEE Transactions on Advanced Packaging,  Vol. 23, No. 1, (2000), 113-120.

9.     Garimella, S.V. and Schroeder, V.P., "Local heat transfer distributions in confined multiple air jet impingement", Journal of Electronic Packaging,  Vol. 123, No. 3, (2001), 165-172.

10.   Chougule, N., Parishwad, G. and Sewatkar, C., "Numerical analysis of pin fin heat sink with a single and multi air jet impingement condition", International Journal of Engineering and Innovative Technology,  Vol. 1, No. 3, (2012), 44-50.

11.   Brignoni, L.A. and Garimella, S.V., "Experimental optimization of confined air jet impingement on a pin fin heat sink", IEEE Transactions on Components and Packaging Technologies,  Vol. 22, No. 3, (1999), 399-404.

12.   Siddique, U.M., Bhise, G.A. and Gulhane, N.P., "On numerical investigation of local nusselt distribution between flat surface and impinging air jet from straight circular nozzle and power law correlations generation", Heat Transfer—Asian Research,  Vol. 47, No. 1, (2018), 126-149.

13.   Umair, S.M. and Gulhane, N.P., "Numerical investigation of non-dimensional constant representing the occurrence of secondary peaks in the nusselt distribution curve", International Journal of Engineering Transaction A,  Vol. 29, No. 10, (2016), 1453-1461.

14.   Umair, S.M. and Gulhane, N.P., "On numerical investigation of nonuniformity in cooling characteristic for different materials of target surfaces being exposed to impingement of air jet", International Journal of Modeling, Simulation, and Scientific Computing,  Vol. 8, No. 03, (2017), 1750024.

15.   Umair, S.M. and Gulhane, N.P., "On numerical investigation of heat transfer augmentation through pin fin heat sink by laterally impinging air jet", Procedia Engineering,  Vol. 157, (2016), 89-97.

16.   Sundaram, M. and Venkatesan, M., "Heat transfer study of perforated fin under forced convection", International Journal of Engineering,  Vol. 28, No. 10, (2015), 1500-1506.

17.   Soleimani, G. and Khoshravan-Azar, E., "A numerical study of natural convection and radiation interaction in vertical circular pin", International Journal of Engineering,  Vol. 10, No. 3, (1997), 163-172.

18.   Moffat, R.J., "Describing the uncertainties in experimental results", Experimental Thermal and Fluid Science,  Vol. 1, No. 1, (1988), 3-17.