Optimal Configuration of An Annular Sector Duct Filled With Porous Media

Hafsa Hareem, Mazhar Iqbal

Abstract


In the current study, optimal configuration for finned annulus, filled with porous media, have been investigated to maximize the convective heat transfer and minimize the friction effect subject to constant heat flux boundary conditions. Genetic Algorithm (GA) has been employed to find out the optimal geometry out of vast choices of geometrical parameters; ratio of radii of the inner to outer pipe and sector angle of channel. Finite Difference Method (FDM) is applied to solve the governing mathematical model. Chilton-Colburn’s j factor is employed as the objective function and numerical solutions of the momentum and energy equations are used as function values to the optimizer. The results indicate that for a fixed Prandtl number (Pr) the optimal geometry transforms with the variation in permeability of the porous media which is in line with the physics of the problem.

Keywords


Optimal configuration; Porous media; Annulus sector duct; Genetic algorithm; \(j\) factor

Full Text:

PDF

References


I.K. Adegun, T.S. Jolayemi, O.A. Olayemi and A.M. Adebisi, Numerical simulation of forced convection heat transfer in inclined elliptical ducts with multiple internal longitudinal fins, Alexandria Engineering Journal (2017), DOI: 10.1016/j.aej.2017.01.014.

J.D. Anderson, Jr., Computational Fluid Dynamics, McGraw Hill (1995).

S. Colle and C.R. Maliska, Optimization of finned double tubes for heat transfer in laminar flow, Brazilian Congress on Mechanical Engineering, Rio de Janeiro, Universidade Fedural, B (1976), 475 – 490.

A.R. Conn, N.I.M. Gould and Ph. L. Toint, Trust-region methods, MPS-SIAM Series on Optimization, SIAM, Philadelphia (2000).

G. Fabbri, A genetic algorithm for fin profile optimization, International Journal of Heat and Mass Transfer 40 (9) (1997), 2165 – 2172, DOI: 10.1016/S0017-9310(96)00294-3.

C.J. Geankoplis, Transport Processes and Separation Process Principles (includes Unit Operations), 4th edition, (2003), 475.

S. Gosselin, Review of utilization of genetic algorithms in heat transfer problems, International Journal of Heat and Mass Transfer 52 (2009), 2169 – 2188, DOI: 10.1016/j.ijheatmasstransfer.2008.11.015.

K. Hooman, H. Gurgenci and A.A. Merrikh, Heat transfer and entropy generation optimization of forced convection in porous-saturated ducts of rectangular cross-section, International Journal of Heat and Mass Transfer 50 (2007) 2051 – 2059, DOI: 10.1016/j.ijheatmasstransfer.2006.11.015.

F.P. Incropera, D.P. DeWitt, T. Bergman and A. Lavine, Fundamentals of Heat and Mass Transfer, J. Wiley, 6 (2007).

M. Iqbal and H. Afaq, Fluid flow and heat transfer through an annular sector duct filled with porous media, Journal of Porous Media 18 (7) (2015), 679 – 687, DOI: 10.1615/JPorMedia.v18.i7.30.

Z. Iqbal, K.S. Syed and M. Ishaq, Optimal configuration of finned annulus in a double pipe with fully developed laminar flow, Applied Thermal Engineering 31 (2011) 1435 – 1446, DOI: 10.1016/j.applthermaleng.2011.01.012.

Z. Iqbal, K.S. Syed and M. Ishaq, Optimal convective heat transfer in double pipe with parabolic fins, International Journal of Heat and Mass Transfer 54 (2011), 5415 – 5426, DOI: 10.1016/j.ijheatmasstransfer.2011.08.001.

Z. Iqbal, K.S. Syed and M. Ishaq, Fin design for conjugate heat transfer optimization in double pipe, International Journal of Thermal Sciences 94 (2015), 242 – 258. DOI: 10.1016.2Fj.ijthermalsci.2015.03.011.

Z. Iqbal, K.S. Syed and M. Ishaq, Optimal fin shape in finned double pipe with fully developed laminar flow, Applied Thermal Engineering 51 (2013), 1202 – 1223.

M. Ishaq, K.S. Syed, Z. Iqbal, A. Hassan and A. Ali, DG-FEM based simulation of laminar convection in an annulus with triangular fins of different heights, International Journal of Thermal Sciences 72 (2013), 125 – 146, DOI: 10.1016/j.ijthermalsci.2013.04.022.

M. Kaviany, Laminar flow through a porous channel bounded by isothermal parallel plates, International Journal Heat Mass Transfer 28 (4) (1985), 851 – 858, DOI: 10.1016/0017-9310(85)90234-0.

I. Kurtbas and N. Celik, Experimental investigation of forced and mixed convection heat transfer in a foam filled horizontal rectangular channel, International Journal of Heat and Mass Transfer 52 (2009), 1313 – 1325, DOI: 10.1016/j.ijheatmasstransfer.2008.07.050.

Z.Y. Li, T.C. Hung and W.Q. Tao, Numerical simulation of fully developed turbulent flow and heat transfer in annular-sector ducts, Heat and Mass Transfer 38 (4-5) (2002), 369 – 377, DOI: 10.1007/s002310100224.

M.J. Lin, Q.W. Wang and W.Q. Tao, Developing laminar flow and heat transfer in annular-sector ducts, Heat Transfer Engineering 21(2) (2000) 53 – 61, DOI: 10.1080/014576300271022.

F. Liu, The effect of geometries on heat transfer enhancement of thermal fluids in curved ducts, Applied Thermal Engineering 90 (2015), 590 – 595, DOI: 10.1016%2Fj.applthermaleng.2015.07.046.

J.M. McDonough, Lectures in Elementary Fluid Dynamics, (2009), http://web.engr.uky.edu/~acfd/me330-lctrs.pdf.

M.R.H. Nobari and M.T. Mehrabani, A numerical study of fluid flow and heat transfer in eccentric curved annuli, International Journal of Thermal Sciences 49 (2010), 380 – 396, DOI: 10.1016/j.ijthermalsci.2009.07.003.

Ö. Yeniay, Penalty function methods for constrained optimization with genetic algorithms, Mathematical and Computational Applications 10 (1) (2005), 45 – 56, DOI: 10.3390/mca10010045.

R.K. Shah and A.L. London, Laminar Flow Forced Convection in Ducts, Academic Press, London (1978).

H.J. Sung, S.Y. Kim and J.M. Hyun, Forced convection from an isolated heat source in a channel with porous medium, International Journal Heat and Fluid Flow 16 (1995), 527 – 535, DOI: 10.1016/0142-727X(95)00032-L.

Y.X. Yauan, A review of trust region algorithms for optimization, J.M. Ball and J.C.R. Hunt (eds.), Proceedings of the Fourth International Congress on Industrial and Applied Mathematics, Oxford University Press (2000), 271 – 282.

E.H. Zaim and S.A.G. Nassab, Numerical investigation of laminar forced convection of water upwards in a narrow annulus at supercritical pressure, Energy 35 (10) (2010), 4172 – 4177, https://www.cheric.org/research/tech/periodicals/doi.php?art_seq=859872.

O. Zeitoun and A.S. Hegazy, Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature, Heat Mass Transfer 40 (2004), 253 – 259, DOI: 10.1007/s00231-003-0446-8.




DOI: http://dx.doi.org/10.26713%2Fcma.v9i3.796

Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905