Role of Surface Roughness during Natural Convection

M. Yousaf, S. Usman

Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, 301W, 14th St., Rolla, MO 65409-0170, USA.

DOI: 10.4236/wjet.2015.33C021                

Abstract

A computational study was performed in a two-dimensional square cavity in the presence of roughness using an algorithm based on mesoscopic method known as Lattice Boltzmann Method (LBM). A single relaxation time Bhatnagar-Gross-Krook (BGK) model of LBM was used to perform numerical study. Sinusoidal roughness elements of dimensionless amplitude of 0.1 were located on both the hot and cold walls of a square cavity. A Newtonian fluid of the Prandtl number (Pr) 1.0 was considered. The range of the Rayleigh (Ra) number explored was from 103 to 106 in a laminar region. Thermal and hydrodynamic behaviors of fluid were studied using sinusoidal roughness elements. Validation of computational algorithm was performed against previous benchmark studies, and a good agreement was found. Average Nu (Nusselt number) has been calculated to observe the effects of the surface roughness on the heat transfer. Results showed that sinusoidal roughness elements considerably affect the thermal and hydrodynamic behaviors of fluid in a square cavity. The maximum reduction in the average heat transfer in the presence of roughness was calculated to be 23.33%.

Keywords

Natural Convection, Rayleigh Number, Surface Roughness, Heat Transfer, Lattice Boltzmann Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Gebhart, B., Jaluria, Y., Mahajan, R.L. and Sammakia, B. (1988) Buoyancy-Induced Flows and Trans-port.
[2]	Lommers, L., Shahrokhi, F., Mayer III, J. and Southworth, F. (2012) AREVA HTR Concept for Near-Term Deployment. Nuclear Engineering and Design, 251, 292-296. http://dx.doi.org/10.1016/j.nucengdes.2011.10.030
[3]	Shi, X. and Khodadadi, J. (2003) Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall. Journal of Heat Transfer, 125, 624-634. http://dx.doi.org/10.1115/1.1571847
[4]	Bhavnani, S. and Bergles, A. (1991) Natural Convection Heat Transfer from Sinusoidal Wavy Surfaces. W?rme-und Stoffübertragung, 26, 341-349. http://dx.doi.org/10.1007/BF01591667
[5]	Ostrach, S. (1988) Natural Convection in Enclosures. Journal of Heat Transfer, 110, 1175-1190. http://dx.doi.org/10.1115/1.3250619
[6]	Bejan, A. and Kraus, A.D. (2003) Heat Transfer Handbook. John Wiley & Sons, Hoboken.
[7]	Bajorek, S. and Lloyd, J. (1982) Experimental Investigation of Natural Convection in Partitioned Enclosures. Journal of Heat Transfer, 104, 527-532. http://dx.doi.org/10.1115/1.3245125
[8]	Anderson, R. and Bohn, M. (1986) Heat Transfer Enhancement in Natural Convection Enclosure Flow. Journal of Heat Transfer, 108, 330-336. http://dx.doi.org/10.1115/1.3246924
[9]	Shakerin, S., Bohn, M. and Loehrke, R. (1988) Natural Convec-tion in an Enclosure with Discrete Roughness Elements on a Vertical Heated Wall. International Journal of Heat and Mass Transfer, 31, 1423-1430. http://dx.doi.org/10.1016/0017-9310(88)90251-7
[10]	Ruhul Amin, M. (1993) Natural Convection Heat Transfer and Fluid Flow in an Enclosure Cooled at the Top and Heated at the Bottom with Roughness Elements. International Journal of Heat and Mass Transfer, 36, 2707-2710. http://dx.doi.org/10.1016/S0017-9310(05)80208-X
[11]	Carrilho, L.A., Khan, J., Conner, M.E., Mandour, A. and Dzodzo, M.B. (2009) Two and Three-Dimensional Simulations of Enhanced Heat Transfer in Nuclear Fuel Rod Bun-dles. ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences, American Society of Mechanical Engineers, 331-334. http://dx.doi.org/10.1115/ht2009-88399
[12]	Carrilho, L. and Khan, J. (2010) Modeling of the Effect of Parallel Rib-Type Roughness on Local, Single-Phase Heat Transfer in Rod Bundles by CFD: Part 1—Flow Resistance. 18th International Conference on Nuclear Engineering, American Society of Mechanical Engineers, 723-727. http://dx.doi.org/10.1115/icone18-29731
[13]	Chang, S.H. and Baek, W.-P. (2003) Understanding, Predicting, and Enhancing Critical Heat Flux. The 10th international Topical Meeting on Nuclear Reactor Thermo-Hydraulics.
[14]	Meyer, L. (1982) Thermohydraulic Characteristics of Single Rods with Three-Dimensional Roughness. International Journal of Heat and Mass Transfer, 25, 1043-1058. http://dx.doi.org/10.1016/0017-9310(82)90079-5
[15]	Firth, R. and Meyer, L. (1983) A Comparison of the Heat Transfer and Friction Factor Performance of Four Different Types of Artificially Roughened Surface. International Journal of Heat and Mass Transfer, 26, 175-183. http://dx.doi.org/10.1016/S0017-9310(83)80024-6
[16]	Jiji, L.M. (2006) Heat Convection. Springer.
[17]	Xu, K. and Lui, S.H. (1999) Rayleigh-Bénard Simulation Using the Gas-Kinetic Bhatnagar-Gross-Krook Scheme in the In-compressible Limit. Physical Review E, 60, 464. http://dx.doi.org/10.1103/PhysRevE.60.464
[18]	Das, P.K. and Mahmud, S. (2003) Numerical Investigation of Natural Convection inside a Wavy Enclosure. International Journal of Thermal Sciences, 42, 397-406. http://dx.doi.org/10.1016/S1290-0729(02)00040-6
[19]	Kao, P.-H. and Yang, R.-J. (2007) Simulating Oscillatory Flows in Rayleigh-Benard Convection Using the Lattice Boltzmann Method. Interna-tional Journal of Heat and Mass Transfer, 50, 3315-3328. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.01.035
[20]	Mohamad, A. (2011) Lattice Boltzmann Method. Springer. http://dx.doi.org/10.1007/978-0-85729-455-5
[21]	Sukop, M.C. and Thorne, D.T. (2007) Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer.
[22]	Shan, X. (1997) Simulation of Rayleigh-Bénard Convection Using a Lattice Boltzmann Method. Physical Review E, 55, 2780. http://dx.doi.org/10.1103/PhysRevE.55.2780
[23]	Wang, J., Wang, D., Lallemand, P. and Luo, L.-S. (2013) Lattice Boltzmann Simulations of Thermal Convective Flows in Two Dimensions. Computers & Mathematics with Applications, 65, 262-286. http://dx.doi.org/10.1016/j.camwa.2012.07.001
[24]	Eggels, J. and Somers, J. (1995) Numerical Simulation of Free Convective Flow Using the Lattice-Boltzmann Scheme. International Journal of Heat and Fluid Flow, 16, 357-364. http://dx.doi.org/10.1016/0142-727X(95)00052-R
[25]	Yang, X., Shi, B. and Chai, Z. (2014) Generalized Modifica-tion in the Lattice Bhatnagar-Gross-Krook Model for Incompressible Navier-Stokes Equations and Convec-tion-Diffusion Equations. Physical Review E, 90, 013309. http://dx.doi.org/10.1103/PhysRevE.90.013309
[26]	Zou, Q. and He, X. (1997) On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model. Physics of Fluids (1994-present), 9, 1591-1598.
[27]	Guo, Z. and Shu, C. (2013) Lattice Boltzmann Method and Its Applications in Engineering (Advances in Computational Fluid Dynamics). World Scientific Publishing Company. http://dx.doi.org/10.1142/8806
[28]	de Vahl Davis, G. (1983) Nat-ural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution. International Journal for Numerical Methods in Fluids, 3, 249-264. http://dx.doi.org/10.1002/fld.1650030305
[29]	Amin, M.R. (1991) The Effect of Adiabatic Wall Roughness Elements on Natural Convection Heat Transfer in Vertical Enclosures. International Journal of Heat and Mass Transfer, 34, 2691-2701. http://dx.doi.org/10.1016/0017-9310(91)90228-7
[30]	Pretot, S., Zeghmati, B. and Caminat, P. (2000) Influence of Surface Roughness on Natural Convection above a Horizontal Plate. Advances in Engineering Software, 31, 793-801. http://dx.doi.org/10.1016/S0965-9978(00)00053-3
[31]	Saidi, C., Legay-Desesquelles, F. and Prunet-Foch, B. (1987) Laminar Flow Past a Sinusoidal Cavity. International Journal of Heat and Mass Transfer, 30, 649-661. http://dx.doi.org/10.1016/0017-9310(87)90195-5
[32]	Vijiapurapu, S. and Cui, J. (2010) Performance of Turbu-lence Models for Flows through Rough Pipes. Applied Mathematical Modelling, 34, 1458-1466. http://dx.doi.org/10.1016/j.apm.2009.08.029