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 OJFD  Vol.7 No.2 , June 2017
Mixed Convection and Heat Transfer Studies in Non-Uniformly Heated Buoyancy Driven Cavity Flow
Abstract: We analyse the mixed convection flow in a cavity flow which is driven by buoyancy generated due to a non-uniformly heated top wall which is moving uniformly. A fourth order accurate finite difference scheme is used in this study and our code is first validated against available data in the literature. The results are obtained for different sets of Reynolds number Re, Prandtl number Pr and Grashof number Gr which are in the ranges 100 - 3000, 0.0152 - 10 and 102 - 106 respectively. Here Gr is related to the Richardson number according to Ri=Gr/Re2. While increasing the Richardson number, the growth of upstream secondary eddy (USE) is observed together with a degradation of downstream secondary eddy (DSE). When mixed convection is dominant, the upstream secondary eddy and the downstream secondary eddy merge to form a large recirculation region. When the effect of Pr is studied in the forced convection regime, Ri<<1, the temperature in the central region of the cavity remains nearly a constant. However, in the mixed convection regime, the temperature in cavity undergoes non-monotonic changes. Finally, using the method of divided differences, it is shown that numerical accuracy of the derived numerical scheme used in this work is four.
Cite this paper: Rejeesh, A. , Udhayakumar, S. , Sekhar, T. and Sivakumar, R. (2017) Mixed Convection and Heat Transfer Studies in Non-Uniformly Heated Buoyancy Driven Cavity Flow. Open Journal of Fluid Dynamics, 7, 231-262. doi: 10.4236/ojfd.2017.72016.
References

[1]   Ghia, U. and Ghia, K.N. and Shin, C.T. (1982) High-Re Solution for Incompressible Flow Usingg the Navier-Stokes Equations and a Multigrid Method. Journal of Computational Physics, 48, 13-15.

[2]   Cha, C.K. and Jaluria, Y. (1984) Recirculating Mixed Convection Flow for Energy Extraction. International Journal of Heat and Mass Transfer, 27, 1801-1812.

[3]   Hsu, T.H. and Hsu, P.T. and How, S.P. (1997) Mixed Convection in a partially Divided Rectrangular Enclosure. Numerical Heat Transfer, Part A: Applications, 31, 655-683.
https://doi.org/10.1080/10407789708914058

[4]   Hsu, T.H. and Wang, S.G. (2000) Mixed Convection in a Rectrangular Enclosure with Discrete Heat Sources. Numerical Heat Transfer, Part A: Applications, 38, 627-652.
https://doi.org/10.1080/104077800750021170

[5]   Fedorov, A.G. and Visakanta, R. (2000) Three-Dimensional Conjugate Heat Transfer in the Microchannel Heat Sink for Electronic Packaging. International Journal of Heat and Mass Transfer, 43, 399-415.

[6]   Leong, C.W. and Ottono, J.M. (1989) Experiments on Mixing Due to Chaotic Advection in a Cavity. Journal of Fluid Mechanics, 209, 463-499. https://doi.org/10.1017/S0022112089003186

[7]   Alleborn, N. and Rasziller, H. (1999) Lid-Driven Cavity with Heat and Mass Transport. International Journal of Heat and Mass Transfer, 42, 833-853.

[8]   Imberger, J. (1982) Dynamics of Lakes, Reservoirs and Cooling Ponds. Annual Review of Fluid Mechanics, 14, 153-187. https://doi.org/10.1146/annurev.fl.14.010182.001101

[9]   Prasad, A.K. and Koseff, J.R. (1996) Combined Forced and Mixed Convection Heat Transfer in a Deep Lid-Driven Cavity Flow. International Journal of Heat and Fluid Flow, 17, 460-467.

[10]   Elsherbiny, S.M. (1996) Free Convection in Inclined Air layers Heated from Above. International Journal of Heat and Mass Transfer, 39, 3925-3930.

[11]   Prasad, Y.S. and Das, M.K. (2007) Hopt Bifurcation in Mixed Convection Flow inside a Rectangular Cavity. International Journal of Heat and Mass Transfer, 50, 3583-3598.

[12]   Basak, T., Roy, S., Sharma, P.K. and Pop, I. (2009) Analysis of Mixed Convection Flows within a Square Cavity with Uniform and Non-Uniform Heating of Bottom Wall. International Journal of Thermal Sciences, 48, 891-912.

[13]   Cheng, T.S. and Liu, W.H. (2010) Effect of Temperature Gradient Orientation on the Characteristics of Mixed Convection Flow in a Lid-Driven Square Cavity. Computers and Fluids, 39, 965-978.

[14]   Erturk, E. and Gokol, C. (2006) Fourth Order Compact Formulation of Navier-Stokes Equations and Driven Cavity Flow at High Reynolds Numbers. Numerical Methods in Fluids, 50, 421-436.

[15]   Cheng, T.S. (2011) Characteristics of Mixed Convection Heat Transfer in a Lid-Driven Square Cavity with Various Richardson and Prandtl Numbers. International Journal of Thermal Sciences, 50, 197-205.

[16]   Ahmed, S.E., Oztop, H.F. and Al-Salem, K. (2016) Effects of Magnetic Field and Viscous Dissipation on Entropy Generation of Mixed Convection in Porous Lid-Driven Cavity with Corner Heater. International Journal of Numerical Methods for Heat and Fluid Flow, 26, 1548-1566. https://doi.org/10.1108/HFF-11-2014-0344

[17]   Malleswaran, A. and Sivasankaran, S. (2016) A Numerical Simulation on MHD Mixed Convection in a Lid-Driven Cavity with Corner Heaters. Journal of Applied Fluid Mechanics, 9, 311-319. https://doi.org/10.18869/acadpub.jafm.68.224.22903

[18]   Kareem, A.K., Gao, S. and Ahmed, A.Q. (2016) Unsteady Simulations of Mixed Convection Heat Transfer in a 3D Closed Lid-Driven Cavity. International Journal of Heat and Mass Transfer, 100, 121-130.

[19]   Bettaibi, S., Sediki, E., Kuznik, F. and Succi, S. (2015) Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-Uniform Heating of the Bottom Wall. Communications in Theoretical Physics, 63, 91-100.
https://doi.org/10.1088/0253-6102/63/1/15

[20]   Hussein, I.Y. and Ali, L.F. (2014) Mixed Convection in a Square Cavity Filled with Porous Medium with Bottom Wall Periodic Boundary Condition. Journal of Engineering, 20, 99-119.

[21]   Ismael, M.A., Pop, I. and Chamkha, A.J. (2014) Mixed Convection in a Lid-Driven Cavity with Partial Slip. International Journal of Thermal Sciences, 82, 47-61.

[22]   Mahapatra, T.R., Pal, D. and Mondal, S. (2013) Effects of Buoyancy Ratio on Double-Diffusive Natural Convection in a Lid-Driven Cavity. International Journal of Heat and Mass Transfer, 57, 771-785.

[23]   Mekroussi, S., Nehari, D., Bouzit, M. and Chemloul, N.E.S. (2013) Analysis of Mixed Convection in an Inclined Lid-Driven Cavity with a Wavy Wall. Journal of Mechanical Science and Technology, 27, 2181-2190. https://doi.org/10.1007/s12206-013-0533-9

[24]   Al-Salem, K., Oztop, H.F., Pop, I. and Varol, Y. (2012) Effects of Moving Lid Direction on MHD Mixed Convection in a Linearly Heated Cavity. International Journal of Heat and Mass Transfer, 55, 1103-1112.

[25]   Basak, T., Pradeep, P.V.K., Roy, S. and Pop, I. (2011) Finite Element Based Heatline Approach to Study Mixed Convection in a Porous Square Cavity with Various Wall Thermal Boundary Conditions. International Journal of Heat and Mass Transfer, 54, 1706-1727.

[26]   Mamourian, M., Shirvan, K.M. and Rahimi, R.E.A.B. (2016) Optimization of Mixed Convection Heat Transfer with Entropy Generation in a Wavy Surface Square Lid-Driven Cavity by means of Taguchi Approach. International Journal of Heat and Mass Transfer, 102, 544-554.

[27]   Nayak, R.K., Bhattacharyya, S. and Pop, I. (2016) Numerical Study of Mixed Convection and Entropy Generation of Cu-Water Nanofluid in a Differentially Heated Skewed Enclosure. International Journal of Heat and Mass Transfer, 85, 620-634.

[28]   Kefayati, G.H.R. (2015) FDLBM Simulation of Mixed Convection in a Lid-Driven Cavity Filled with Non-Newtonian Nanofluid in the Presence of Magnetic Field. International Journal of Thermal Sciences, 95, 29-46.

[29]   Kefayati, G.H.R. (2014) Mixed Convection of Non-Newtonian Nanofluid in a Lid-Driven Enclosure with Sinusoidal Temperature Profile using FDLBM. Powder Technology, 256, 268-281.

[30]   Jamai, H., Fakhreddine, S.O. and Sammouda, H. (2014) Numerical Study of Sinusoidal Temperature in Magneto-Convection. Journal of Applied Fluid Mechanics, 3, 493-502.

[31]   Kefayati, G.H.R., Bandpy, M.G., Sajjadi, H. and Ganji, D.D. (2012) Lattice Boltzmann Simulation of MHD Mixed Convection in Lid-Driven Square Cavity with Linearly Heated Wall. Scientia Iranica, 19, 1053-1065.

[32]   Arani, A.A.A., Sebdani, S.M., Mahmoodi, M., Ardeshiri, A. and Aliakbari, M. (2012) Numerical Study of Mixed Convection Flow in a Lid-Driven Cavity with Sinusoidal on Sidewalls Using Nanofluid. Superlattices and Microstructures, 51, 893-911.

[33]   Nasrin, R. (2010) Mixed Magnetoconvection in a Lid-Driven Cavity with a Sinusoidal Wavy Wall and a Central Heat Conducting Body. Journal of Naval Architecture and Marine Engineering, 7, 13-24. https://doi.org/10.3329/jname.v8i1.6793

[34]   Karimipour, A., Efse, M.H., Safaei, M.R., Semiromi, D.T., Jafari, S. and Kazi, S.N. (2014) Mixed Convection of Copper-Water Nanofluid in a Shallow Inclined Lid Driven Cavity Using the Lattice Boltzmann Method. Physica A: Statistical Mechanics and Its Applications, 402, 150-168.

[35]   Chamkha, A.J. and Abu-Nada, E. (2012) Mixed Convection Flow in Single- and Double-Lid Driven Square Cavities Filled with Water-Al2O3 Nanofluid: Effect of Viscosity Models. European Journal of Mechanics B-Fluids, 36, 82-96.

[36]   Garoosi, F. and Rashidi, M.M. (2015) Two Phase Simulation of Natural Convection and Mixed Convection of the Nanofluid in a Square Cavity. Powder Technology, 275, 239-256.

[37]   Billah, M.M., Rahman, M.M., Sharif, U.M., Rahim, N.A., Sadidur, R. and Hasanuzzaman, M. (2011) Numerical Analysis of Fluid Flow Due to Mixed Convection in a Lid-Driven Cavity Having a Heated Circular Hollow Cylinder. International Communications in Heat and Mass Transfer, 38, 1093-1103.

[38]   Wesseling, P. (1982) Theoretical and Practical Aspects of a Multigrid Method. SIAM Journal on Scientific and Statistical Computing, 3, 387-407. https://doi.org/10.1137/0903025

[39]   Zhang, J. (2003) Numerical Simulation of 2D Square Driven Cavity Using Fourth Order Compact Finite Difference Scheme. Computers and Mathematics with Applications, 45, 43-52.

[40]   Botella, O. and Peyret, R. (1998) Benchmark Spectral Results on the Lid-Driven Cavity Flow. Computers and Fluids, 27, 421-433.

[41]   Bruneau, C.H. and Saad, M. (1998) The 2D Lid-Driven Cavity Problem Revised. Computers and Fluids, 35, 326-348.

[42]   Iwatsu, R., Hyun, J.M. and Kuwamura, K. (1993) Mixed Convection in a Driven Cavity with a Stable Vertical Temperature Gradient. International Journal of Heat and Mass Transfer, 36, 1601-1608.

[43]   Sharif, M.A.R. (2007) Laminar Mixed Convection in Shallwl Inclined Driven Cavities with Hot Moving Lid on Top and Cooled from Bottom. Applied Thermal Engineering, 27, 1036-1042.

[44]   Koseff, J.R. and Street, R.L. (1984) Visualization Studies of a Shear Driven Three-Dimensional Re-Circulating Flow. Journal of Fluids Engineering, 106, 21-29.
https://doi.org/10.1115/1.3242393

[45]   Koseff, J.R. and Street, R.L. (1984) The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations. Journal of Fluids Engineering, 106, 390-398.
https://doi.org/10.1115/1.3243136

[46]   Moallemi, M.K. and Jang, K.S. (1992) Prandtl Number Effects on Laminar Mixed Convection Heat Transfer in a Lid-Driven Cavity. International Journal of Heat and Mass Transfer, 35, 1881-1892.

[47]   Torrance, K., Davis, R., Eike, K., Gill, P., Gutman, D., Hsui, A., Lyons, S. and Zien, H. (1972) Cavity Flows Driven by Buoyancy and Shear. Journal of Fluid Mechanics, 51, 221-213.
https://doi.org/10.1017/S0022112072001181

[48]   Schreiber, R. (1983) Driven Cavity Flows by Efficient Numerical Techniques. Journal of Computational Physics, 49, 310-333.

 
 
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