Abstract
A two dimensional steady and laminar mixed convection flow in lid-driven porous cavity filled with Cu-water nanofluid is presented in this numerical investigation. The vertical side walls are considered with two spatially varying sinusoidal temperature distributions of different amplitude ratios and phase deviations while the horizontal walls are thermally insulated. The transport equations are solved using finite volume method on a uniformly staggered grid system. The variations of fluid flow, heat transfer, mid-plane velocity, and Nusselt number were discussed over a wide range of Richardson number
Funding statement: This work was supported by the National Foundation of Korea (NRF) grant funded by the Human Resource Training Program for Regional Innovation and Creativity through the Ministry of Education (NRF-2015H1C1A1035890).
References
Abu-Nada, E., and A. J. Chamkha. 2010. “Mixed Convection Flow in a Lid-Driven Inclined Square Enclosure Filled with a Nanofluid.” European Journal of Mechanics – B Fluids 29: 472–482.10.1016/j.euromechflu.2010.06.008Search in Google Scholar
Al-Amiri, Abdalla M. 2000. “Analysis of Momentum and Energy Transfer in a Lid-Driven Cavity Filled with a Porous Medium.” International Journal of Heat Mass Transfer 43: 3513–3527.10.1016/S0017-9310(99)00391-9Search in Google Scholar
Arefmanesh, A., and M. Mahmoodi. 2011. “Effects of Uncertainties of Viscosity Models for Al2O3- Water Nanofluid on Mixed Convection Numerical Simulations.” International Journal of Thermal Sciences 50: 1706–1719.10.1016/j.ijthermalsci.2011.04.007Search in Google Scholar
Basak, Tanmay, S., Roy, Pawan Kumar Sharma, and I. Pop. 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: 891–912.10.1016/j.ijthermalsci.2008.08.003Search in Google Scholar
Basak, Tanmay, S., Roy, Sandeep Kumar Singh, and I. Pop. 2010. “Analysis of Mixed Convection in a Lid-Driven Porous Square Cavity with Linearly Heated Side Wall(s).” International Journal of Heat Mass Transfer 53: 1819–1840.10.1016/j.ijheatmasstransfer.2010.01.007Search in Google Scholar
Bilgen, E., and R. Ben Yedder. 2007. “Natural Convection in Enclosure with Heating and Cooling by Sinusoidal Temperature Profiles on One Side.” International Journal of Heat and Mass Transfer 50: 139–150.10.1016/j.ijheatmasstransfer.2006.06.027Search in Google Scholar
Chamkha, A. J., and A. M. Aly. 2010. “MHD Free Convection Flow of a Nanofluid Past a Vertical Plate in the Presence of Heat Generation or Absorption Effects.” Chemical Engineering Communications 198: 425–441.10.1080/00986445.2010.520232Search in Google Scholar
Chattopadhyay, A., S. K. Pandit, S. S. Sarma, and I. Pop. 2016. “Mixed Convection in a Double Lid-Driven Sinusoidally Heated Porous Cavity.” International Journal of Heat and Mass Transfer 93: 361–378.10.1016/j.ijheatmasstransfer.2015.10.010Search in Google Scholar
Cheng, P., and W. J. Minkowycz. 1977. “Free Convection about a Vertical Flat Plate Embedded in a Porous Medium with Application to Heat Transfer from a Dike.” Journal of Geophysical Research 82: 2040–2044.10.1029/JB082i014p02040Search in Google Scholar
Choi, S.U.S. 1995. “Enhancing Thermal Conductivity of Fluids with Nanoparticles.” ASME Fluids Engineering Division 231: 99–105.Search in Google Scholar
Das, S. K., N. Putra, P. Thiesen, and W. Roetzel. 2003. “Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids.” Journal of Heat Transfer 125: 567–574.10.1115/1.1571080Search in Google Scholar
Deng, Qi-Hong, and Juan-Juan Chang. 2008. “Natural Convection in a Rectangular Enclosure with Sinusoidal Temperature Distributions on Both Side Walls.” In Numerical Heat Transfer, Part A: Applications., 507–524.Search in Google Scholar
Du, Z. G., and E. Bilgen. 1990. “Natural Convection in Vertical Cavities with Partially Filled Heat-Generating Porous Media.” Numerical Heat Transfer, Part A: Applications 18: 371–386.10.1080/10407789008944800Search in Google Scholar
Eastman, J. A., S. U. S. Choi, S. Li, L. J. Thompson, and S. Lee. 1997. “Enhancement Thermal Conductivity through the Development of Nanofluids.” In 1996 Fall meeting of the Materials Research Society (MRS). Boston, USA.10.1557/PROC-457-3Search in Google Scholar
Eastman, J. A., S. U. S. Choi, S. Li, W. Yu, and L. J. Thompson. 2001. “Anomalously Increased Effective Thermal Conductivities of Ethy- lene Glycol-Based Nanofluids Containing Copper Nanoparticles.” Applied Physics Letters 78: 718–720.10.1063/1.1341218Search in Google Scholar
Ergun, S. 1952. “Fluid Flow through Packed Columns.” Chemical Engineering Programs 48: 89–94.Search in Google Scholar
Fu, W. S., C. J. Chen, Y. C. Lai, and S. H. Huang. 2014. “Effects of a Porous Medium on Forced Convection of a Reciprocating Curved Channel.” International Journal of Heat and Mass Transfer 58: 63–70.10.1016/j.icheatmasstransfer.2014.08.007Search in Google Scholar
Ghazvini, M., and H. Shokouhmand. 2009. “Investigation of a Nanofluid- Cooled Microchannel Heat Sink Using Fin and Porous Media Approaches.” Energy Conversion and Management 50: 2373–2380.10.1016/j.enconman.2009.05.021Search in Google Scholar
Gutt, R., and T. Grosan. 2015. “On the Lid-Driven Problem in a Porous Cavity: A Theoretical and Numerical Approach.” Applied Mathematics and Computation 266: 1070–1082.10.1016/j.amc.2015.06.038Search in Google Scholar
Hayase, T., J.A.C. Humphrey, and R. Grief. 1992. “A Consistently Formulated QUICK Scheme for Fast and Stable Convergence Using Finite-Volume Iterative Procedures.” Journal of Computational Physics 98:108–: 118.10.1016/0021-9991(92)90177-ZSearch in Google Scholar
Iwatsu, R., J. M. Hyun, and K. Kuwahara. 1993. “Mixed Convection in a Driven Cavity with a Stable Vertical Temperature Gradient.” International Journal of Heat Mass Transfer 36: 1601–1608.10.1016/S0017-9310(05)80069-9Search in Google Scholar
Kefayati, GH. R. 2014a. “Mesoscopic Simulation of Double-Diffusive Mixed Convection of Pseudoplastic Fluids in an Enclosure with Sinusoidal Boundary Conditions.” Computers & Fluids 97: 94–109.10.1016/j.compfluid.2014.04.007Search in Google Scholar
Kefayati, GH. R. 2014b. “Double-Diffusive Mixed Convection of Pseudoplastic Fluids in a Two Sided Lid-Driven Cavity Using FDLBM.” Journal of the Taiwan Institute of Chemical Engineers 45: 2122–2139.10.1016/j.jtice.2014.05.026Search in Google Scholar
Kefayati, GH. R. 2014c. “Mesoscopic Simulation of Magnetic Field Effect on Double-Diffusive Mixed Convection of Shear-Thinning Fluids in a Two Sided Lid-Driven Cavity.” Journal of Molecular Liquids 198: 413–429.10.1016/j.molliq.2014.07.024Search in Google Scholar
Kefayati, GH. R. 2015a. “Mesoscopic Simulation of Mixed Convection on Non-Newtonian Nanofluids in a Two Sided Lid-Driven Enclosure.” Advanced Powder Technology 26: 576–588.10.1016/j.apt.2015.01.005Search in Google Scholar
Kefayati, GH. R. 2015b. “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: 29–46.10.1016/j.ijthermalsci.2015.03.018Search in Google Scholar
Khanafer, K.M., and A. J. Chamkha. 1999. “Mixed Convection Flow in a Lid-Driven Enclosure Filled with a Fluid-Saturated Porous Medium.” International Journal of Heat and Mass Transfer 42: 2465–2481.10.1016/S0017-9310(98)00227-0Search in Google Scholar
Khanafer, K., and K. Vafai. 2002. “Double-Diffusive Mixed Convection in a Lid-Driven Enclosure Filled with a Fluid-Saturated Porous Medium.” Numerical Heat Transfer, Part A: Applications 42: 465–486.10.1080/10407780290059657Search in Google Scholar
Kumar, S., S.K. Prasad, and J. Banerjee. 2010. “Analysis of Flow and Ther- mal Field in Nanofluid Using a Single Phase Thermal Dispersion Model.” Applied Mathematical Modelling 34: 573–592.10.1016/j.apm.2009.06.026Search in Google Scholar
Maxwell, J. C. 1904. A Treatise on Electricity and Magnetism., 2nd 435–441. Cam- bridge: Oxford University Press.Search in Google Scholar
Muthtamilselvan, M., and D. H. Doh. 2014. “Mixed Convection of Heat Gen- erating Nanofluid in a Lid-Driven Cavity with Uniform and Non-Uniform Heating of Bottom Wall.” Applied Mathematical Modelling 38: 3164–3174.10.1016/j.apm.2013.11.033Search in Google Scholar
Muthtamilselvan, M., P. Kandaswamy, and J. Lee. 2010. “Heat Transfer En- hancement of Copper-Water Nanofluids in a Lid-Driven Enclosure.” Communications in Nonlinear science and Numerical simulation 15: 1501–1510.10.1016/j.cnsns.2009.06.015Search in Google Scholar
Nguyen, Minh Tuan, Abdelraheem M. Aly, and Sang-Wook Lee. 2015. “Natural Convection in a Non-Darcy Porous Cavity Filled with CuWa- ter Nanofluid Using the Characteristic-Based Split Procedure in Finite- Element Method.” Journal Numerical Heat Transfer, Part A: Applications 67: 224–247.10.1080/10407782.2014.923225Search in Google Scholar
Nield, D. A., and A. V. Kuznetsov. 2009. “The ChengMinkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Satu- rated by a Nanofluid.” International Journal of Heat and Mass Transfer 52: 5792–5795.10.1016/j.ijheatmasstransfer.2009.07.024Search in Google Scholar
Patankar, S.V. 1980. Numerical Heat Transfer and Fluid Flow. Washington, DC: Hemisphere.Search in Google Scholar
Rohni, A. M., S. Ahmad, J. H. Merkin, and I. Pop. 2013. “Mixed Convection Boundary Layer Flow along a Vertical Cylinder Embedded in a Porous Medium Filled by a Nanofluid.” Transport in Porous Media 96: 237–253.10.1007/s11242-012-0085-ySearch in Google Scholar
Rosca, A. V., N. C. Rosca, T. Grosan, and I. Pop. 2012. ““Non-Darcy Mixed Convection from a Horizontal Plate Embedded in a Nanofluid Saturated Porous Media.” International Communications in Heat and Mass Transfer 39: 1080–1085.10.1016/j.icheatmasstransfer.2012.06.025Search in Google Scholar
Talebi, F., A.H. Mahmoudi, and M. Shahi. 2010. “Numerical Study of Mixed Convection Flows in a Square Lid-Driven Cavity Utilizing Nanofluid.” International Communications in Heat and Mass Transfer 37: 79–90.10.1016/j.icheatmasstransfer.2009.08.013Search in Google Scholar
Tiwari, R.K., and M.K. Das. 2007. “Heat Transfer Augmentation in a Two- Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanoflu- ids.” International Journal of Heat Mass Transfer 50: 2002–2018.10.1016/j.ijheatmasstransfer.2006.09.034Search in Google Scholar
Vafai, K., and P. C. Huang. 1994. “Analysis of Heat Transfer Regulation and Modification Employing Intermittently Emplaced Porous Cavities.” ASME Journal of Heat Transfer 116: 155–164.10.1115/1.2910912Search in Google Scholar
Van Doormaal, J. P., and G. D. Raithby. 1984. “Enhancements of the SIM- PLE Method for Predicting Incompressible Fluid Flows.” Numerical Heat Transfer, Part A: Applications 7: 147–163.Search in Google Scholar
Vishnuvardhanarao, Elaprolu, and Manab Kumar Das. 2008. “Laminar Mixed Convection in a Parallel Two-Sided Lid-Driven Differentially Heated Square Cavity Filled with a Fluid-Saturated Porous Medium.” Numerical Heat Transfer, Part A: Applications 53: 88–110.10.1080/10407780701454006Search in Google Scholar
Yu, W., and S. U. S. Choi. 2003. “The Role of Inter Facial Layers in the Enhanced Thermal Conductivity of Nanofluids: A Renovated Maxwell model.” Journal of Nanoparticle Research 5: 167–171.10.1023/A:1024438603801Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston