Abstract
This research is a numerical analysis exhaustively investigating two-dimensional (2D) transient convective heat transfer in a differentially heated rectangle, possessing sinusoidal corrugated side walls at constant temperatures. The quadrilateral space is filled with a power-law non-Newtonian fluid, plus the right and left walls are uniformly cooled and heated, respectively. The top and bottom walls are retained as adiabatic and the side walls are recast exploiting sinusoidal corrugated shape. The governing equations of the problem are solved using the finite volume method. The evaluation of fluid flow and heat transfer is conducted in such a manner that the power law index n varies from 0.6 to 1.4, the Rayleigh number Ra from 103 to 107, the corrugation amplitude CA from 0.1 to 0.5, and the corrugation frequency CF of the sinusoidal side walls is in the range of 1 to 5. The results are studied at different values of Ra, n, CA, and CF; they are presented in the form of streamlines, isotherms, and average Nusselt numbers (\(\overline{\rm{Nu}}\)) of the hot side wall. Further, the heat transfer characteristics are presented and the effect of sudden differential heating, as well as its consequential transient behavior, on the fluid flow, velocity, and temperature plots are demonstrated in accordance with the scope of the governing parameters.
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References
G. De Vahl Davis, “Natural convection of air in a square cavity: a benchmark numerical solution,” Int. J. Numer. Methods Fluids. 3, 249–264 (1983).
A. F. Emery and J. W. Lee, “The effects of property variations on natural convection in a square enclosure,” J. Heat Transfer 121, 57 (1999).
O. Aydin, A. Ünal, and T. Ayhan, “Natural convection in rectangular enclosures heated from one side and cooled from the ceiling,” Int. J. Heat Mass Transfer 42, 2345–2355 (1999).
S.Ostrach “Naturalconvectioninenclosures” Adv.HeatTransf. 8, 161–227 (1972)
D. V. Boger, “Demonstration of upper and lower newtonian fluid behaviour in a pseudoplastic fluid,” Nature 265, 126–128 (1977).
A. Acrivos, “A theoretical analysis of laminar natural convection heat transfer to non-newtonian f luids,” AIChE J. 6, 584–590 (1960).
A. F. Emery, H. W. Chi, and J. D. Dale, “Free convection through vertical plane layers of non-newtonian power law fluids,” J. Heat Transfer 93, 164 (1971).
T. Y. W. Chen and D.E. Wollersheim, “Free convection at a vertical plate with uniform flux condition in non-newtonian power-law fluids,” J. Heat Transfer 95, 123–124 (1973).
S. W. Churchill and H. H. S. Chu, “Correlating equations for laminar and turbulent free convection from a vertical plate,” Int. J. Heat Mass Transfer 18, 1323–1329 (1975).
Z. P. Shulman, V. I. Baikov, and E. A. Zaltsgendler, “An approach to prediction of free convection in non-newtonian fluids,” Int. J. Heat Mass Transfer 19, 1003–1007 (1976).
S. Haq, C. Kleinstreuer, and J. C. Mulligan, “Transient free convection of a non-newtonian fluid along a vertical wall,” J. Heat Transfer 110, 604 (1988).
J. F. T. Pittman, J. F. Richardson, and C. P. Sherrard, “Anexperimental study of heat transfer by laminar natural convection between an electrically-heated vertical plate and both newtonian and non-newtonian fluids,” Int. J. Heat Mass Transfer 42, 657–671 (1999).
G. Bin Kim, J. Min Hyun, and H. Sang Kwak, “Transient buoyant convection of a power-law non-newtonian fluid in an enclosure,” Int. J. Heat Mass Transfer 46, 3605–3617 (2003).
O. Turan, A. Sachdeva, R. J. Poole, and N. Chakraborty, “Laminar natural convection of power-law fluids in a square enclosure with differentially heated sidewalls subjected to constant wall heat flux,” J. Heat Transfer 134, 122504 (2012).
O. Turan, A. Sachdeva, R. J. Poole, and N. Chakraborty, “Aspect ratio and boundary conditions effects on laminar natural convection of power-law fluids in a rectangular enclosure with differentially heated side walls,” Int. J. Heat Mass Transfer 60, 722–738 (2013).
C. Cianfrini, M. Corcione, E. Habib, and A. Quintino, “Effects of the aspect ratio on the optimal tilting angle for maximum convection heat transfer across air-filled rectangular enclosures differentially heated at sides,” J. Therm. Sci. 26, 245–254 (2017).
H. T. Cheong, Z. Siri, and S. Sivasankaran, “Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition,” Int. Commun. Heat Mass Transfer 45, 75–85 (2013).
C.-C. Cho, C.-L. Chen, J.-J. Hwang, and C.-K. Chen, “Natural convection heat transfer performance of non-newtonian power-law fluids enclosed in cavity with complex-wavy surfaces,” J. Heat Transfer 45, 14502 (2013).
A. Sojoudi, S. C. Saha, Y. T. Gu, and M. A. Hossain, “Steady natural convection of non-newtonian power-law fluid in a trapezoidal enclosure,” Adv. Mech. Eng. 2013 1 (2013).
M. A. Sheremet, T. Groşan, and I. Pop, “Steady-state free convection in right-angle porous trapezoidal cavity filled by a nanofluid: buongiornos mathematical model,” Eur. J. Mech.—B/Fluids 45, 241–250 (2015).
G. R. Kefayati, “Simulation of magnetic field effect on natural convection of non-newtonian power-law fluids in a sinusoidal heated cavity using FDLBM,” Int. Commun. Heat Mass Transfer 45, 139–153 (2014).
C. C. Cho, C. L. Chen, and C. K. Chen, “Natural convection heat transfer performance in complex-wavy-wall enclosed cavity filled with nanofluid,” Int. J. Therm. Sci. 60. 255–263 (2012).
M. Sairamu and R. P. Chhabra, “Natural convection in power-law fluids from a tilted square in an enclosure,” Int. J. Heat Mass Transfer 45, 319–339 (2013).
G. S. Mun, J. H. Doo, and M. Y. Ha, “Thermo-dynamic irreversibility induced by natural convection in square enclosure with inner cylinder. Part-I: effect of tilted angle of enclosure,” Int. J. Heat Mass Transfer 45, 1102–1119 (2016).
V. Vivek, A. K. Sharma, and C. Balaji, “Interaction effects between laminar natural convection and surface radiation in tilted square and shallow enclosures,” Int. J. Therm. Sci. 45, 70–84 (2012).
R. L. Webb and N.-H. Kim, Principle of Enhanced HeatTtransfer (Taylor Fr., New York, 1994).
A. E. Bergles, “Techniques to Augment Heat Transfer,” in: Handbook of Heat Transfer (McGraw-Hill, New York, 1973), p. 10–11.
Y. Liu, C. Lei, and J. C. Patterson, “Natural convection in a differentially heated cavity with two horizontal adi-abatic fins on the sidewalls,” Int. J. Heat Mass Transfer 45, 23–36 (2014).
M. A. Sheremet, H. F. Oztop, I. Pop, and K. Al-Salem, “MHD free convection in a wavy open porous tall cavity filled with nanofluids under an effect of corner heater,” Int. J. Heat Mass Transfer 45, 955–964 (2016).
G. R. Kefayati, “Simulation of heat transfer and entropy generation of mhd natural convection of non-newtonian nanofluid in an enclosure,” Int. J. Heat Mass Transfer 45, 1066–1089 (2016).
G. H. R. Kefayati, “Heat transfer and entropy generation of natural convection on non-newtonian nanofluids in a porous cavity,” Powder Technol. 45, 127–149 (2016).
F. Selimefendigil, H. F. Öztop, and A. J. Chamkha, “Fluid structure-magnetic field interaction in a nanofluid filled lid-driven cavity with flexible side wall,” Eur. J. Mech. B/Fluids 45, 77–85 (2017).
M. Hatami, “Numerical study of nanofluids natural convection in a rectangular cavity including heated fins,” J. Mol. Liq. 45, 1–8 (2017).
R. Mebrouk, M. Kadja, M. Lachi, and S. Fohanno, “Numerical study of natural turbulent convection of nano-fluids in a tall cavity heated from below,” Therm. Sci. 45, 2051–2064 (2016).
P. K. Das and S. Mahmud, “Numerical investigation of natural convection inside a wavy enclosure,” Int. J. Therm. Sci. 45, 397–406 (2003).
C. Saidi, F. Legay-Desesquelles, and B. Prunet-Foch, “Laminar flow past a sinusoidal cavity,” Int. J. Heat Mass Transfer 45, 649–661 (1987).
G. Wang and S.P. Vanka, “Convective heat transfer in periodic wavy passages,” Int. J. Heat Mass Transfer 45, 3219–3230 (1995).
T. Nishimura, Y. Ohori, and Y. Kawamura, “Flow characteristics in a channel with symmetric wavy wall for steady flow,” J. Chem. Eng. Japan 45, 466–471 (1984).
Y. Asako and M. Faghri, “Finite-volume solutions for laminar flow and heat transfer in a corrugated duct,” J. Heat Transfer 45, 627 (1987).
M. N. Hasan, S. C. Saha, and Y. T. Gu, “Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls,” Int. J. Heat Mass Transfer 45, 5696–5708 (2012).
A. Sojoudi, S. C. Saha, M. Khezerloo, and Y. T. Gu, “Unsteady natural convection within a porous enclosure of sinusoidal corrugated side walls,” Transp. Porous Media 45, 537–552 (2014).
S. H. Hussain, “Analysis of heatlines and entropy generation during double-diffusive mhd natural convection within a tilted sinusoidal corrugated porous enclosure,” Eng. Sci. Technol. Int. J. 45, 926–945 (2016).
S. Mahmud, P. K. Das, N. Hyder, and A. K. M. S. Islam, “Free convection in an enclosure with vertical wavy walls,” Int. J. Therm. Sci. 45, 440–446 (2002).
C. Cho, C. Chen, and C. Chen, “Natural convection heat transfer performance in complex-wavy-wall enclosed cavity filled with nanofluid,” Int. J. Therm. Sci. 45, 255–263 (2012).
M. Esmaeilpour and M. Abdollahzadeh, “Free convection and entropy generation of nanofluid inside an enclosure with different patterns of vertical wavy walls,” Int. J. Therm. Sci. 45, 127–136 (2012).
H. F. Oztop, E. Abu-nada, Y. Varol, and A. Chamkha, “Natural convection in wavy enclosures with volumetric heat sources,” Int. J. Therm. Sci. 45, 502–514 (2011).
Y. Varol and H. F. Oztop, “Free convection in a shallow wavy enclosure,” Int. Comm. Heat Mass Transfer 45, 764–771 (2006).
S. Patankar, Numerical Heat Transfer and Fluid Flow (CRC Press, Boca Raton, 1980).
P. D. Thomas and J. F. Middlecoff, “Direct control of the grid point distribution in meshes generated by elliptic equations,” AIAA J. 18 (6), 652–656 (1980).
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Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 2, pp. 14–30.
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Salehpour, A., Abdolahi Sadatlu, M.A. & Sojoudi, A. Unsteady Natural Convection in a Differentially Heated Rectangular Enclosure Possessing Sinusoidal Corrugated Side Walls Loaded with Power Law Non-Newtonian Fluid. Fluid Dyn 54, 159–176 (2019). https://doi.org/10.1134/S0015462819010129
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DOI: https://doi.org/10.1134/S0015462819010129