Esfandiari, M., Mehmandoust, B., Karimpour, A. (2016). Investigation of nanoparticles diameter on free convection of Aluminum Oxide-Water nanofluid by single phase and two phase models. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 9(1), 167-180.

meissam Esfandiari; Babak Mehmandoust; Arash Karimpour. "Investigation of nanoparticles diameter on free convection of Aluminum Oxide-Water nanofluid by single phase and two phase models". Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 9, 1, 2016, 167-180.

Esfandiari, M., Mehmandoust, B., Karimpour, A. (2016). 'Investigation of nanoparticles diameter on free convection of Aluminum Oxide-Water nanofluid by single phase and two phase models', Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 9(1), pp. 167-180.

Esfandiari, M., Mehmandoust, B., Karimpour, A. Investigation of nanoparticles diameter on free convection of Aluminum Oxide-Water nanofluid by single phase and two phase models. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2016; 9(1): 167-180.

Investigation of nanoparticles diameter on free convection of Aluminum Oxide-Water nanofluid by single phase and two phase models

In this research, effect of nanoparticles dimeter on free convection of aluminum oxide-water was investigated in a cavity by single phase and two phase models. The range of Rayleigh number is considered 105-107 in volume fractions of 0.01 to 0.03 for nanoparticles with various diameters (25, 33, 50 and 100 nm). Given that the two phase nature of nanofluids, necessity of modeling by this method is increasing. Single phase approach (in contrary of two phase) for nanofluids is based on that the behaviors of each two solid phase (nanoparticles) and liquid phase (base fluid) are completely similar. In this study, Eulerian-Eulerian approach and mixture model was used given that Brownian motion and thermophoresis effects. Brownian motion and thermophoresis creates under influences of volume fraction gradient and temperature gradient, respectively that cause to creating slip between nanoparticles and base fluid; thus, kind of non-uniformity creates on behavior between nanoparticles and base fluid. This non-uniformity leads to significant effects on results of two phase modeling that creates better agreement to single phase modeling with experimental results. Results indicate that heat transfer decreases with increasing diameter and volume fraction of nanoparticles. Also, effect of nanoparticle diameter on flow and heat transfer is tangible.

[1] Karimipour A., Esfe M.H., Safaei M.R., Semiromi T.D., Jafari S., Kazi S.N., Mixed convection of copper–water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method, Physica A, 150, 2014, pp. 150-168.

[2] Rahman M.M., Mojumder S., Saha S., Mekhilef S., Saidur R., Effect of solid volume fraction and tilt angle in a quarter circular solar thermal collectors ﬁlled with CNT–water nanoﬂuid, International Communications in Heat and Mass Transfer, 57, 2014, pp. 79-90.

[3] Karimipour A., New correlation for Nusselt number of nanoﬂuid with Ag / Al_{2}O_{3}/Cunanoparticles in a microchannel considering slip velocity and temperature jump by using lattice Boltzmann method, International Journal of Thermal Sciences, 91, 2015, pp. 146-156.

[4] Karimipour A., H. Nezhad A., D’Orazio A., Esfe M.H., Safaei M.R., Shirani E., Simulation of copper–water nanofluid in a microchannel in slip flow regime using lattice Boltzmann method, European Journal of Mechanics B/Fluids, 49, 2015, pp. 89-99.

[5] Xuan Y., Li Q., Investigation on Convective Heat Transfer and Flow Features of Nanofluids, Journal of Heat Transfer, 125, 2003, pp. 151-155. [6] Wen D., Ding Y., Experimental investigation into the pool boiling heat transfer of aqueous based γ-alumina nanoﬂuids, Journal of Nanoparticle Research, 7, 2005, pp. 265-274. [7] Ding Y., Alias H., Wen D., Williams R.A., Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanoﬂuids), International Journal of Heat and Mass Transfer, 49, 2006, pp. 240-250.

[8] Zeinali Heris S., Nasr Esfahany M., Etemad S.Gh., Experimental investigation of convective heat transfer of Al_{2}O_{3} /water nanoﬂuid in circular tube, International Journal of Heat and Fluid Flow, 28, 2007, pp. 203-210.

[9] Guo Sh.Zh., Li Y., Etemad S.Gh., Jiang J.S., Xie H.Q., Nanoﬂuids Containing γ-Fe_{2}O_{3} Nanoparticles and Their Heat Transfer Enhancements, Nanoscale Res Lett, 5, 2010, pp. 1222-1227.

[10] Santra K.A., Sen S., Chakraborty N., Study of heat transfer due to laminar ﬂow of copper–water nanoﬂuid through two isothermally heated parallel plates, International Journal of Thermal Sciences, 48, 2009, pp. 391-400.

[11] He Y., Men Y., Zhao Y., Lu H., Ding Y., Numerical investigation into the convective heat transfer of TiO_{2} ﬂowing through a straight tube under the laminar ﬂow conditions nanoﬂuids, Applied Thermal Engineering, 29, 2009, pp. 1965-1972.

[12] Khorasanizadeh H., Nikfar M., Amani J., Entropy generation of Cu–water nanofluid mixed convection in a cavity, European Journal of Mechanics B/Fluids, 37, 2013, pp. 143-152.

[13] Togun H., Safaei M.R., Sadri R., Kazi S.N., Badarudin A., Hooman K., Sadeghinezhad E., Numerical simulation of laminar to turbulent nanoﬂuid ﬂow and heat transfer over a backward-facing step, Applied Mathematics and Computation, 239, 2014, pp. 153-170.

[14] Khanafer Kh., Vafai K., Lightstone M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanoﬂuids, International Journal of Heat and Mass Transfer, 46, 2003, pp. 3639-3653.

[15] Oztop H.F., Abu-Nada E., Numerical study of natural convection in partially heated rectangular enclosures ﬁlled with nanoﬂuids, InternationalJournal of Heat and Fluid Flow, 29, 2008, pp. 1326-1336.

[16] Ogut E.B., Natural convection of water-based nanoﬂuids in an inclined enclosure with a heat source, International Journal of Thermal Sciences, 48, 2009, pp. 2063-2073.

[17] Kefayati GH.R., Hosseinizadeh S.F., Gorji M., Sajjadi H., Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanoﬂuid, International Communications in Heat and Mass Transfer, 38, 2011, pp. 798-805.

[18] Sheikhzadeh G.A., Arefmanesh A., Kheirkhah

M.H., Abdollahi R., Natural convection of Cu–water nanofluid in a cavity with partially active side walls, European Journal of Mechanics B/Fluids, 30, 2011, pp. 166-176.

[19] Sheikhzadeh G.A., Nikfar M., Fattahi A., Numerical study of natural convection and entropy generation of Cu-water nanofluid around an obstacle in a cavity, Journal of Mechanical Science and Technology, 26, 2012, pp. 3347-3356.

[20] Sheikhzadeh G.A., Nikfar M, Aspect ratio effects of an adiabatic rectangular obstacle on natural convection and entropy generation of a nanofluid in an enclosure, Journal of Mechanical Science and Technology, 27, 2013, pp. 3495-3504.

[21] Cho Ch.Ch., Heat transfer and entropy generation of natural convection in nanoﬂuid-ﬁlled square cavity with partially-heated wavy surface, International Journal of Heat and Mass Transfer, 77, 2014, pp. 818-827.

[22] Nnanna A.G.A., Experimental Model of Temperature-Driven Nanoﬂuid, Journal of Heat Transfer, 129, 2007, pp. 697-704.

[23] Kh. Mahrood M.R., Etemad S.Gh., Bagheri R., Free convection heat transfer of non Newtonian nanoﬂuids under constant heat ﬂux condition, International Communications in Heat and Mass Transfer, 38, 2011, pp. 1449-1454.

[24] Hu Y., He Y., Qi C., Jiang B., Inaki Schlaberg H., Experimental and numerical study of natural convection in a square enclosure ﬁlled with nanoﬂuid, International Journal of Heat and Mass Transfer, 78, 2014, pp. 380-392.

[25] Putra N., Roetzel W., Das S.K., Natural convection of nano-fluids, Heat and Mass Transfer, 39, 2003, pp. 775-784.

[26] Wen D., Ding Y., Formulation of nanoﬂuids for natural convective heat transfer applications, International Journal of Heat and Fluid Flow, 26, 2005, pp. 855-864.

[27] Wen D., Ding Y., Natural Convective Heat Transfer of Suspensions of Titanium Dioxide Nanoparticles (Nanoﬂuids), IEEE Transactions on nanotechnology, 5, 2006, pp. 220-227.

[28] Chang B.H., Miis A.F., Hernandez E., Natural convection of microparticle suspensions in thin enclosures, International Journal of Heat and Mass Transfer, 51, 2008, pp. 1332-1341.

[29] Li C.H., Peterson G.P., Experimental Studies of Natural Convection Heat Transfer of Al_{2}O_{3}/DI Water Nanoparticle Suspensions (Nanoﬂuids), Advances in Mechanical Engineering, Article ID 742739, 2010, 10 pages.

[30] Ho C.J., Liu W.K., Chang Y.S., W.K., Lin C.C., Natural convection heat transfer of alumina-water nanoﬂuid in vertical square enclosures: An experimental study, International Journal of Thermal Sciences, 49, 2010, pp. 1345-1353.

[31] Hu Y., He Y., Wang Sh., Wang Q., Schlaberg H.I., Experimental and Numerical Investigation on Natural Convection Heat Transfer of TiO_{2}–Water Nanofluids in a Square Enclosure, Journal of Heat Transfer, 136, 2014, pp. 1-8.

[32] Ho C.J., Chen M.W., Li Z.W., Numerical simulation of natural convection of nanoﬂuid in a square enclosure: Eﬀects due to uncertainties of viscosity and thermal conductivity, International Journal of Heat and Mass Transfer, 51, 2008, pp. 4506-4516.

[33] Abouali O., Falahatpisheh A., Numerical investigation of natural convection of Al_{2}O_{3 }nanoﬂuid in vertical annuli, Heat Mass Transfer, 46, 2009, pp. 15-23.

[34] Abu-Nada E., Chamkha A.J., Effect of nanoﬂuid variable properties on natural convection in enclosures ﬁlled with a CuO-EG-Water nanoﬂuid, International Journal of Thermal Sciences, 49, 2010, pp. 2339-2352.

[35] Brinkman H.C., The Viscosity of Concentrated Suspensions and Solutions, Journal of Chemical Physics, 20, 1952, p. 571.

[36] Abouali O., Ahmadi G., Computer simulations of natural convection of single phase nanoﬂuids in simple enclosures: A critical review, J Applied Thermal Engineering, 36, 2012, pp. 1-13.

[37] Esmaeilpour M., Abdollahzadeh M., Free convection and entropy generation of nanoﬂuid inside an enclosure with different patterns of vertical wavy walls, International Journal of Thermal Sciences, 52, 2012, pp. 127-136.

[38] Corcione M., Heat transfer features of buoyancy-driven nanoﬂuids inside rectangular enclosures differentially heated at the sidewalls, International Journal of Thermal Sciences, 49, 2010, pp. 1536-1546.

[39] Bird R.B., Stewart W.E., Lightfoot, E. N., Transport Phenomena, Wiley, New York, 1960. [40] Buongiorno J., Convective Transports in Nanofluids, Journal of Heat Transfer, 128, 2006, pp. 240-250.

[41] Weaver J.A., Viskanta R., Natural Convection due to Horizontal Temperature and Concentration Gradients e 2. Species Interdiffusion, Soret and Dufour Effects, International Journal of Heat and Mass Transfer, 34, 1991, pp. 3121-3133.

[42] Nithyadevi N., Yang R.J., Double Diffusive Natural Convection in a Partially Heated Enclosure with Soret and Dufour Effects, International Journal of Heat and Fluid Flow, 30, 2009, pp. 902-910.

[43] Sheikhzadeh G.A., Dastmalchi M., Khorasanizadeh H., Effects of nanoparticles transport mechanisms on Al_{2}O_{3}-water nanoﬂuid natural convection in a square enclosure, International Journal of Thermal Sciences, 66, 2013, pp. 51-62.

[44] Khanafer Kh., Vafai K., A critical synthesis of thermophysical characteristics of nanoﬂuids, International Journal of Heat and Mass Transfer, 54, 2011, pp. 4410-4428.

[45] Brenner H., Bielenberg J.R., A continuum approach to phoretic motions: thermophoresis, Phys. A, 355, 2005, pp. 251-273.