**ABSTRACT**

This paper studies the effect of a constant magnetic field on the mixed convection heat transfer and the entropy generation of CuO-water nanofluid in an open C-shaped cavity with a numerical method. The governing equations are presented by control volume method and they are solved simultaneously by the SIMPLE algorithm. This study examines the effect of the Hartman number, aspect ratio, Reynolds number, and Richardson number parameters for different solid volume fraction of nanoparticles. Also Nusselt number, entropy generation, thermal performance criteria and coefficient of performance is studied in this research. The calculated parameters are the Hartman number, aspect ratio, Reynolds number, Richardson number, nanofluid solid volume fraction, Nusselt number, and coefficient of performance. The results show that increasing the Hartmann number reduces the entropy generation. However, the thermal performance increases. Increasing the aspect ratio raises heat transfer and thermal performance. The effects of nanofluid solid volume fraction on mixed convection heat transfer and entropy generation are also investigated and discussed.

**KEYWORDS**

PAPER SUBMITTED: 2017-12-13

PAPER REVISED: 2018-03-05

PAPER ACCEPTED: 2018-03-08

PUBLISHED ONLINE: 2018-04-28

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 6**, PAGES [3455 - 3465]

- Dawood, HK, Mohammed, H., Che Sidik, N., Munisamy, K., Wahid M, Forced, natural and mixed-convection heat transfer and fluid flow in annulus A review. Int. Comm. Heat & Mass Tr, 62(2015), pp. 45-57.
- Mandal, S., Dipak Sen, A., Brief review on mixed convection heat transfer in channel flow with vortex generator for electronic chip cooling. Int. J. of Engineering Research and Application, 6(2016) 6, pp.74-82.
- Garoosi, F., Hoseininejad, F., Rashidi, M. M., Numerical study of natural convection heat transfer in a heat exchanger filled with nanofluids. Energy, 109 (2016), pp. 664-78.
- Garoosi, F, Rohani, B, Rashidi, M. M., Two-phase mixture modeling of mixed convection of nanofluids in a square cavity with internal and external heating. Powder Technology, 275 (2015).
- Mahmoudi, A., Shahi, M, Talebi, F., Effect of inlet and outlet location on the mixed convective cooling inside the ventilated cavity subjected to an external nanofluid. International Communication Heat and Mass Transfer 8(2010), pp. 1158-1173.
- Shahi, M, Mahmoudi AH, Talebi F., Numerical study of mixed convective cooling in a square cavity ventilated and partially heated from the below utilizing nanofluid. International Communication Heat and Mass Transfer 28(2010), 37(2), pp. 201-213.
- Sourtiji, E, Gorji-Bandpy, M., Ganji, D. D., Hosseinizadeh, S. F., Numerical analysis of mixed convection heat transfer of Al 2 O 3-water nanofluid in a ventilated cavity considering different positions of the outlet port. Powder Technology, 31(2014), 262, pp. 71-81.
- Mansour, M., Bakeir, M., Chamkha, AJ, Natural convection inside a C-shaped nanofluid filled enclosure with localized heat sources. Int. J. of Numerical Methods for Heat & Fluid Flow, (2013). pp.1954-1978.
- Moojumder, S, Saha, S, Rahman M. R, Rahman M. Khan M., Rabbi Md., Ibrahim Talaat A, Numerical study on mixed convection heat transfer in a porous L-shaped cavity. Eng. Sc. and Tech., Int. J, 20(2017), 1.
- Kasaeipoor, A, Ghasemi, B, Aminossadati, SM. Convection of Cu-water nanofluid in a vented T-shaped cavity in the presence of magnetic field. International Journal of Thermal Science, 94 (2015), pp. 50-60.
- Armaghani T., Ismael M. A., Chamkha A. J., Analysis of entropy generation and natural convection in an inclined partially porous layered cavity filled with a nanofluid, Canadian J Physics, 95(2017), pp 238-252.
- Chamkha A.J., Rashad A.M., Mansour M.A., Armaghani T., Ghalambaz M., Effects of heat sink and source and entropy generation on MHD mixed convection of a Cu-water nanofluid in a lid-driven square porous enclosure with partial slip, Physics of Fluids 29 (2017).
- Chamkha A.J., A.M. Rashad, T. Armaghani, M.A. Mansour, Effects of partial slip on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu-water nanofluid, Journal of Thermal Analysis and Calorimetry, Journal of Thermal Analysis and Calorimetry, (2017)
- Chamkha A.J., Rashad A.M., Armaghani T., Mansour M.A., Entropy Generation and MHD Natural Convection of a Nanofluid in an Inclined Square Porous Cavity: Effects of a Heat Sink and Source Size and Location, Chinese J of Physics, 56(2018),pp. 193-211.
- Armaghani T., Esmaeili H., Mohammadpoor Y.A., I. Pop, MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Heat and Mass Transfer
- Nazari, M., Maghrebi, M.., Armaghani, T., Chamkha, A. J., New models for heat flux splitting at the boundary of a porous medium: three energy equations for nanofluid flow under local thermal nonequilibrium conditions, Canadian Journal of physics., 92, (2014), pp. 1312-1319.
- Armaghani, T., Maghrebi, M. J., Chamkha, Ali J., Nazari, M., Effects of particle migration on nanofluid forced convection heat transfer in a local thermal nonequilibrium porous channel, J. of nanofluids, 3(2014).
- Armaghani, T., Maghrebi, M. J., Chamkha, A. J., Al-Mudhaf, A. F., Forced convection heat transfer of nanofluids in a channel filled with porous media under local thermal non-equilibrium condition with three new models for absorbed heat flux, J. of nanofluids, 6(2017), pp. 362-367.
- Armaghani, T., Chamkha, A.J., Maghrebi, M.J., Nazari, M., Numerical analysis of a nanofluid forced convection in a porous channel: A new heat flux model in ‘L.T.N.E.' condition. J. Porous Media, 17(2014).
- Maghrebi, M.J., Nazari, M., Armaghani, T., Forced convection heat transfer of nanofluids in a porous channel. Transp. Porous Media, 93(2012), pp. 401-4013.
- Saryazdi, A., B., Talebi, F., Armaghani, T., Pop, I., Numerical study of forced convection flow and heat transfer of a nanofluid flowing inside a straight circular pipe filled with a saturated porous medium. Eur. Phys. J. Plus, 131, (2016), pp. 78-88.
- Makulati N, Kasaeipoor A, Rashidi MM. Numerical study of natural convection of a water-alumina nanofluid in inclined C-shaped enclosures under the effect of M. field. Adv. Powder Tech.
- Rahman M, Parvin S, Saidur R, Rahim NA.. Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity. International Communication in Heat and Mass Transfer, 38, (2011), 2 pp. 184-193.
- Rashidi MM, Abelman S, Mehr NF. Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. International Journal of Heat and Mass Transfer, 62(2013), pp. 515-25.
- Daniel YS. Steady MHD Boundary-layer Slip Flow and Heat Transfer of Nanofluid over a Convectively Heated of a Non-linear Permeable Sheet. Journal of Advanced Mechanical Engineering. 3(2016), 1, pp. 1-4.
- Rashidi MM, Mahmud S, Freidoonimehr N, Rostami B. Analysis of entropy generation in an MHD flow over a rotating porous disk with variable physical properties. Int. J. of Exergy. 16(2015)4, pp.481-503.
- Bejan, A., A study of entropy generation in fundamental convective heat trans, J. Heat Tran, 101(1979).
- Bejan A., Second-law analysis in heat and thermal design, Advance Heat Transfer., 15 (1982).
- Bejan A, Entropy Generation Minimization,.Entropy generation minimization: The new thermodynamics of finite‐size devices and finite‐time processes, J. of Applied Physics 79(1996).
- Daniel YS, Daniel SK. Effects of buoyancy and thermal radiation on MHD flow over a stretching porous sheet using homotopy analysis method. Alexandria Engineering Journal, 54(2015)3, pp. 705-712.
- Daniel YS, Aziz ZA, Ismail Z, Salah F. Effects of thermal radiation, viscous and Joule heating on electrical MHD nanofluid with double stratification. Chinese Journal of Physics, 55(2017) 3, pp. 630-51.
- Jafari SS, Freidoonimehr N. Second law of thermodynamics analysis of hydro-magnetic nano-fluid slip flow over a stretching permeable surface. J. of the Brazilian Soc. of Mech. Sc. and Eng. 37(2015), 4.
- Daniel YS. Laminar Convective Boundary Layer Slip Flow over a Flat Plate using Homotopy Analysis Method. Journal of The Institution of Engineers (India): Series E.; 97(2016), 2, pp.115-21.
- Rashidi M, Ali M, Freidoonimehr N, Nazari F, Parametric analysis and optimization of entropy generation in unsteady MHD flow over a stretching rotating disk using artificial neural networkand particle swarm optimization algorithm. Energy, 55(2013), pp. 497-510.
- Al-Zamily A, Ruhul Amin M, Natural convection and entropy generation in Nanofluid-filled semi-circular enclosure with heat flux source. Procedia Eng., 105(2015), pp. 418-24.
- Chamkha A., Ismael M., Kasaeipoor A., Armaghani T., Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field, Entropy 18 (2016)2.
- Ismael M, Armaghani T, Chamkha A, Conjugate heat transfer and entropy generation in a cavity filled with a nanofluid-saturated porous media and heated by a triangular solid, J. of the T. Inst. Ch. Eng. 59(2015).
- Das SK, Putra N, Theisen P, Roetzel W: Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer, 125(2003), pp. 567-574.
- Patel HE, Das SK, Sundararajan T, Sreekumanran NA, George B, Pradeep T: Thermal conductivities of naked and monolayer protected metal nanoparticle based nanofluids: manifestation of anomalous enhancement and chemical effects. Applied Physics Letters, 83 (2003).
- Chon CH, Kihm KD, Lee SP, Choi SUS: Empirical correlation finding the role of temperature and particle size for nanofluid thermal conductivity enhancement. Ap. Physics Letters. 87 (2005), pp. 1-3.
- Beck MP, Yuan Y, Warrier P, Teja AS: The effect of particle size on the thermal conductivity of alumina nanofluids. Journal of Nanoparticle Research, 11(2009), pp. 1129-1136.
- Moghadassi AR, Hosseini SM, Henneke DE: Effect of CuO nanoparticles in enhancing the thermal conductivities of monoethylene glycol and paraffin fluids. Industrial Engineering and Chemistry Research, Mathematical Formulation 49(2010), pp. 1900-1904.
- Ganguly,S., Sikdar, S., Basu, S., Experimental investigation of the effective electrical conductivity of aluminum oxide nanofluids, Powder Technology 196 (2009), pp. 326-330.
- Armaghani, T., Kasaeipoor A, Alavi N, Rashidi M. Numerical investigation of water-alumina nanofluid natural convection heat transfer and entropy generation in a baffled L-shaped c., J of Mol. Liq.: 223(2016).
- Mahmoudi, AH., Pop, I., Shahi, M., Effect of Magnetic field on natural Convection in a triangular enclosure filled with nanofluid International Journal of Thermal Science. 59(2012), pp. 126-140.
- Bhatti, M.M., Rashidi, M.M., Numerical simulation of entropy generation on MHD nanofluid towards a stagnation point flow over a stretching surface. International Journal of Applied and Computational Mathematics, 3(2017)3. pp. 2275-2289.
- Brinkman, H., The viscosity of concentrated suspensions and solutions. The J. Ch. Phy., 20(1952).
- Patel HE, Anoop KB, Sundararajan T, Das SK. A,. Micro-convection model for thermal conductivity of nanofluids. International Heat Transfer Conference 13, (2005), Begel House Inc.
- Santra AK, Sen S, Chakraborty N. Study of heat transfer due to laminar flow of copper-water nanofluid through two isothermally heated parallel plates. International J. of Thermal Scie. 48(2009)2, pp. 391-400.
- Patankar S. Numerical heat transfer and fluid flow. CRC press, 1980.
- Mahmoodi M, Hashemi SM., Numerical study of natural convection of a nanofluid in C-shaped enclosures. International J. of Thermal Scie. 55 (2012), pp. 76-89.
- Pourmahmoud N., Ghafouri A. and Mirzaee I., Numerical comparison of viscosity models on mixed convection in double lid-driven cavity utilized cuo-water nanofluid, Thermal Science, 20(2016), 1, pp. 347-359.
- Akdag U., Akcay S., Demiral D., heat transfer in a triangular wavy channel with cuo/water nanofluids under pulsating flow, Thermal Science, doi.org/10.2298/TSCI161018015A.