Effect of magnetic field orientation on nanofluid free convection in a porous cavity A heat visualiz

Iman Zahmatkesh; Razieh Akhlaghi Ardekani

doi:10.18186/thermal.672297

Article Open Access1 January 2020

Effect of magnetic field orientation on nanofluid free convection in a porous cavity A heat visualiz

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İman ZAHMATKESH ¹

¹Islamic Azad University

Journal of Thermal Engineering 2020, Vol. 6, Issue 1, pp. 170-186; doi.org/10.18186/thermal.672297

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Abstract

Effect of magnetic field orientation on free convection of several water–based nanofluids in a square porous cavity is analyzed in this study. To this aim, the heatline visualization technique is implemented for the first time. Moreover, streamlines and isotherms are employed to present fluid flow and temperature distribution. The governing equations are transformed into a dimensionless form and then solved using the finite–volume method. Computations are undertaken for different orientations and magnitudes of the imposed magnetic field in circumstances with distinct Rayleigh numbers and the nanoparticles types and volume fractions. The corresponding results are presented in terms of dimensionless distributions of streamlines, isotherms, and heatlines as well as numerical values of the flow strength and the average Nusselt number. Inspection of the results demonstrates that increase in the magnetic field strength deteriorates the heat transfer rate. This effect, however, diminishes with rise in the magnetic field inclination angle.

Keywords: Magnetohydrodynamics; Heatline; Porous Media; Nanofluid; Cavity

References

Alchaar S, Vasseur P, Bilgen E. Hydromagnetic natural convection in a tilted rectangular enclosure. Numer Heat Transfer, Part A 1995;27:107–127. doi:10.1080/10407789508913691.
Bian W, Vasseur P, Bilgen E. Effect of an external magnetic field on buoyancy driven flow in a shallow porous cavity. Numer Heat Transfer, Part A 1996;29:625–638. doi:10.1080/1040778960891381.
Bian W, Vasseur P, Bilgen E, Meng F. Effect of an electromagnetic field on natural convection in an inclined porous layer. Int J Heat Fluid Flow 1996;17:36–44. doi:10.1016/0142-727X(95)00070-7.
Khanafer K, Chamkha AJ. Hydromagnetic natural convection from an inclined porous square enclosure with heat generation. Numer Heat Transfer, Part A 1998;33:891–910. doi:10.1080/10407789808913972.
Mahmud S, Fraser RA. Magnetohydrodynamic free convection and entropy generation in a square cavity. Int J Heat Mass Transfer 2004;47:3245–3256. doi:10.1016/j.ijheatmasstransfer.2004.02.005.
Grosan T, Revnic C, Pop I, Ingham DB. Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium. Int J Heat Mass Transfer 2009;52:1525–1533. doi:10.1016/j.ijheatmasstransfer.2016.08.025.
Pekmen B, Tezer–Sezgin M. DRBEM solution of free convection in porous enclosures under the effect of a magnetic field. Int J Heat Mass Transfer 2013;56:454–468. doi:10.1016/j.ijheatmasstransfer.2012.09.019.
Kumar V, Krishna Murthy SVSSNVG, Rathish Kumar BV. Influence of MHD forces on Bejan’s heatlines and masslines in a doubly stratified fluid saturated Darcy porous enclosure in the presence of Soret and Dufour effects – A numerical study. Int J Heat Mass Transfer 2018;117:1041–1062. doi:10.1016/j.ijheatmasstransfer.2017.10.054.
Geridönmez BP. Numerical simulation of natural convection in a porous cavity filled with ferrofluid in presence of magnetic source. J Thermal Eng 2018;4:1756–1769. doi:10.18186/journal-of-thermal-engineering.369169.
Mahfoud B, Bendjaghloli A. Natural convection of a nanofluid in a conical container. J Thermal Eng 2018;4:1713–1723. doi:10.18186/journal-of-thermal-engineering.367407.
Singh P, Sharma P, Gupta R, Wanchoo RK. Heat transfer characteristics of propylene glycol/water based magnesium oxide nanofluid flowing through straight tubes and helical coils. J Thermal Eng 2018;4:1737–1755. doi:10.18186/journal-of-thermal-engineering.369007.
Zahmatkesh I, Naghedifar SA. Oscillatory mixed convection in jet impingement cooling of a horizontal surface immersed in a nanofluid–saturated porous medium. Numer Heat Transfer, Part A 2017;72:401–416. doi:10.1080/10407782.2017.1376961.
Zahmatkesh I, Torshizi E. Scrutiny of unsteady flow and heat transfer in a backward–facing step under pulsating nanofluid blowing using the Eulerian–Eulerian approach. J Mech 2019;35:93-105. doi:10.1017/jmech.2017.73.
Zahmatkesh I, Habibi MR. Natural and mixed convection of nanofluid in porous cavities: A critical analysis using the Buongiorno’s model. J Theor Appl Mech 2019;57:221–233. doi:10.15632/jtam-pl.57.1.221.
Koopaee MK, Jelodari I. Numerical investigation of magnetic field inclination angle on transient natural convection in an enclosure filled with nanofluid, Engineering Computations 2014;31:1342–1360. doi:10.1108/EC-12-2012-0320.
Koopaee MK, Omidvar A, Jelodari I. Numerical study on the steady–state heat transfer rate of nanofluid filled within square cavity in the presence of oriented magnetic field. Proc Inst Mech Eng, Part C: J Mech Eng Sci 2014;228:1348–1362. doi:10.1177/0954406213507860.
Akinshilo A, Ilegbusi AO. Investigation of Lorentz force effect on steady nanofluid flow and heat transfer through parallel plates. J Thermal Eng 2019;5:482–497. doi:10.18186/thermal.625919.
Malik S, Nayak AK. MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating. Int J Heat Mass Transfer 2017;111:329–345. doi:10.1016/j.ijheatmasstransfer.2017.03.123.
Mansour MA, Ahmed SE, Chamkha A. Entropy generation optimization for MHD natural convection of a nanofluid in porous media–filled enclosure with active parts and viscous dissipation. Int J Numer Methods Heat Fluid Flow 2017;27:379–399. doi:10.1108/HFF-10-2015-0408.
Sheikholeslami M, Rokni HB. Magnetohydrodynamic CuO–water nanofluid in a porous complex-shaped enclosure. J Thermal Sci Eng Appl 2017;9;041007. doi:10.1115/1.4035973.
Rashad AM, Rashidi MM, Lorenzini G, Ahmed SE, Aly AM. Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu–water nanofluid. Int J Heat Mass Transfer 2017;104:878–889. doi:10.1016/j.ijheatmasstransfer.2016.08.025.
Rashad AM, Armaghani T, Chamkha AJ, Mansour MA. 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. Chin J Phys 2018;56:193–211. doi:10.1016/j.cjph.2017.11.026. 185 Journal of Thermal Engineering, Research Article, Vol. 6, No. 1, pp. 170-186, January, 2020
Balla CS, Kishan N, Gorla RSR, Gireesha BJ. MHD boundary layer flow and heat transfer in an inclined porous square cavity filled with nanofluids. Ain Shams Eng J 2017;8:237–254. doi:10.1016/j.asej.2016.02.010.
Zahmatkesh I, Shandiz MRH. Optimum constituents for MHD heat transfer of nanofluids within porous cavities: A Taguchi analysis in natural and mixed convection configurations, J Thermal Anal Calorim 2019;138:1669–1681. doi:10.1007/s10973-019-08191-y.
Kimura S, Bejan A. The ‘‘heatline” visualization of convective heat transfer. J Heat Transfer 1983;105:916–919. doi:10.1115/1.3245684.
Saleh H, Hashim I. Heatline visualization of natural convection in an inclined square porous enclosure with sinusoidal boundary conditions. J Porous Med 2013;16:875–885. doi:10.1615/JPorMedia.v16.i10.10.
Saleh H, Hashim I. Heatline visualization of conjugate heat transfer in square porous enclosure. J Porous Med 2013;16:1119–1132. doi:10.1615/JPorMedia.v16.i12.50.
Zahmatkesh I. Heatline visualization for buoyancy–driven flow inside a nanofluid–saturated porous enclosure. Jordan J Mech Indust Eng 2015;9:149–157.
Alsabery AI, Chamkha AJ, Hussain SH, Saleh H, Hashim I. Heatline visualization of natural convection in a trapezoidal cavity partly filled with nanofluid porous layer and partly with non–Newtonian fluid layer. Adv Powder Technol 2015;26:1230–1244. doi:10.1016/j.apt.2015.06.005.
Hussain S.H. Analysis of heatlines and entropy generation during double–diffusive MHD natural convection within a tilted sinusoidal corrugated porous enclosure. Eng Sci Technol 2016;19:926–945. doi:10.1016/j.jestch.2015.12.001.
Bondareva NS, Sheremet MA, Abu–Hamdeh N. Heatline visualization of MHD natural convection in an inclined wavy open porous cavity filled with a nanofluid with a local heater. Int J Heat Mass Transfer 2016;99:872–881. doi:10.1016/j.ijheatmasstransfer.2016.04.055.
Maxwell JA. Treatise on Electricity and Magnetism. Cambridge: Oxford University Press; 1904. doi:10.1017/CBO9780511709340.
Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys 1952;20:571–581. doi:10.1063/1.1700493.
Bourantas GC, Skouras ED, Loukopoulos VC, Burganos VN. Heat transfer and natural convection of nanofluids in porous media. Eur J Mech–B/Fluids 2014;43:45–56. doi:10.1016/j.euromechflu.2013.06.013.
Zahmatkesh I. On the suitability of the volume–averaging approximation for the description of thermal expansion coefficient of nanofluids. Proc Inst Mech Eng, Part C: J Mech Eng Sci 2015;229:2835–2841. doi:10.1177/0954406214563735.
Sun Q, Pop I. Free convection in a triangle cavity filled with a porous medium saturated with nanofluids with flush mounted heater on the wall. International Journal of Thermal Sciences 2011;50:2141–2153. doi:10.1016/j.ijthermalsci.2011.06.005.
Chamkha AJ, Ismael MA. Conjugate heat transfer in a porous cavity filled with nanofluids and heated by a triangular thick wall. Int J Thermal Sci 2013;67:135–151. doi:10.1016/j.ijthermalsci.2012.12.002. 186

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Zahmatkesh, I.; Ardekani, R.A. Effect of magnetic field orientation on nanofluid free convection in a porous cavity A heat visualiz. Journal of Thermal Engineering 2020, Vol. 6, pp. 170-186. https://doi.org/10.18186/thermal.672297

Export:

Effect of magnetic field orientation on nanofluid free convection in a porous cavity A heat visualiz

¹Islamic Azad University

Abstract

References

Alchaar S, Vasseur P, Bilgen E. Hydromagnetic natural convection in a tilted rectangular enclosure. Numer Heat Transfer, Part A 1995;27:107–127. doi:10.1080/10407789508913691.
Bian W, Vasseur P, Bilgen E. Effect of an external magnetic field on buoyancy driven flow in a shallow porous cavity. Numer Heat Transfer, Part A 1996;29:625–638. doi:10.1080/1040778960891381.
Bian W, Vasseur P, Bilgen E, Meng F. Effect of an electromagnetic field on natural convection in an inclined porous layer. Int J Heat Fluid Flow 1996;17:36–44. doi:10.1016/0142-727X(95)00070-7.
Khanafer K, Chamkha AJ. Hydromagnetic natural convection from an inclined porous square enclosure with heat generation. Numer Heat Transfer, Part A 1998;33:891–910. doi:10.1080/10407789808913972.
Mahmud S, Fraser RA. Magnetohydrodynamic free convection and entropy generation in a square cavity. Int J Heat Mass Transfer 2004;47:3245–3256. doi:10.1016/j.ijheatmasstransfer.2004.02.005.
Grosan T, Revnic C, Pop I, Ingham DB. Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium. Int J Heat Mass Transfer 2009;52:1525–1533. doi:10.1016/j.ijheatmasstransfer.2016.08.025.
Pekmen B, Tezer–Sezgin M. DRBEM solution of free convection in porous enclosures under the effect of a magnetic field. Int J Heat Mass Transfer 2013;56:454–468. doi:10.1016/j.ijheatmasstransfer.2012.09.019.
Kumar V, Krishna Murthy SVSSNVG, Rathish Kumar BV. Influence of MHD forces on Bejan’s heatlines and masslines in a doubly stratified fluid saturated Darcy porous enclosure in the presence of Soret and Dufour effects – A numerical study. Int J Heat Mass Transfer 2018;117:1041–1062. doi:10.1016/j.ijheatmasstransfer.2017.10.054.
Geridönmez BP. Numerical simulation of natural convection in a porous cavity filled with ferrofluid in presence of magnetic source. J Thermal Eng 2018;4:1756–1769. doi:10.18186/journal-of-thermal-engineering.369169.
Mahfoud B, Bendjaghloli A. Natural convection of a nanofluid in a conical container. J Thermal Eng 2018;4:1713–1723. doi:10.18186/journal-of-thermal-engineering.367407.
Singh P, Sharma P, Gupta R, Wanchoo RK. Heat transfer characteristics of propylene glycol/water based magnesium oxide nanofluid flowing through straight tubes and helical coils. J Thermal Eng 2018;4:1737–1755. doi:10.18186/journal-of-thermal-engineering.369007.
Zahmatkesh I, Naghedifar SA. Oscillatory mixed convection in jet impingement cooling of a horizontal surface immersed in a nanofluid–saturated porous medium. Numer Heat Transfer, Part A 2017;72:401–416. doi:10.1080/10407782.2017.1376961.
Zahmatkesh I, Torshizi E. Scrutiny of unsteady flow and heat transfer in a backward–facing step under pulsating nanofluid blowing using the Eulerian–Eulerian approach. J Mech 2019;35:93-105. doi:10.1017/jmech.2017.73.
Zahmatkesh I, Habibi MR. Natural and mixed convection of nanofluid in porous cavities: A critical analysis using the Buongiorno’s model. J Theor Appl Mech 2019;57:221–233. doi:10.15632/jtam-pl.57.1.221.
Koopaee MK, Jelodari I. Numerical investigation of magnetic field inclination angle on transient natural convection in an enclosure filled with nanofluid, Engineering Computations 2014;31:1342–1360. doi:10.1108/EC-12-2012-0320.
Koopaee MK, Omidvar A, Jelodari I. Numerical study on the steady–state heat transfer rate of nanofluid filled within square cavity in the presence of oriented magnetic field. Proc Inst Mech Eng, Part C: J Mech Eng Sci 2014;228:1348–1362. doi:10.1177/0954406213507860.
Akinshilo A, Ilegbusi AO. Investigation of Lorentz force effect on steady nanofluid flow and heat transfer through parallel plates. J Thermal Eng 2019;5:482–497. doi:10.18186/thermal.625919.
Malik S, Nayak AK. MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating. Int J Heat Mass Transfer 2017;111:329–345. doi:10.1016/j.ijheatmasstransfer.2017.03.123.
Mansour MA, Ahmed SE, Chamkha A. Entropy generation optimization for MHD natural convection of a nanofluid in porous media–filled enclosure with active parts and viscous dissipation. Int J Numer Methods Heat Fluid Flow 2017;27:379–399. doi:10.1108/HFF-10-2015-0408.
Sheikholeslami M, Rokni HB. Magnetohydrodynamic CuO–water nanofluid in a porous complex-shaped enclosure. J Thermal Sci Eng Appl 2017;9;041007. doi:10.1115/1.4035973.
Rashad AM, Rashidi MM, Lorenzini G, Ahmed SE, Aly AM. Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu–water nanofluid. Int J Heat Mass Transfer 2017;104:878–889. doi:10.1016/j.ijheatmasstransfer.2016.08.025.
Rashad AM, Armaghani T, Chamkha AJ, Mansour MA. 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. Chin J Phys 2018;56:193–211. doi:10.1016/j.cjph.2017.11.026. 185 Journal of Thermal Engineering, Research Article, Vol. 6, No. 1, pp. 170-186, January, 2020
Balla CS, Kishan N, Gorla RSR, Gireesha BJ. MHD boundary layer flow and heat transfer in an inclined porous square cavity filled with nanofluids. Ain Shams Eng J 2017;8:237–254. doi:10.1016/j.asej.2016.02.010.
Zahmatkesh I, Shandiz MRH. Optimum constituents for MHD heat transfer of nanofluids within porous cavities: A Taguchi analysis in natural and mixed convection configurations, J Thermal Anal Calorim 2019;138:1669–1681. doi:10.1007/s10973-019-08191-y.
Kimura S, Bejan A. The ‘‘heatline” visualization of convective heat transfer. J Heat Transfer 1983;105:916–919. doi:10.1115/1.3245684.
Saleh H, Hashim I. Heatline visualization of natural convection in an inclined square porous enclosure with sinusoidal boundary conditions. J Porous Med 2013;16:875–885. doi:10.1615/JPorMedia.v16.i10.10.
Saleh H, Hashim I. Heatline visualization of conjugate heat transfer in square porous enclosure. J Porous Med 2013;16:1119–1132. doi:10.1615/JPorMedia.v16.i12.50.
Zahmatkesh I. Heatline visualization for buoyancy–driven flow inside a nanofluid–saturated porous enclosure. Jordan J Mech Indust Eng 2015;9:149–157.
Alsabery AI, Chamkha AJ, Hussain SH, Saleh H, Hashim I. Heatline visualization of natural convection in a trapezoidal cavity partly filled with nanofluid porous layer and partly with non–Newtonian fluid layer. Adv Powder Technol 2015;26:1230–1244. doi:10.1016/j.apt.2015.06.005.
Hussain S.H. Analysis of heatlines and entropy generation during double–diffusive MHD natural convection within a tilted sinusoidal corrugated porous enclosure. Eng Sci Technol 2016;19:926–945. doi:10.1016/j.jestch.2015.12.001.
Bondareva NS, Sheremet MA, Abu–Hamdeh N. Heatline visualization of MHD natural convection in an inclined wavy open porous cavity filled with a nanofluid with a local heater. Int J Heat Mass Transfer 2016;99:872–881. doi:10.1016/j.ijheatmasstransfer.2016.04.055.
Maxwell JA. Treatise on Electricity and Magnetism. Cambridge: Oxford University Press; 1904. doi:10.1017/CBO9780511709340.
Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys 1952;20:571–581. doi:10.1063/1.1700493.
Bourantas GC, Skouras ED, Loukopoulos VC, Burganos VN. Heat transfer and natural convection of nanofluids in porous media. Eur J Mech–B/Fluids 2014;43:45–56. doi:10.1016/j.euromechflu.2013.06.013.
Zahmatkesh I. On the suitability of the volume–averaging approximation for the description of thermal expansion coefficient of nanofluids. Proc Inst Mech Eng, Part C: J Mech Eng Sci 2015;229:2835–2841. doi:10.1177/0954406214563735.
Sun Q, Pop I. Free convection in a triangle cavity filled with a porous medium saturated with nanofluids with flush mounted heater on the wall. International Journal of Thermal Sciences 2011;50:2141–2153. doi:10.1016/j.ijthermalsci.2011.06.005.
Chamkha AJ, Ismael MA. Conjugate heat transfer in a porous cavity filled with nanofluids and heated by a triangular thick wall. Int J Thermal Sci 2013;67:135–151. doi:10.1016/j.ijthermalsci.2012.12.002. 186

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Export:

[1] Alchaar S, Vasseur P, Bilgen E. Hydromagnetic natural convection in a tilted rectangular enclosure. Numer Heat Transfer, Part A 1995;27:107–127. doi:10.1080/10407789508913691.

[2] Bian W, Vasseur P, Bilgen E. Effect of an external magnetic field on buoyancy driven flow in a shallow porous cavity. Numer Heat Transfer, Part A 1996;29:625–638. doi:10.1080/1040778960891381.

[3] Bian W, Vasseur P, Bilgen E, Meng F. Effect of an electromagnetic field on natural convection in an inclined porous layer. Int J Heat Fluid Flow 1996;17:36–44. doi:10.1016/0142-727X(95)00070-7.

[4] Khanafer K, Chamkha AJ. Hydromagnetic natural convection from an inclined porous square enclosure with heat generation. Numer Heat Transfer, Part A 1998;33:891–910. doi:10.1080/10407789808913972.

[5] Mahmud S, Fraser RA. Magnetohydrodynamic free convection and entropy generation in a square cavity. Int J Heat Mass Transfer 2004;47:3245–3256. doi:10.1016/j.ijheatmasstransfer.2004.02.005.

[6] Grosan T, Revnic C, Pop I, Ingham DB. Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium. Int J Heat Mass Transfer 2009;52:1525–1533. doi:10.1016/j.ijheatmasstransfer.2016.08.025.

[7] Pekmen B, Tezer–Sezgin M. DRBEM solution of free convection in porous enclosures under the effect of a magnetic field. Int J Heat Mass Transfer 2013;56:454–468. doi:10.1016/j.ijheatmasstransfer.2012.09.019.

[8] Kumar V, Krishna Murthy SVSSNVG, Rathish Kumar BV. Influence of MHD forces on Bejan’s heatlines and masslines in a doubly stratified fluid saturated Darcy porous enclosure in the presence of Soret and Dufour effects – A numerical study. Int J Heat Mass Transfer 2018;117:1041–1062. doi:10.1016/j.ijheatmasstransfer.2017.10.054.

[9] Geridönmez BP. Numerical simulation of natural convection in a porous cavity filled with ferrofluid in presence of magnetic source. J Thermal Eng 2018;4:1756–1769. doi:10.18186/journal-of-thermal-engineering.369169.

[10] Mahfoud B, Bendjaghloli A. Natural convection of a nanofluid in a conical container. J Thermal Eng 2018;4:1713–1723. doi:10.18186/journal-of-thermal-engineering.367407.

[11] Singh P, Sharma P, Gupta R, Wanchoo RK. Heat transfer characteristics of propylene glycol/water based magnesium oxide nanofluid flowing through straight tubes and helical coils. J Thermal Eng 2018;4:1737–1755. doi:10.18186/journal-of-thermal-engineering.369007.

[12] Zahmatkesh I, Naghedifar SA. Oscillatory mixed convection in jet impingement cooling of a horizontal surface immersed in a nanofluid–saturated porous medium. Numer Heat Transfer, Part A 2017;72:401–416. doi:10.1080/10407782.2017.1376961.

[13] Zahmatkesh I, Torshizi E. Scrutiny of unsteady flow and heat transfer in a backward–facing step under pulsating nanofluid blowing using the Eulerian–Eulerian approach. J Mech 2019;35:93-105. doi:10.1017/jmech.2017.73.

[14] Zahmatkesh I, Habibi MR. Natural and mixed convection of nanofluid in porous cavities: A critical analysis using the Buongiorno’s model. J Theor Appl Mech 2019;57:221–233. doi:10.15632/jtam-pl.57.1.221.

[15] Koopaee MK, Jelodari I. Numerical investigation of magnetic field inclination angle on transient natural convection in an enclosure filled with nanofluid, Engineering Computations 2014;31:1342–1360. doi:10.1108/EC-12-2012-0320.

[16] Koopaee MK, Omidvar A, Jelodari I. Numerical study on the steady–state heat transfer rate of nanofluid filled within square cavity in the presence of oriented magnetic field. Proc Inst Mech Eng, Part C: J Mech Eng Sci 2014;228:1348–1362. doi:10.1177/0954406213507860.

[17] Akinshilo A, Ilegbusi AO. Investigation of Lorentz force effect on steady nanofluid flow and heat transfer through parallel plates. J Thermal Eng 2019;5:482–497. doi:10.18186/thermal.625919.

[18] Malik S, Nayak AK. MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating. Int J Heat Mass Transfer 2017;111:329–345. doi:10.1016/j.ijheatmasstransfer.2017.03.123.

[19] Mansour MA, Ahmed SE, Chamkha A. Entropy generation optimization for MHD natural convection of a nanofluid in porous media–filled enclosure with active parts and viscous dissipation. Int J Numer Methods Heat Fluid Flow 2017;27:379–399. doi:10.1108/HFF-10-2015-0408.

[20] Sheikholeslami M, Rokni HB. Magnetohydrodynamic CuO–water nanofluid in a porous complex-shaped enclosure. J Thermal Sci Eng Appl 2017;9;041007. doi:10.1115/1.4035973.

[21] Rashad AM, Rashidi MM, Lorenzini G, Ahmed SE, Aly AM. Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu–water nanofluid. Int J Heat Mass Transfer 2017;104:878–889. doi:10.1016/j.ijheatmasstransfer.2016.08.025.

[22] Rashad AM, Armaghani T, Chamkha AJ, Mansour MA. 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. Chin J Phys 2018;56:193–211. doi:10.1016/j.cjph.2017.11.026. 185 Journal of Thermal Engineering, Research Article, Vol. 6, No. 1, pp. 170-186, January, 2020

[23] Balla CS, Kishan N, Gorla RSR, Gireesha BJ. MHD boundary layer flow and heat transfer in an inclined porous square cavity filled with nanofluids. Ain Shams Eng J 2017;8:237–254. doi:10.1016/j.asej.2016.02.010.

[24] Zahmatkesh I, Shandiz MRH. Optimum constituents for MHD heat transfer of nanofluids within porous cavities: A Taguchi analysis in natural and mixed convection configurations, J Thermal Anal Calorim 2019;138:1669–1681. doi:10.1007/s10973-019-08191-y.

[25] Kimura S, Bejan A. The ‘‘heatline” visualization of convective heat transfer. J Heat Transfer 1983;105:916–919. doi:10.1115/1.3245684.

[26] Saleh H, Hashim I. Heatline visualization of natural convection in an inclined square porous enclosure with sinusoidal boundary conditions. J Porous Med 2013;16:875–885. doi:10.1615/JPorMedia.v16.i10.10.

[27] Saleh H, Hashim I. Heatline visualization of conjugate heat transfer in square porous enclosure. J Porous Med 2013;16:1119–1132. doi:10.1615/JPorMedia.v16.i12.50.

[28] Zahmatkesh I. Heatline visualization for buoyancy–driven flow inside a nanofluid–saturated porous enclosure. Jordan J Mech Indust Eng 2015;9:149–157.

[29] Alsabery AI, Chamkha AJ, Hussain SH, Saleh H, Hashim I. Heatline visualization of natural convection in a trapezoidal cavity partly filled with nanofluid porous layer and partly with non–Newtonian fluid layer. Adv Powder Technol 2015;26:1230–1244. doi:10.1016/j.apt.2015.06.005.

[30] Hussain S.H. Analysis of heatlines and entropy generation during double–diffusive MHD natural convection within a tilted sinusoidal corrugated porous enclosure. Eng Sci Technol 2016;19:926–945. doi:10.1016/j.jestch.2015.12.001.

[31] Bondareva NS, Sheremet MA, Abu–Hamdeh N. Heatline visualization of MHD natural convection in an inclined wavy open porous cavity filled with a nanofluid with a local heater. Int J Heat Mass Transfer 2016;99:872–881. doi:10.1016/j.ijheatmasstransfer.2016.04.055.

[32] Maxwell JA. Treatise on Electricity and Magnetism. Cambridge: Oxford University Press; 1904. doi:10.1017/CBO9780511709340.

[33] Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys 1952;20:571–581. doi:10.1063/1.1700493.

[34] Bourantas GC, Skouras ED, Loukopoulos VC, Burganos VN. Heat transfer and natural convection of nanofluids in porous media. Eur J Mech–B/Fluids 2014;43:45–56. doi:10.1016/j.euromechflu.2013.06.013.

[35] Zahmatkesh I. On the suitability of the volume–averaging approximation for the description of thermal expansion coefficient of nanofluids. Proc Inst Mech Eng, Part C: J Mech Eng Sci 2015;229:2835–2841. doi:10.1177/0954406214563735.

[36] Sun Q, Pop I. Free convection in a triangle cavity filled with a porous medium saturated with nanofluids with flush mounted heater on the wall. International Journal of Thermal Sciences 2011;50:2141–2153. doi:10.1016/j.ijthermalsci.2011.06.005.

[37] Chamkha AJ, Ismael MA. Conjugate heat transfer in a porous cavity filled with nanofluids and heated by a triangular thick wall. Int J Thermal Sci 2013;67:135–151. doi:10.1016/j.ijthermalsci.2012.12.002. 186

Published	1 January 2020
Version	v1
Access	Open Access

Published	1 January 2020
Version	v1
Access	Open Access

Effect of magnetic field orientation on nanofluid free convection in a porous cavity A heat visualiz

Abstract

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