EFFECTS OF SLIP VELOCITY AND VISCOUS DISSIPATION ON MHD BOUNDARY LAYER FLOW OF A MICROPOLAR-NANOFLUID OVER A WEDGE WITH INTERNAL HEAT GENERATION
Asian Journal of Mathematics and Computer Research, Volume 29, Issue 4,
Page 23-45
DOI:
10.56557/ajomcor/2022/v29i48001
Abstract
A numerical model is developed to examine the boundary layer flow of an electrically conducting, viscous incompressible micropolar nanofluid (Al2O3/water) over a wedge in the presence of a transverse magnetic field and viscous dissipation with internal heat generation/absorption.
The combined effect of both cases constant fluid suction and injection is considered, also the velocity slip’s effect is also taken into account. The governing equations have been solved using the Runge-Kutta numerical integration procedure after reducing them to boundary layer equations. Various effects of parameters that govern the flow like velocity, micro-rotation, temperature as well as for local skin friction coefficient, local Nusselt number and local wall couple stress have been illustrated graphically.
Keywords:
- Micropolar- nanofluid
- MHD
- viscous dissipation
- heat generation
- slip velocity
How to Cite
ABDOU, M. M. M., & AL-RASHIDI, E. A. (2022). EFFECTS OF SLIP VELOCITY AND VISCOUS DISSIPATION ON MHD BOUNDARY LAYER FLOW OF A MICROPOLAR-NANOFLUID OVER A WEDGE WITH INTERNAL HEAT GENERATION. Asian Journal of Mathematics and Computer Research, 29(4), 23–45. https://doi.org/10.56557/ajomcor/2022/v29i48001
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Hatami M, Ganji DD. Heat transfer and nanofluid flow in suction and blowing process between parallel disks in presence of variable magnetic field. J Mol Liq. 2014;190:159-68.
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Kocić MM, Stamenković Z, Petrović JD, Bogdanović-Jovanović JB, Nikodijević MD. Heat transfer in micropolar fluid flow under the influence of magnetic field. Therm Sci. 2016;20(suppl. 5):1391-404.
DOI: 10.2298/TSCI16S5391K
Murthy JVR, Sai KS, Bahali NK. Steady flow of micropolar fluid in a rectangular channel under transverse magnetic field with suction. AIP Adv. 2011;1(3).
DOI: 10.1063/1.3624837
Haque MM. Heat and mass transfer analysis on magneto micropolar fluid flow with heat absorption in induced magnetic field. Fluids. 2021;6(3):126.
DOI: 10.3390/fluids6030126
Ismail HNA, Abourabia AM, Hammad DA, Ahmed NA, el Desouky AA. On the MHD flow and heat transfer of a micropolar fluid in a rectangular duct under the effects of the induced magnetic field and slip boundary conditions. SN Appl Sci. 2020;2(1):25.
DOI: 10.1007/s42452-019-1615-9
Ferdows M, Liu D. Natural convective flow of a magneto-micropolar fluid along a vertical plate. Propul Power Res. 2018;7(1):43-51.
DOI: 10.1016/j.jppr.2018.01.005
Kocić MM, Stamenković Z, Petrović JD, Bogdanović-Jovanović JB, Nikodijević MD. Heat transfer in micropolar fluid flow under the influence of magnetic field. Therm Sci. 2016;20(suppl. 5):1391-404.
DOI: 10.2298/TSCI16S5391K
Rout PK, Sahoo SN, Dash GC, Mishra SR. Chemical reaction effect on MHD free convection flow in a micropolar fluid. Alex Eng J. 2016;55(3):2967-73.
DOI: 10.1016/j.aej.2016.04.033
Ashraf M, Wehgal AR. MHD flow and heat transfer of micropolar fluid between two porous disks. Appl Math Mech.-Engl. Ed. 2012;33(1):51-64. doi: 10.1007/s10483-012-1533-6.
Srinivasacharya D, Shiferaw M. Numerical solution to the MHD flow of micropolar fluid between parallel porous plates. Int J Fluid Mech Res. 2008;35(4):365-73.
DOI: 10.1615/InterJFluidMechRes.v35.i4.60
Sultana S, Roy NC. Natural convection flow of MHD micropolar fluid along a vertical wavy surface. Dhaka Univ J Sci. 2017;65(2):91-6. doi: 10.3329/dujs.v65i2.54514.
Murthy JVR, Sai KS, Bahali NK. Steady flow of micropolar fluid in a rectangular channel under transverse magnetic field with suction. AIP Adv. 2011;1(3).
DOI: 10.1063/1.3624837
Bourantas GC, Loukopoulos VC. MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid. Int J Heat Mass Transf. 2014;79:930-44.
DOI: 10.1016/j.ijheatmasstransfer.2014.08.075
Stepha NG, Jacob DK. Analysis on physical properties of micropolar nanofluid past a constantly moving porous plate. IOP Conf S Mater Sci Eng. 2021;1206(1).
DOI: 10.1088/1757-899X/1206/1/012004
Modather M, EL-Kabeir SMM. MHD forced convective boundary-layer flow of a micropolar-nanofluid from a stretching sheet. J Comp Theor Nanosci. 2018;15(4):1275-82.
DOI: 10.1166/jctn.2018.7303
Ibrahim W, Zemedu C. MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk. J Heat Transf. 2021;50(1):564-95.
DOI: 10.1002/htj.21894
Anwar MI, Shafie S, Hayat T, Shehzad SA, Salleh MZ. Numerical study for MHD stagnation-point flow of a micropolar nanofluid towards a stretching sheet. J Braz Soc Mech Sci Eng. 2017;39(1):89-100.
DOI: 10.1007/s40430-016-0610-y
Kumar TS, Kumar BR, Makinde OD, Vijaya Kumar AGV. Magneto-convective heat transfer in micropolar nanofluid over a stretching sheet with non-uniform heat source/sink. Defect Diffus Forum. 2018;387:78-90.
DOI: 10.4028/www.scientific.net/DDF.387.78
Yacob NA, Ishak A, Pop I. Falkner-Skan problem for a static or moving wedge in nanofluids. Int J Therm Sci. 2011;50(2):133-9.
DOI: 10.1016/j.ijthermalsci.2010.10.008
Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluid with submicron metallic oxide particles. Exp Heat Transf. 1998;11(2):151-70.
DOI: 10.1080/08916159808946559
Ahmadi G. Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite flat plate. Int J Eng Sci. 1976;14(7):639-46.
DOI: 10.1016/0020-7225(76)90006-9
Rees DAS, Pop I. Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate. IMA J Appl Math. 1998;61(2):179-97.
DOI: 10.1093/imamat/61.2.179
Aminossadati SM, Ghasemi B. Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure. Eur J Mech B Fluids. 2009;28(5):630-40.
DOI: 10.1016/j.euromechflu.2009.05.006
Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA. Anomalously thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett. 2001;79(14):2252-4.
DOI: 10.1063/1.1408272
Masuda H, Ebata A, Teramae K, Hishinuma V. Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, Netsu Bussei. 1993;7:227-33.
Buongiorno J, Hu W. Nanofluid coolants for advanced nuclear power plants. In: Proceedings of the ICAPP’05, Seoul. 2005;5705.
Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf. 2003;46(19):3639-53.
DOI: 10.1016/S0017-9310(03)00156-X
Buongiorno J. Convective transport in nanofluids. J Heat Transf. 2006;128(3):240-50.
DOI: 10.1115/1.2150834
Ganji DD, Malvandi A. Natural convection of nanofluids inside a vertical enclosure in the presence of a uniform magnetic field. Powder Technol. 2014;263:50-7.
DOI: 10.1016/j.powtec.2014.04.089
Abdulkadhim A, Hamzah HK, Ali FH, Yıldız Ç, Abed AM, Abed EM, et al. Effect of heat generation and heat absorption on natural convection of Cu-water nanofluid in a wavy enclosure under magnetic field. Int Commun Heat Mass Transf. 2021;120.
DOI: 10.1016/j.icheatmasstransfer.2020.105024
Medebber MA, Aissa A, Slimani MEA, Retiel N. Numerical study of natural convection in vertical cylindrical annular enclosure filled with Cu-water nanofluid under magnetic fields. Defect Diffus Forum. 2019;392:123-37.
DOI: 10.4028/www.scientific.net/DDF.392.123
Tagawa T, Ozoe H. Natural convection in a rectangular enclosure in the presence of a uniform magnetic field. Proceedings of Thermal Engineering Conference. 2002;2002(0):231-2.
DOI: 10.1299/jsmeptec.2002.0_231
Berrahil F, Filali A, Abid C, Benissaad S, Bessaih R, Matar O. Numerical investigation on natural convection of Al2 O3/water nanofluid with variable properties in an annular enclosure under magnetic field. Int Commun Heat Mass Transf. 2021;126.
DOI: 10.1016/j.icheatmasstransfer.2021.105408
Hatami M, Ganji DD. Heat transfer and nanofluid flow in suction and blowing process between parallel disks in presence of variable magnetic field. J Mol Liq. 2014;190:159-68.
DOI: 10.1016/j.molliq.2013.11.005
Hamad MAA, Pop I, Md Ismail AI. Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate. Nonlinear Anal Real World Appl. 2011;12(3):1338-46.
DOI: 10.1016/j.nonrwa.2010.09.014
Malvandi A, Ganji DD. Magnetic field and slip effects on free convection inside a vertical enclosure filled with alumina/water nanofluid. Chem Eng Res Des. 2015;94:355-64.
DOI: 10.1016/j.cherd.2014.08.013
Ferdows M, Adesanya SO, Alzahrani F, Yusuf TA. Numerical investigation of a boundary layer water-based nanofluid flow with induced magnetic field. Phys A. 2021;570.
DOI: 10.1016/j.physa.2020.125492
Tezer-Sezgin M, Bozkaya C, Türk Ö. Natural convection flow of a nanofluid in an enclosure under an inclined uniform magnetic field. Eur J Comp Mech. 2016;25(1-2):(2-23).
DOI: 10.1080/17797179.2016.1181029
Fakour M, Vahabzadeh A, Ganji DD. Study of heat transfer and flow of nanofluid in permeable channel in the presence of magnetic field. Propul Power Res. 2015;4(1):50-62.
DOI: 10.1016/j.jppr.2015.02.005
Sheikholeslami M, Ellahi R, Vafai K. Study of Fe3O4-water nanofluid with convective heat transfer in the presence of magnetic source. Alex Eng J. 2018;57(2):565-75.
DOI: 10.1016/j.aej.2017.01.027
Eringen AC. Simple micropolar fluids. Int J Eng Sci. 1964;2.
Eringen AC. Theory of micropolar fluids. J Math Mech. 1966;6:1-18.
Mehmood R, Nadeem S, Masood S. Effects of transverse magnetic field on a rotating micropolar fluid between parallel plates with heat transfer. J Magn Magn Mater. 2016;401:1006-14.
DOI: 10.1016/j.jmmm.2015.10.102
Kocić MM, Stamenković Z, Petrović JD, Bogdanović-Jovanović JB, Nikodijević MD. Heat transfer in micropolar fluid flow under the influence of magnetic field. Therm Sci. 2016;20(suppl. 5):1391-404.
DOI: 10.2298/TSCI16S5391K
Murthy JVR, Sai KS, Bahali NK. Steady flow of micropolar fluid in a rectangular channel under transverse magnetic field with suction. AIP Adv. 2011;1(3).
DOI: 10.1063/1.3624837
Haque MM. Heat and mass transfer analysis on magneto micropolar fluid flow with heat absorption in induced magnetic field. Fluids. 2021;6(3):126.
DOI: 10.3390/fluids6030126
Ismail HNA, Abourabia AM, Hammad DA, Ahmed NA, el Desouky AA. On the MHD flow and heat transfer of a micropolar fluid in a rectangular duct under the effects of the induced magnetic field and slip boundary conditions. SN Appl Sci. 2020;2(1):25.
DOI: 10.1007/s42452-019-1615-9
Ferdows M, Liu D. Natural convective flow of a magneto-micropolar fluid along a vertical plate. Propul Power Res. 2018;7(1):43-51.
DOI: 10.1016/j.jppr.2018.01.005
Kocić MM, Stamenković Z, Petrović JD, Bogdanović-Jovanović JB, Nikodijević MD. Heat transfer in micropolar fluid flow under the influence of magnetic field. Therm Sci. 2016;20(suppl. 5):1391-404.
DOI: 10.2298/TSCI16S5391K
Rout PK, Sahoo SN, Dash GC, Mishra SR. Chemical reaction effect on MHD free convection flow in a micropolar fluid. Alex Eng J. 2016;55(3):2967-73.
DOI: 10.1016/j.aej.2016.04.033
Ashraf M, Wehgal AR. MHD flow and heat transfer of micropolar fluid between two porous disks. Appl Math Mech.-Engl. Ed. 2012;33(1):51-64. doi: 10.1007/s10483-012-1533-6.
Srinivasacharya D, Shiferaw M. Numerical solution to the MHD flow of micropolar fluid between parallel porous plates. Int J Fluid Mech Res. 2008;35(4):365-73.
DOI: 10.1615/InterJFluidMechRes.v35.i4.60
Sultana S, Roy NC. Natural convection flow of MHD micropolar fluid along a vertical wavy surface. Dhaka Univ J Sci. 2017;65(2):91-6. doi: 10.3329/dujs.v65i2.54514.
Murthy JVR, Sai KS, Bahali NK. Steady flow of micropolar fluid in a rectangular channel under transverse magnetic field with suction. AIP Adv. 2011;1(3).
DOI: 10.1063/1.3624837
Bourantas GC, Loukopoulos VC. MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid. Int J Heat Mass Transf. 2014;79:930-44.
DOI: 10.1016/j.ijheatmasstransfer.2014.08.075
Stepha NG, Jacob DK. Analysis on physical properties of micropolar nanofluid past a constantly moving porous plate. IOP Conf S Mater Sci Eng. 2021;1206(1).
DOI: 10.1088/1757-899X/1206/1/012004
Modather M, EL-Kabeir SMM. MHD forced convective boundary-layer flow of a micropolar-nanofluid from a stretching sheet. J Comp Theor Nanosci. 2018;15(4):1275-82.
DOI: 10.1166/jctn.2018.7303
Ibrahim W, Zemedu C. MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk. J Heat Transf. 2021;50(1):564-95.
DOI: 10.1002/htj.21894
Anwar MI, Shafie S, Hayat T, Shehzad SA, Salleh MZ. Numerical study for MHD stagnation-point flow of a micropolar nanofluid towards a stretching sheet. J Braz Soc Mech Sci Eng. 2017;39(1):89-100.
DOI: 10.1007/s40430-016-0610-y
Kumar TS, Kumar BR, Makinde OD, Vijaya Kumar AGV. Magneto-convective heat transfer in micropolar nanofluid over a stretching sheet with non-uniform heat source/sink. Defect Diffus Forum. 2018;387:78-90.
DOI: 10.4028/www.scientific.net/DDF.387.78
Yacob NA, Ishak A, Pop I. Falkner-Skan problem for a static or moving wedge in nanofluids. Int J Therm Sci. 2011;50(2):133-9.
DOI: 10.1016/j.ijthermalsci.2010.10.008
Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluid with submicron metallic oxide particles. Exp Heat Transf. 1998;11(2):151-70.
DOI: 10.1080/08916159808946559
Ahmadi G. Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite flat plate. Int J Eng Sci. 1976;14(7):639-46.
DOI: 10.1016/0020-7225(76)90006-9
Rees DAS, Pop I. Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate. IMA J Appl Math. 1998;61(2):179-97.
DOI: 10.1093/imamat/61.2.179
Aminossadati SM, Ghasemi B. Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure. Eur J Mech B Fluids. 2009;28(5):630-40.
DOI: 10.1016/j.euromechflu.2009.05.006
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