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Effect of MHD on the flow and heat transfer characteristics of nanofluid in a grooved channel with internal heat generation

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Abstract Purpose – The purpose of this study is numerical simulation of magnetohydrodynamics (MHD) water– Al2O3 nanofluid mixed convection in a grooved channel with internal heat generation in solid cylinders. Simulations were carried out at Reynolds
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  International Journal of Numerical Methods for Heat & Fluid Flow Effect of MHD on the flow and heat transfer characteristics of nanofluid in agrooved channel with internal heat generation Mohammad Sadegh Dehghani, Davood Toghraie, Babak Mehmandoust, Article information: To cite this document:Mohammad Sadegh Dehghani, Davood Toghraie, Babak Mehmandoust, (2018) "Effect of MHDon the flow and heat transfer characteristics of nanofluid in a grooved channel with internal heatgeneration", International Journal of Numerical Methods for Heat & Fluid Flow, https://doi.org/10.1108/ HFF-05-2018-0235 Permanent link to this document: https://doi.org/10.1108/HFF-05-2018-0235 Downloaded on: 24 October 2018, At: 03:46 (PT)References: this document contains references to 56 other documents.To copy this document: permissions@emeraldinsight.comThe fulltext of this document has been downloaded 3 times since 2018*Access to this document was granted through an Emerald subscription provided byToken:Eprints:URNBQV7JNVIAFGVTCHQR: For Authors If you would like to write for this, or any other Emerald publication, then please use our Emeraldfor Authors service information about how to choose which publication to write for and submissionguidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.com Emerald is a global publisher linking research and practice to the benefit of society. The companymanages a portfolio of more than 290 journals and over 2,350 books and book series volumes, aswell as providing an extensive range of online products and additional customer resources andservices. Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of theCommittee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative fordigital archive preservation. *Related content and download information correct at time of download.    D  o  w  n   l  o  a   d  e   d   b  y   1   0   9 .   1   2   2 .   2   0   4 .   2   A   t   0   3  :   4   6   2   4   O  c   t  o   b  e  r   2   0   1   8   (   P   T   )  E ff ectofMHDonthe fl owandheattransfercharacteristicsofnano fl uidinagroovedchannelwithinternalheatgeneration Mohammad Sadegh Dehghani  Department of Mechanical Engineering, Islamic Azad University, Isfahan, Iran Davood Toghraie  Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr, Iran, and  Babak Mehmandoust  Department of Mechanical Engineering, Islamic Azad University, Isfahan, Iran Abstract Purpose  –   The purpose of this study is numerical simulation of magnetohydrodynamics (MHD) water  –  Al 2 O 3  nano fl uid mixed convection in a grooved channel with internal heat generation in solid cylinders.Simulations were carried out at Reynolds numbers 50 # Re # 100, Hartmann numbers 0 # Ha # 15, Grashof numbers 5,000 # Gr # 10  4 and volume fraction 0 # w  # 0.04. The effect of Reynolds number and thein fl uence of magnetic  fi eld and pressure drop on convective heat transfer coef  fi cient were studied in differentvolumefractionsofnanoparticlesatdifferentReynoldsnumbers. Design/methodology/approach  –   The results show that average Nusselt number increases byincreasing Reynolds and Hartman numbers. Also, when Hartman number increases, velocity pro fi le becomesasymmetric. Pressure distribution shows that magnetic fi eld applies Lorentz force at opposite direction of the fl ow, which causes asymmetric distribution of pressure. As a result, pressure in the upper half of the cylinderis higher than the lower half. Finally, velocity and temperature contours along the channel for differentHartmannnumbers,volumefraction3percent,Re=50and100andGr=10,000,arepresented. Findings  –   The effect of Reynoldsnumber and thein fl uence of magnetic fi eld and pressure drop on convectiveheattransfercoef  fi cientwerestudiedindifferentvolumefractionsofnanoparticlesatdifferentReynoldsnumbers. Originality/value  –   EffectofMHDonthe fl owandheat transfercharacteristicsofWater  –  Al 2 O 3 nano fl uidinagroovedchannelwithinternalheatgenerationinsolidcylinders. Keywords  Mixed convection, Nano fl uid, Numerical simulation, MHD, Grooved channel Papertype Research paper 1.Introduction Mixed convection with nano fl uids and MHD are interesting subjects of investigation. Themost application of the mixed convection can be found in atmospheric  fl ows, solar energystorage, heat exchangers, lubrication technologies and cooling of the electronic devices.Several investigations have been carried out on mixed convection, especially withnano fl uidsandMHD,throughchannelsandcavities.Aminossadati etal. (2011)studiedthelaminarforcedconvectionofawater  –  Al 2 O 3 nano fl uid fl owing through a horizontal microchannel. Their results show that for all values of theReynolds and Hartmann numbers, the average Nusselt number on the middle section surfaceof the microchannel increases as the solid volume fraction increases. Hamad  et al.  (2011) Flow and heattransfer Received22May2018Revised6June2018Accepted9July2018 International Journal of NumericalMethods for Heat & Fluid Flow© EmeraldPublishingLimited0961-5539 DOI 10.1108/HFF-05-2018-0235 The current issue and full text archive of this journal is available on Emerald Insight at: www.emeraldinsight.com/0961-5539.htm    D  o  w  n   l  o  a   d  e   d   b  y   1   0   9 .   1   2   2 .   2   0   4 .   2   A   t   0   3  :   4   6   2   4   O  c   t  o   b  e  r   2   0   1   8   (   P   T   )  studied the magnetic  fi eld effects on free convection  fl ow of a nano fl uid past a vertical semi-in fi nite  fl at plate. They found that nanoparticles have the highest cooling performance forthisproblem.Mahmoudi etal. (2012)studiedtheeffectofmagnetic fi eldonnaturalconvectionin a triangular enclosure  fi lled with nano fl uid. Their results show that in presence of magnetic  fi eld  fl ow fi eld is suppressed and heat transfer decreases. Ashorynejad  et al.  (2013)studied magnetic  fi eld effects on natural convection  fl ow of a nano fl uid in a horizontalcylindrical annulus.Theyfoundthatthe average Nusseltnumberisanincreasingfunctionof nanoparticle volume fraction and Rayleigh number, while it is a decreasing function of Hartmann number. Sheikholeslami et al.  (2013) studiednatural convection betweena circularenclosure and a sinusoidal cylinder. They showed that streamlines, isotherms and thenumber, size and formation of the cells inside the enclosure strongly depend on the Rayleighnumber, values of amplitude and the number of undulations of the enclosure. Bourantas andLoukopoulos (2014) studied MHD natural convection  fl ow in an inclined square enclosure fi lled with a nano fl uid. They found that the  fl ow characteristics and the convection heattransfer inside the tilted enclosure depend strongly upon the strength and orientation of themagnetic  fi eld. Malvandi  et al.  (2014) investigated the effect of magnetic  fi elds on heatconvectioninsidea concentricannulus fi lled withAl 2 O 3  –  waternano fl uid.Theyfoundthat inthe presence of the magnetic fi eld, the velocity gradients near the wall grow, which increasestheslipvelocityatboundariesandthus,theheattransferrateintensi fi es.Shehzad etal. (2015)investigated the in fl uence of convective heat and mass conditions in MHD fl ow of nano fl uid.They concluded that higher values of magnetic parameter enhance the temperature andconcentration pro fi les. Sheikholeslami and Ellahi (2015) presented magnetohydrodynamicsnano fl uid hydrothermal treatment in a cubic cavity heated from below. Their results showthat the average Nusselt number increases with the increase of Rayleigh number and thedecrease in Hartmann number. Malvandia and Ganji (2015) studied magnetic  fi eld and slipeffects on free convection inside a vertical enclosure  fi lled with nano fl uid. They found thatthatinthepresenceofthemagnetic fi eld,thenearwallvelocitygradientsincrease,enhancingtheslipvelocityandreducetheheattransferrate.Sheremet etal. (2016)studiedmagnetic fi eldeffect on the unsteady natural convection in a wavy-walled cavity  fi lled with a nano fl uid.They found that an increase in the Hartmann number leads to an attenuation of convective fl ow and heat transfer and a formation of a double-core convective cell for high values of Ha.Sheikholeslami  et al.  (2017) investigated in fl uence of external magnetic source in two-dimensional Fe 3 O 4  –  water nano fl uid. Their results indicated that augmenting nano fl uidvolume fraction, Rayleigh and magnetic numbers leads to the improvement in thetemperature gradient.Sarlak etal. (2017) investigatedheattransferofwater  –  Al 2 O 3  nano fl uidin a close enclosure by applying homogeneous magnetic fi eld. They found that enhancementof volume fraction of nanoparticles and the reduction of Richardson and Hartmann numberssigni fi cantlyenhancetheheattransferofenclosurewithcold fl uid.In this paper, numerical simulation of MHD water  –  Al 2 O 3  nano fl uid mixed convection ina grooved channel with internal heat generation in solid cylinders was carried out.Simulations were carried out at 50 # Re # 100, 0 # Ha # 15, 5,000 # Gr # 10  4 and0 # w  # 0.04. The effect of Reynolds number and the in fl uence of magnetic  fi eld andpressure drop on convective heat transfer coef  fi cient were studied in different volumefractionsofnanoparticlesatdifferentReynoldsnumbers. 2.Basicequations  2.1 Problem de  fi  nition Figure 1 shows schematic views of the  fl ow in a grooved channel with internal heatgeneration in solid cylinders. The depth, width and length of the channel are shown as w, h HFF    D  o  w  n   l  o  a   d  e   d   b  y   1   0   9 .   1   2   2 .   2   0   4 .   2   A   t   0   3  :   4   6   2   4   O  c   t  o   b  e  r   2   0   1   8   (   P   T   )  and 4 h (L = 2 m, h = 0.5 m and w = 0.5 m), respectively. Calculations are performedconsidering squared grooves 0.1    0.1 m (Ag = 0.01 m 2  ) in the upper and lower walls of thechannel. Boundary condition of constant heat fl ux was also applied to upper and lower wallsof the channel ð q 00 0  ¼  80 W   m 2  ), and the rest of the walls were insulated. Radius of the heatgenerating cylinders was 0.1 m (d = 0.2 m). The distance between the two cylinders was0.6 m. Internal heat generation rates (q 1  and q 2  ) in the cylinders were 4 ; 000 W   m 3 . The  fl uid fl ow was under the in fl uence of a uniform magnetic  fi eld with B 0  power, which was appliedto upper wall of the channel at  y -axis. The  fl uid temperature at entrance to the channel was T  c =298  K  . Base  fl uid was water  –  Al 2 O 3  with a diameter of 30 nm, and volume fractions of 0, 1, 2 and 3 per cent were added to the base  fl uid. Nano fl uid  fl ow was assumed as three-dimensional, incompressible, Newtonian, laminar and single-phase. The  fl uid  fl ow atentrance region of the channel was laminar. Governing equations were solved using a  fi nitevolumemethodwiththehelpoftheSIMPLEalgorithm.  2.2 Thermophysical properties of nano  fl  uids Density(  Pak and Cho, 1998 ): r  nf   ¼  wr   p  þ  1    w  ð Þ r   f   (1) Figure1. Schematicofthegroovedchannelwithinternalheatgenerationinsolidcylinders Flow and heattransfer    D  o  w  n   l  o  a   d  e   d   b  y   1   0   9 .   1   2   2 .   2   0   4 .   2   A   t   0   3  :   4   6   2   4   O  c   t  o   b  e  r   2   0   1   8   (   P   T   )  Here,  w   represents nanoparticle volume fraction and f, p and nf subscripts show  fl uid,particleandnano fl uid,respectively. Speci   fi  cheatcapacity (   Xuan and  Roetzel  ,2000 ): r  C   p  nf   ¼  w r  C   p   p  þ  1    w  ð Þ  r  C   p   f   (2) Thermalconductivity (  Chonetal  .,2005 ): k nf  k  f  ¼  1  þ  64 : 7 w  0 : 7460  d   f  d   p ! 0 : 3690 k  p k  f  ! 0 : 7476 Pr 0 : 9955  Re 1 : 2321 (3)Here:  Pr   ¼  m r   f  a   f  ;  m   ¼  a : 10  bt   c ;  a   f   ¼  k  f  r   f  C   p :  f  c  ¼  140 ;  b  ¼  247 ;  a  ¼  2 : 414 e    5 b  c  ¼  1 : 3807    10  23 ;  L bf   ¼  0 : 17 nm ;  Re  ¼ r   f  b  c T3 p  m  2  L bf  d   f   ¼  0 : 1 6 m N  pr   f  ! 13 ;  N   ¼  6 : 022    10 23 (4)  Dynamicviscosity (   Brinkman ,1952 ): m  nf   ¼ m  bf  1    f  ð Þ 2 : 5  (5) Thermaldiffusivity : a  nf   ¼  k nf  r  C   p  nf  (6) Thermalexpansioncoef   fi  cient  (  Victor  and Sreedhara ,2017 ): rb  ð Þ nf   ¼  w rb  ð Þ  s  þ  1    w  ð Þ  rb  ð Þ  f   (7) HFF    D  o  w  n   l  o  a   d  e   d   b  y   1   0   9 .   1   2   2 .   2   0   4 .   2   A   t   0   3  :   4   6   2   4   O  c   t  o   b  e  r   2   0   1   8   (   P   T   )
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