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Research Papers: Micro/Nanoscale Heat Transfer

# Radiative Heat and Mass Transfer Analysis of Micropolar Nanofluid Flow of Casson Fluid Between Two Rotating Parallel Plates With Effects of Hall Current

[+] Author and Article Information
Zahir Shah

Department of Mathematics,
Abdul Wali Khan University,
Mardan 23200, KP, Pakistan
e-mail: zahir1987@yahoo.com

Saeed Islam

Department of Mathematics,
Abdul Wali Khan University,
Mardan 23200, KP, Pakistan
e-mail: proud_pak@hotmail.com

Hamza Ayaz

Islamic University of Technology,
Board Bazar,
e-mail: hamzaayaz@iut-dhaka.edu

Saima Khan

Department of Physics,
Abdul Wali Khan University,
Mardan 23200, KP, Pakistan
e-mail: saima@awkum.edu.pk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 14, 2018; final manuscript received May 17, 2018; published online November 26, 2018. Assoc. Editor: Yuwen Zhang.

J. Heat Transfer 141(2), 022401 (Nov 26, 2018) (13 pages) Paper No: HT-18-1027; doi: 10.1115/1.4040415 History: Received January 14, 2018; Revised May 17, 2018

## Abstract

The present research aims to examine the micropolar nanofluid flow of Casson fluid between two parallel plates in a rotating system with effects of thermal radiation. The influence of Hall current on the micropolar nanofluids have been taken into account. The fundamental leading equations are transformed to a system of nonlinear differential equations using appropriate similarity variables. An optimal and numerical tactic is used to get the solution of the problem. The convergence and comparison have been shown numerically. The impact of the Hall current, Brownian movement, and thermophoresis phenomena of Casson nanofluid have been mostly concentrated in this investigation. It is found that amassed Hall impact decreases the operative conductivity which intends to increase the velocity field. The temperature field enhances with larger values of Brownian motion thermophoresis effect. The impacts of the Skin friction coefficient, heat flux, and mass flux have been deliberate. The skin friction coefficient is observed to be larger for $k=0$, as compared to the case of $k=0.5$. Furthermore, for conception and visual demonstration, the embedded parameters have been deliberated graphically.

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## References

Eringen, A. C. , 1964, “ Simple Micropolar Fluids,” Int. J. Eng. Sci., 2(2), pp. 205–217.
Eringen, A. C. , 1966, “ Theory of Micropolar Fluid,” J. Math. Mech., 16(1), pp. 1–18.
Lukaszewicz, G. , 1999, Micropolar Fluids: Theory and Applications (Modeling and Simulation in Science, Engineering and Technology), Springer, New York, p. 253.
Mohammeadein, A. A. , and Gorla, R. S. R. , 1966, “ Effects of Transverse Magnetic Field on a Mixed Convection in a Micropolar Fluid on a Horizontal Plate With Vectored Mass Transfer,” Acta. Mech., 118(1–4), pp. 1–12.
Kasivishwanathan, S. R. , and Gandhi, M. V. , 1992, “ A Class of Exact Solutions for the Magnetohydrodynamic Flow of a Micropolar Fluid,” Int. J. Eng. Sci., 3(4), pp. 409–417.
Agarwal, R. S. , and Dhanapal, C. , 1998, “ Numerical Solution of Free Convection Micropolar Fluid Flow Between Two Parallel Porous Vertical Plates,” Int. J. Eng. Sci., 26(12), pp. 1247–1255.
Bhargava, R. , Kumar, L. , and Takhar, H. S. , 2003, “ Finite Element Solution of Mixed Convection Micropolar Flow Driven by a Porous Stretching Sheet,” Int. J. Eng. Sci., 41(18), pp. 2161–2178.
Nazar, R. , Amin, N. , Filip, D. , and Pop, I. , 2004, “ Stagnation Point Flow of a Micropolar Fluid Towards a Stretching Sheet,” Int. J. Nonlinear Mech., 3(7), pp. 1227–1235.
Ishak, A. , Nazar, R. , and Pop, I. , 2008, “ Magneto hydrodynamic (MHD) Flow of a Micropolar Fluid Towards a Stagnation Point on Vertical Surface,” Comput. Math. Appl., 58(12), pp. 3188–3194.
Nadeem, S. , Sadaf, M. , Rashid, M. , and Muhammad, A. S. , 2016, “ Optimal and Numerical Solutions for an MHD Micropolar Nanofluid Between Rotating Horizontal Parallel Plates,” Plos One, 10(6), p. 0124016.
Alfven, H. , 1942, “ Existence of Electromagnetic-Hydrodynamic Waves,” Nature, 150(3805), pp. 405–406.
Hall, E. , 1879, “ On a New Action of the Magnet on Electric Currents,” Am. J. Math., 2(3), pp. 287–292.
Pop, I. , and Soundalgekar, V. M. , 1974, “ Effects of Hall Currents on Hydrodynamic Flow Near a Porous Plate,” Acta Mech., 20(3–4), pp. 315–318.
Ahmed, S. , and Zueco, J. , 2011, “ Modeling of Heat and Mass Transfer in a Rotating Vertical Porous Channel With Hall Current,” Chem. Eng. Commun., 198(10), pp. 1294–1308.
Aziz, A. M. , 2013, “ Effects of Hall Current on the Flow and Heat Transfer of a Nanofluid Over a Stretching Sheet With Partial Slip,” Int. J. Mod. Phys., 24(7), p. 1350044.
Hayat, T. , Nawaz, M. , Iram, S. , and Alsaedi, A. , 2013, “ Mixed Convection Three-Dimensional Flow With Hall and Ion-Slip Effects,” Int. J. Nonlinear Sci. Numer. Simul., 14(3–4), pp. 167–177.
Wang, X. Q. , and Mujumdar, S. A. , 2008, “ Review on Nanofluids—Part II:Experiments and Applications,” Braz. J. Chem. Eng., 25(4), pp. 631–648.
Goodman, S. , 1957, “ Radiant-Heat Transfer Between Nongray Parallel Plates,” J. Res. Natl. Bur. Stand., 58(1), p. 2732.
Borkakoti, A. K. , and Bharali, A. , 1983, “ Hydromagnetic Flow and Heat Transfer Between Two Horizontal Plates, the Lower Plate Being a Stretching Sheet,” Q. Appl. Math., 40(4), pp. 461–467.
Sheikholeslami, M. , 2017, “ Influence of Magnetic Field on Nanofluid Free Convection in an Open Porous Cavity by Means of Lattice Boltzmann Method,” J. Mol. Liq., 234, p. 364.
Sheikholeslami, M. , 2017, “ Magnetic Field Influence on Nanofluid Thermal Radiation in a Cavity With Tilted Elliptic Inner Cylinder,” J. Mol. Liq., 229, pp. 137–147.
Sheikholeslami, M. , 2017, “ Magnetohydrodynamic Nanofluid Forced Convection in a Porous Lid Driven Cubic Cavity Using Lattice Boltzmann Method,” J. Mol. Liq., 231, pp. 555–565.
Sheikholeslami, M. , 2017, “ Numerical Simulation of Magnetic Nanofluid Natural Convection in Porous Media,” Phys. Lett. A., 381(5), pp. 494–503.
Sheikholeslami, M. , 2014, “ Numerical Study of Heat Transfer Enhancement in a Pipe Filled With Porous Media by Axisymmetric TLB Model Based on GPU,” Int. J. Heat Mass Transfer, 70, pp. 1040–1049.
Sheikholeslami, M. , 2016, “ CVFEM for Magnetic Nanofluid Convective Heat Transfer in a Porous Curved Enclosure,” Eur. Phys. J. Plus., 131(11), p. 413.
Sheikholeslami, M. , 2017, “ CuO-Water Nanofluid Free Convection in a Porous Cavity Considering Darcy Law,” Eur. Phys. J. Plus., 132(1), p. 55.
Sheikholeslami, M. , 2017, “ Numerical Investigation of MHD Nanofluid Free Convective Heat Transfer in a Porous Tilted Enclosure,” Eng. Comput., 34(6), pp. 1939–1955.
Sheikholeslami, M. , and Rokni, H. B. , 2017, “ Magnetohydrodynamic CuO-Water Nanofluid in a Porous Complex Shaped Enclosure,” ASME J. Therm. Sci. Eng. Appl., 9(4), p. 041007.
Sheikholeslami, M. , 2018, “ CuO-Water Nanofluid Flow Due to Magnetic Field Inside a Porous Media Considering Brownian Motion,” J. Mol. Liq., 249, pp. 921–929.
Sheikholeslami, M. , 2017, “ Influence of Lorentz Forces on Nanofluid Flow in a Porous Cylinder Considering Darcy Model,” J. Mol. Liq., 225, pp. 903–912.
Sheikholeslami, M. , and Rokni, H. B. , 2017, “ Simulation of Nanofluid Heat Transfer in Presence of Magnetic Field—A Review,” Int. J. Heat Mass Transfer, 115(Pt. B), pp. 1203–1233.
Sheikholeslami, M. , and Rokni, H. B. , 2017, “ Free Convection of CuO–H2O Nanofluid in a Curved Porous Enclosure Using Mesoscopic Approach,” Int. J. Heat Mass Transfer, 42(22), pp. 14942–14949.
Sheikholeslami, M. , and Rokni, H. B. , 2018, “ Numerical Simulation for Impact of Coulomb Force on Nanofluid Heat Transfer in a Porous Enclosure in Presence of Thermal Radiation,” Int. J. Heat Mass Transfer, 118, pp. 823–831.
Mahmoodi, M. , and Kandelousi, S. , 2015, “ Application of DTM for Kerosene-Alumina Nanofluid Flow and Heat Transfer Between Two Rotating Plate,” Eur. Phys. J. Plus., 130(7), p. 142.
Tauseef, M. S. , Ali, Z. , Khan, K. Z. , and Ahmed, N. , 2015, “ On Heat and Mass Transfer Analysis for the Flow of a Nanofluid Between Rotating Parallel Plates,” Aerosp. Sci. Technol., 46, pp. 514–522.
Rokni, H. B. , Alsaad, D. M. , and Valipour, P. , 2016, “ Electrohydrodynamic Nanofluid Flow and Heat Transfer Between Two Plates,” J. Mol. Liq., 216, pp. 583–589.
Tawade, L. , Abel, M. , Metri, G. , and Koti, A. , 2016, “ Thin Film Flow and Heat Transfer Over an Unsteady Stretching Sheet With Thermal Radiation, Internal Heating in Presence of External Magnetic Field,” Int. J. Adv. Appl. Math. Mech., 3, pp. 29–40.
Bakier, A. Y. , 2001, “ Thermal Radiation Effect on Mixed Convection From Vertical Surface in Saturated Porous Media,” Int. Commun. Heat Mass Transfer, 28(1), pp. 119–126.
Moradi, A. , Ahmadikia, H. , Hayat, T. , and Alsaedi, A. , 2013, “ On Mixed Convection Radiation Interaction About an Inclined Plate Through a Porous Medium,” Int. J. Therm. Sci., 64, pp. 129–136.
Chaudhary, S. , Singh, S. , and Chaudhary, S. , 2015, “ Thermal Radiation Effects on MHD Boundary Layer Flow Over an Exponentially Stretching Surface,” Sci. Res. Publ. Appl. Math., 6(2), pp. 295–303.
Eldabe, N. T. , Elsaka, A. G. , Radwan, A. E. , and Eltaweel, M. A. M. , 2010, “ Effects of Chemical Reaction and Heat Radiation on the MHD Flow of Viscoelastic Fluid Through a Porous Medium Over a Horizontal Stretching Flat Plate,” J. Am. Sci., 9 pp. 126–136.
Das, K. , 2012, “ Effects of Thermophoresis and Thermal Radiation on MHD Mixed Convective Heat and Mass Transfer Flow,” Afr. Math., 24(4), pp. 511–524.
TaylorGeoffrey, S. , 1921, “ Experiments With Rotating Fluids,” Proc. R. London A, 100(703), pp. 114–121.
Greenspan, H. P. , 1969, “ The Theory of Rotating Fluids. H. P. Greenspan. Cambridge University Press, New York, 1968. xii + 328 pp., illus. \$15. Cambridge Monographs on Mechanics and Applied Mathematics,” Science, 164(3882), p. 938.
Liao, S. J. , 2004, “ On the Homotopy Analysis Method for Nonlinear Problems,” Appl. Math. Comput., 147(2), pp. 499–513.
Shah, Z. , Gul, T. , Khan, A. M. , Ali, I. , and Islam, S. , 2017, “ Effects of Hall Current on Steady Three Dimensional Non-Newtonian Nanofluid in a Rotating Frame With Brownian Motion and Thermophoresis Effects,” J. Eng. Technol., 6, pp. 280–296.
Shah, Z. , Islam, S. , Gul, T. , Bonyah, E. , and Khan, M. A. , 2018, “ The Electrical MHD and Hall Current Impact on Micropolar Nanofluid Flow Between Rotating Parallel Plates,” Results Phys., 9, pp. 1201–1214.
Hammed, H. , Haneef, M. , Shah, Z. , Islam, S. , Khan, W. , and Muhammad, S. , 2018, “ The Combined Magneto Hydrodynamic and Electric Field Effect on an Unsteady Maxwell Nanofluid Flow Over a Stretching Surface Under the Influence of Variable Heat and Thermal Radiation,” Appl. Sci., 8(2), p. 160.
Muhammad, S. , Ali, G. , Shah, Z. , Islam, S. , and Hussain, A. , 2018, “ The Rotating Flow of Magneto Hydrodynamic Carbon Nanotubes Over a Stretching Sheet With the Impact of Non-Linear Thermal Radiation and Heat Generation/Absorption,” Appl. Sci., 8(4), p. 482.
Casson, N. A. , 1999, “ A Flow Equation for Pigment Oil Suspension of Printing Ink Type,” Rheology of Dispersed System, C. C. Mill , ed., Pergamon Press, Oxford, UK.
Mehmood, Z. , Mehmood, R. , and Iqbal, Z. , 2017, “ Numerical Investigation of Micropolar Casson Fluid Over a Stretching Sheet With Internal Heating,” Commun. Theor. Phys., 67(4), pp. 443–448.
Abolbashari, M. H. , Freidoonimehr, N. , and Rashidi, M. M. , 2015, “ Analytical Modeling of Entropy Generation for Casson Nano-Fluid Flow Induced by a Stretching Surface,” Adv. Powder Technol., 2(2), pp. 542–552.
Megahe, A. M. , 2016, “ Effect of Slip Velocity on Casson Thin Film Flow and Heat Transfer Due to Unsteady Stretching Sheet in Presence of Variable Heat Flux and Viscous Dissipation,” Appl. Math. Mech.-Engl. Ed., 36(10), p. 1273.
Qasim, M. , and Noreen, S. , 2014, “ Heat Transfer in the Boundary Layer Flow of a Casson Fluid Over a Permeable Shrinking Sheet With Viscous Dissipation,” Eur. Phys. J. Plus, 7(1), pp. 129–137.

## Figures

Fig. 1

The h curves graphs of function f′(η),g(η),Θ(η),G(η), and Φ(η)

Fig. 2

Impact of Re on f′(η) and g(η)

Fig. 3

Impact of Re on Θ(η),G(η), and Φ(η)

Fig. 4

Impact of β on f′(η) and g(η)

Fig. 5

Impact of Kr on f′(η) and g(η)

Fig. 6

Impact of N1 on f′(η),g(η), and G(η)

Fig. 7

Impact of M on f′(η)andg(η)

Fig. 8

Impact of m on f′(η)andg(η)

Fig. 9

Impact of N2 on f′(η),g(η), and G(η)

Fig. 10

Impact of Rd on Θ(η) and Φ(η)

Fig. 11

Impact of Sc on Θ(η) and Φ(η)

Fig. 12

Impact of Nb on Θ(η) and Φ(η)

Fig. 13

Impact of Nt on Θ(η) and Φ(η)

Fig. 14

Impact of Pr on Θ(η) and Φ(η)

Fig. 15

Physical description of the flow problem

## Errata

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