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Research Papers: Micro/Nanoscale Heat Transfer

Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of Nanofluids Past a Bidirectional Exponential Permeable Stretching/Shrinking Sheet With Viscous Dissipation Effect

[+] Author and Article Information
Rahimah Jusoh

Faculty of Industrial Sciences and Technology,
Universiti Malaysia Pahang,
Gambang, Kuantan 26300, Pahang, Malaysia
e-mail: rahimahj@ump.edu.my

Roslinda Nazar

School of Mathematical Sciences,
Faculty of Science and Technology,
Universiti Kebangsaan Malaysia,
UKM Bangi, Selangor 43600, Malaysia
e-mail: rmn@ukm.edu.my

Ioan Pop

Department of Mathematics,
Babes-Bolyai University,
Cluj-Napoca R-400084, Romania
e-mail: popm.ioan@yahoo.co.uk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 4, 2018; final manuscript received September 22, 2018; published online November 21, 2018. Assoc. Editor: Thomas Beechem.

J. Heat Transfer 141(1), 012406 (Nov 21, 2018) (10 pages) Paper No: HT-18-1071; doi: 10.1115/1.4041800 History: Received February 04, 2018; Revised September 22, 2018

The problem of boundary layer flow and heat transfer of magnetohydrodynamic (MHD) nanofluids which consist of Fe3O4, Cu, Al2O3, and TiO2 nanoparticles and water as the base fluid past a bidirectional exponentially permeable stretching/shrinking sheet is studied numerically. The mathematical model of the nanofluid incorporates the effect of viscous dissipation in the energy equation. By employing a suitable similarity transformation, the conservative equations for mass, momentum, and energy are transformed into the ordinary differential equations. These equations are then numerically solved with the utilization of bvp4c function in matlab. The effects of the suction parameter, magnetic parameter, nanoparticle volume fraction parameter, Eckert number, Prandtl number, and temperature exponent parameter to the reduced skin friction coefficient as well as the local Nusselt number are graphically presented. Cu is found to be prominently good in the thermal conductivity. Nevertheless, higher concentration of nanoparticles leads to the deterioration of heat transfer rate. The present result negates the previous literature on thermal conductivity enhancement with the implementation of nanofluid. Stability analysis is conducted since dual solutions exist in this study, and conclusively, the first solution is found to be stable.

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References

Crane, L. J. , 1970, “ Flow Past a Stretching Plate,” Z. Angew. Math. Phys., 21(4), pp. 645–647. [CrossRef]
Fang, T. , 2008, “ Boundary Layer Flow Over a Shrinking Sheet With Power-Law Velocity,” Int. J. Heat Mass Transfer, 51(25–26), pp. 5838–5843. [CrossRef]
Nadeem, S. , and Haq, R. U. , 2015, “ MHD Boundary Layer Flow of a Nanofluid Passed Through a Porous Shrinking Sheet With Thermal Radiation,” J. Aerosp. Eng., 28(2), p. 4014061. [CrossRef]
Mondal, S. , Haroun, N. A. H. , and Sibanda, P. , 2015, “ The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow Over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity With Navier Slip,” PLoS One, 10(9), p. e0138355.
Magyari, E. , and Keller, B. , 1999, “ Heat and Mass Transfer in the Boundary Layers on an Exponentially Stretching Continuous Surface,” J. Phys. D: Appl. Phys., 32(5), pp. 577–585. [CrossRef]
Hayat, T. , Shehzad, S. A. , and Alsaedi, A. , 2014, “ MHD Three-Dimensional Flow by an Exponentially Stretching Surface With Convective Boundary Condition,” J. Aerosp. Eng., 27(4), pp. 1–8. [CrossRef]
Khan, J. A. , Mustafa, M. , Hayat, T. , Sheikholeslami, M. , and Alsaedi A. , 2015, “ Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy,” PLoS One, 10(3), p. e0116603.
Ur Rehman, F. , and Nadeem, S. , 2018, “ Heat Transfer Analysis for Three-Dimensional Stagnation Point Flow of Water-Based Nanofluid Over an Exponentially Stretching Surface,” ASME J. Heat Transfer, 140(5), p. 052401. [CrossRef]
Choi, S. U. S. , and Eastman, J. A. , 1995, “ Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Developments and Applications of Non-Newtonian Flows, Vol. 66, D. A. Siginer and H. P. Wang, eds., American Society of Mechanical Engineers, New York, pp. 99–105.
Das, S. K. , Choi, S. U. S. , Yu, W. , and Pradeep, T. , 2008, Nanofluids: Science and Technology, Wiley, Hoboken, NJ, pp. 10–25.
Saidur, R. , Leong, K. Y. , and Mohammad, H. A. , 2011, “ A Review on Applications and Challenges of Nanofluids,” Renewable Sustainable Energy Rev., 15(3), pp. 1646–1668. [CrossRef]
Wong, K. V. , and Leon, O. D. , 2010, “ Applications of Nanofluids: Current and Future,” Adv. Mech. Eng., 2, pp. 1–11.
Ding, Y. , Chen, H. , Wang, L. , Yang, C. Y. , He, Y. , Yang, W. , Lee, W. P. , Zhang, L. , and Huo, R. , 2007, “ Heat Transfer Intensification Using Nanofluids,” KONA Powder Part. J., 25, pp. 23–38. [CrossRef]
Ma, J. , Xu, Y. , Li, W. , Zhao, J. , Zhang, S. , and Basov, S. , 2013, “ Experimental Investigation Into the Forced Convective Heat Transfer of Aqueous Fe3O4 Nanofluids Under Transition Region,” J. Nanopart., 2013, pp. 1–5. [CrossRef]
Li, C. H. , and Peterson, G. P. , 2010, “ Experimental Studies of Natural Convection Heat Transfer of Al2O3/DI Water Nanoparticle Suspensions (Nanofluids),” Adv. Mech. Eng., 2, pp. 1–10.
Kouloulias, K. , Sergis, A. , and Hardalupas, Y. , 2016, “ Sedimentation in Nanofluids During a Natural Convection Experiment,” Int. J. Heat Mass Transfer, 101, pp. 1193–1203. [CrossRef]
Myers, T. G. , Ribera, H. , and Cregan, V. , 2017, “ Does Mathematics Contribute to the Nanofluid Debate?,” Int. J. Heat Mass Transfer, 111, pp. 279–288. [CrossRef]
Nield, D. A. , and Bejan, A. , 2013, Convection in Porous Media, 4th ed., Springer, New York.
Minkowycz, W. J. , Sparrow, E. M. , and Abraham, J. P. , 2013, Nanoparticle Heat Transfer and Fluid Flows, CRC Press/Taylor & Fracis Group, New York.
Shenoy, A. , Sheremet, M. , and Pop, I. , 2016, Convective Flow and Heat Transfer From Wavy Surfaces: Viscous Fluids, Porous Media and Nanofluids, CRC Press/Taylor & Francis Group, New York.
Buongiorno, J. , Venerus, D. C. , Prabhat, N. , McKrell, T. , Townsend, J. , Christianson, R. , Tolmachev, Y. V. , Keblinski, P. , Hu, L. W. , Alvarado, J. L. , Bang, I. C. , Bishnoi, S. W. , Bonetti, M. , Botz, F. , Cecere, A. , Chang, Y. , Chen, G. , Chen, H. , Chung, S. J. , Chyu, M. K. , Das, S. K. , Paola, R. D. , Ding, Y. , Dubois, F. , Dzido, G. , Eapen, J. , Escher, W. , Funfschilling, D. , Galand, Q. , Gao, J. , Gharagozloo, P. E. , Goodson, K. E. , Gutierrez, J. G. , Hong, H. , Horton, M. , Hwang, K. S. , Iorio, C. S. , Jang, S. P. , Jarzebski, A. B. , Jiang, Y. , Jin, L. , Kabelac, S. , Kamath, A. , Kedzierski, M. A. , Kieng, L. G. , Kim, C. , Kim, J. H. , Kim, S. , Lee, S. H. , Leong, K. C. , Manna, I. , Michel, B. , Ni, R. , Patel, H. E. , Philip, J. , Poulikakos, D. , Reynaud, C. , Savino, R. , Singh, P. K. , Song, P. , Sundararajan, T. , Timofeeva, E. , Tritcak, T. , Turanov, A. N. , Vaerenbergh, S. V. , Wen, D. , Witharana, S. , Yang, C. , Yeh, W. H. , Zhao, X. Z. , and Zhou, S. Q. , 2009, “ A Benchmark Study on the Thermal Conductivity of Nanofluids,” J. Appl. Phys., 106(9), p. 094312. [CrossRef]
Kakaç, S. , and Pramuanjaroenkij, A. , 2009, “ Review of Convective Heat Transfer Enhancement With Nanofluids,” Int. J. Heat Mass Transfer, 52(13–14), pp. 3187–3196. [CrossRef]
Fan, J. , and Wang, L. , 2011, “ Review of Heat Conduction in Nanofluids,” ASME J. Heat Transfer, 133(4), p. 040801. [CrossRef]
Mahian, O. , Kianifar, A. , Kalogirou, S. A. , Pop, I. , and Wongwises, S. , 2013, “ A Review of the Applications of Nanofluids in Solar Energy,” Int. J. Heat Mass Transfer, 57(2), pp. 582–594. [CrossRef]
Sheikholeslami, M. , and Ganji, D. D. , 2016, “ Nanofluid Convective Heat Transfer Using Semi Analytical and Numerical Approaches: A Review,” J. Taiwan Inst. Chem. Eng., 65, pp. 43–77. [CrossRef]
Noreen, S. , 2016, “ Effects of Joule Heating and Convective Boundary Conditions on Magnetohydrodynamic Peristaltic Flow of Couple-Stress Fluid,” ASME J. Heat Transfer, 138(9), p. 094502. [CrossRef]
Davidson, P. A. , 2011, An Introduction to Magnetohydrodynamics, Cambridge University Press, Cambridge, UK.
Kim, S. D. , Lee, E. , and Choi, W. , 2017, “ Newton's Algorithm for Magnetohydrodynamic Equations With the Initial Guess From Stokes-Like Problem,” J. Comput. Appl. Math., 309, pp. 1–10. [CrossRef]
Motozawa, M. , Chang, J. , Sawada, T. , and Kawaguchi, Y. , 2010, “ Effect of Magnetic Field on Heat Transfer in Rectangular Duct Flow of a Magnetic Fluid,” Phys. Procedia, 9, pp. 190–193. [CrossRef]
Kishore, P. M. , Rajesh, V. , and Varma, S. V. K. , 2010, “ Effects of Heat Transfer and Viscous Dissipation on MHD Free Convection Flow Past an Exponentially Accelerated Vertical Plate With Variable Temperature,” J. Nav. Archit. Mar. Eng., 7(2), pp. 101–110.
Mabood, F. , Khan, W. A. , and Ismail, A. I. M. , 2015, “ MHD Boundary Layer Flow and Heat Transfer of Nanofluids Over a Nonlinear Stretching Sheet: A Numerical Study,” J. Magn. Magn. Mater, 374, pp. 569–576. [CrossRef]
Khader, M. M. , and Megahed, A. M. , 2014, “ Differential Transformation Method for the Flow and Heat Transfer Due to a Permeable Stretching Surface Embedded in a Porous Medium With a Second Order Slip and Viscous Dissipation,” ASME J. Heat Transfer, 136(7), p. 072602. [CrossRef]
Abbasbandy, S. , Magyari, E. , and Shivanian, E. , 2009, “ The Homotopy Analysis Method for Multiple Solutions of Nonlinear Boundary Value Problems,” Commun. Nonlinear Sci. Numer. Simul., 14(9–10), pp. 3530–3536. [CrossRef]
Abbasbandy, S. , Shivanian, E. , Vajravelu, K. , and Kumar, S. , 2017, “ A New Approximate Analytical Technique for Dual Solutions of Nonlinear Differential Equations Arising in Mixed Convection Heat Transfer in a Porous Medium,” Int. J. Numer. Methods Heat Fluid Flow, 27(2), pp. 486–503. [CrossRef]
Abbasbandy, S. , and Shivanian, E. , 2010, “ Prediction of Multiplicity of Solutions of Nonlinear Boundary Value Problems: Novel Application of Homotopy Analysis Method,” Commun. Nonlinear Sci. Numer. Simul., 15(12), pp. 3830–3846. [CrossRef]
Abbasbandy, S. , and Shivanian, E. , 2011, “ Predictor Homotopy Analysis Method and Its Application to Some Nonlinear Problems,” Commun. Nonlinear Sci. Numer. Simul., 16(6), pp. 2456–2468. [CrossRef]
Abbasbandy, S. , and Shivanian, E. , 2011, “ Multiple Solutions of Mixed Convection in a Porous Medium on Semi-Infinite Interval Using Pseudo-Spectral Collocation Method,” Commun. Nonlinear Sci. Numer. Simul., 16(7), pp. 2745–2752. [CrossRef]
Vosoughi, H. , Shivanian, E. , and Abbasbandy, S. , 2012, “ Unique and Multiple PHAM Series Solutions of a Class of Nonlinear Reactive Transport Model,” Numer. Algorithms, 61(3), pp. 515–524. [CrossRef]
Ahmad Soltani, L. , Shivanian, E. , and Ezzati, R. , 2017, “ Shooting Homotopy Analysis Method: A Fast Method to Find Multiple Solutions of Nonlinear Boundary Value Problems Arising in Fluid Mechanics,” Eng. Comput., 34(2), pp. 471–498. [CrossRef]
Tiwari, R. K. , and Das, M. K. , 2007, “ Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” Int. J. Heat Mass Transfer, 50(9–10), pp. 2002–2018. [CrossRef]
Khanafer, K. , Vafai, K. , and Lightstone, M. , 2003, “ Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids,” Int. J. Heat Mass Transfer, 46(19), pp. 3639–3653. [CrossRef]
Brinkman, H. C. , 1952, “ The Viscosity of Concentrated Suspensions and Solutions,” J. Chem. Phys., 20(4), pp. 571–581. [CrossRef]
Oztop, H. F. , and Nada, E. A. , 2008, “ Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled With Nanofluids,” Int. J. Heat Fluid Flow, 29(5), pp. 1326–1336. [CrossRef]
Sheikholeslami, M. , and Ganji, D. D. , 2014, “ Ferrohydrodynamic and Magnetohydrodynamic Effects on Ferrofluid Flow and Convective Heat Transfer,” Energy, 75, pp. 400–410. [CrossRef]
Merkin, J. H. , 1985, “ On Dual Solutions Occurring in Mixed Convection in a Porous Medium,” J. Eng. Math., 20(2), pp. 171–179. [CrossRef]
Weidman, P. D. , Kubitschek, D. G. , and Davis, A. M. J. , 2006, “ The Effect of Transpiration on Self-Similar Boundary Layer Flow Over Moving Surfaces,” Int. J. Eng. Sci., 44(11–12), pp. 730–737. [CrossRef]
Roşca, A. V. , and Pop, I. , 2013, “ Flow and Heat Transfer Over a Vertical Permeable Stretching/Shrinking Sheet With a Second Order Slip,” Int. J. Heat Mass Transfer, 60, pp. 355–364. [CrossRef]
Nazar, R. , Noor, A. , Jafar, K. , and Pop, I. , 2014, “ Stability Analysis of Three-Dimensional Flow and Heat Transfer Over a Permeable Shrinking Surface in a Cu-Water Nanofluid,” Int. J. Math. Comput. Stat. Nat. Phys. Eng., 8(5), pp. 782–788. https://waset.org/publications/9998253/stability-analysis-of-three-dimensional-flow-and-heat-transfer-over-a-permeable-shrinking-surface-in-a-cu-water-nanofluid
Jusoh, R. , Nazar, R. , and Pop, I. , 2017, “ Flow and Heat Transfer of Magnetohydrodynamic Three-Dimensional Maxwell Nanofluid Over a Permeable Stretching/Shrinking Surface With Convective Boundary Conditions,” Int. J. Mech. Sci., 124–125, pp. 166–173. [CrossRef]
Harris, S. D. , Ingham, D. B. , and Pop, I. , 2009, “ Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model With Slip,” Transp. Porous Media, 77(2), pp. 267–285. [CrossRef]
Ahmad, R. , Mustafa, M. , Hayat, T. , and Alsaedi, A. , 2016, “ Numerical Study of MHD Nanofluid Flow and Heat Transfer past a Bidirectional Exponentially Stretching Sheet,” J. Magn. Magn. Mater., 407, pp. 69–74. [CrossRef]
Liu, I. , Wang, H. H. , and Peng, Y. , 2013, “ Flow and Heat Transfer for Three-Dimensional Flow Over an Exponentially Stretching Surface,” Chem. Eng. Commun., 200(2), pp. 253–268. [CrossRef]
Miklavčič, M. , and Wang, C. Y. , 2006, “ Viscous Flow Due to a Shrinking Sheet,” Q. Appl. Math., 64, pp. 283–290. [CrossRef]
Fang, T. G. , Zhang, J. , and Yao, S. S. , 2009, “ Viscous Flow Over an Unsteady Shrinking Sheet With Mass Transfer,” Chin. Phys. Lett., 26(1), p. 14703. [CrossRef]
Putra, N. , Roetzel, W. , and Das, S. K. , 2003, “ Natural Convection of Nanofluids,” Heat Mass Transfer, 39(8–9), pp. 775–784. [CrossRef]
Ali, K. , Ashraf, M. , Ahmad, S. , and Batool, K. , 2012, “ Viscous Dissipation and Radiation Effects in MHD Stagnation Point Flow Towards a Stretching Sheet With Induced Magnetic Field,” World Appl. Sci. J., 16(1), pp. 1638–1648. https://pdfs.semanticscholar.org/1458/ba7dce69232c759c30f65d42e1317163229d.pdf
Narla, V. K. , Prasad, K. M. , and Ramanamurthy, J. V. , 2015, “ Peristaltic Transport of Jeffrey Nanofluid in Curved Channels,” Procedia Eng., 127, pp. 869–876. [CrossRef]
Rehman, F. U. , Nadeem, S. , and Haq, R. U. , 2017, “ Heat Transfer Analysis for Three Dimensional Stagnation-Point Flow Over an Exponentially Stretching Surface,” Chin. J. Phys, 55(4), pp. 1552–1560. [CrossRef]
Zin, N. A. M. , Khan, I. , and Shafie, S. , 2016, “ The Impact Silver Nanoparticles on MHD Free Convection Flow of Jeffrey Fluid Over an Oscillating Vertical Plate Embedded in a Porous Medium,” J. Mol. Liq., 222, pp. 138–150. [CrossRef]
Aaiza, G. , Khan, I. , and Shafie, S. , 2015, “ Energy Transfer in Mixed Convection MHD Flow of Nanofluid Containing Different Shapes of Nanoparticles in a Channel Filled With Saturated Porous Medium,” Nanoscale Res. Lett., 10(1), pp. 1–14. [CrossRef] [PubMed]
Das, S. , and Jana, R. N. , 2015, “ Natural Convective Magneto-Nanofluid Flow and Radiative Heat Transfer past a Moving Vertical Plate,” Alexandria Eng. J., 54(1), pp. 55–64. [CrossRef]
Babu, M. J. , Sandeep, N. , Raju, C. S. K. , Reddy, J. V. R. , and Sugunamma, V. , 2016, “ Nonlinear Thermal Radiation and Induced Magnetic Field Effects on Stagnation-Point Flow of Ferrofluids,” J. Adv. Phys., 5(4), pp. 302–308. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Physical model and coordinate system

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Fig. 2

Variations of f″(0)(reduced skin friction coefficient in the x-direction) with λ for different types of nanoparticles when Pr = 6.2, c = 1, ϕ= 0.1, s = 3.5; M = 0.5, and Ec = 1

Grahic Jump Location
Fig. 3

Variations of g″(0)(reduced skin friction coefficient in the y-direction) with λ for different types of nanoparticles when Pr = 6.2, c = 1, ϕ = 0.1, s = 3.5; M = 0.5, and Ec = 1

Grahic Jump Location
Fig. 4

Variations of f″(0)(reduced skin friction coefficient in the x-direction) for several values of s with λ for: (a) Fe3O4-water nanofluid and (b) Cu-water nanofluid

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Fig. 5

Variations of g″(0)(reduced skin friction coefficient in the y-direction) for several values of s with λ for: (a) Fe3O4-water nanofluid and (b) Cu-water nanofluid

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Fig. 6

Effect of nanoparticles volume fraction ϕ on −θ′(0) for: (a) Fe3O4-water nanofluid and (b) Cu-water nanofluid

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Fig. 7

Effect of magnetic parameter M on −θ′(0) for: (a) Fe3O4-water nanofluid and (b) Cu-water nanofluid

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Fig. 8

Effect of viscous dissipation on the temperature profiles for Fe3O4-water nanofluid when Pr = 6.2, c = 1, ϕ= 0.01, s = 3.5, λ = −0.05, and M = 0.5

Grahic Jump Location
Fig. 9

Effect of viscous dissipation on −θ′(0) for: (a) Fe3O4-water nanofluid and (b) Cu-water nanofluid

Grahic Jump Location
Fig. 10

Effect of temperature exponent parameter on the temperature profiles for Fe3O4-water nanofluid when Pr = 6.2, ϕ= 0.01, s = 3.5, λ = −0.05, M = 0.5, and Ec = 1

Grahic Jump Location
Fig. 11

Effect of temperature exponent parameter c on −θ′(0) for: (a) Fe3O4-water nanofluid and (b) Cu-water nanofluid

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Fig. 12

Effect of Prandtl number on the temperature profiles for Fe3O4-water nanofluid when c = 1, ϕ= 0.01, s = 3.5, λ = −0.05, M = 0.5, and Ec = 1

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