## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### On dissipative MHD mixed convection boundary layer flow of Jeffrey fluid over an inclined stretching sheet with nanoparticles: Buongiorno model

**ABSTRACT**

Present paper utilizes a combination of non-Newtonian fluid model (Jeffrey fluid) with Buongiorno model (nanofluid). The Jeffery fluid, which is regarded as a base fluid, together with suspended nanoparticles are examined over an inclined stretching sheet with the amalgamated impacts of mixed convection and viscous dissipation. The mathematical formulation of this model is done by choosing the appropriate similarity variables for the aim to reduce the complexity of governing partial differential equations. The Runge-Kutta-Fehlberg (RKF45) method is then applied to the resulting of nonlinear ordinary differential equations to generate numerical results for highlighting the impact of emerging parameters towards specified distributions. Both the graphical and tabular representations of vital engineering physical quantities are also shown and deliberated. For the increase of Eckert number, thermophoresis diffusion and Brownian motion parameters, the elevation of temperature profiles is observed. Besides, the thermophoresis diffusion parameter tends to accelerate the nanoparticle concentration profile while Brownian motion parameter displays the opposite behavior.

**KEYWORDS**

PAPER SUBMITTED: 2017-11-20

PAPER REVISED: 2018-06-18

PAPER ACCEPTED: 2018-06-23

PUBLISHED ONLINE: 2018-09-22

- Kasim, A. R. M., et al., Constant Heat Flux Solution for Mixed Convection Boundary Layer Viscoelastic Fluid, Heat and Mass Transfer, 49 (2013), 2, pp. 163-171
- Anwar, M., et al., Numerical Study for MHD Stagnation-point Flow of a Micropolar Nanofluid towards a Stretching Sheet, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39 (2017), 1, pp. 89-100
- Hashim, et al., Numerical Investigation on Time-dependent Flow of Williamson Nanofluid Along with Heat and Mass Transfer Characteristics past a Wedge Geometry, International Journal of Heat and Mass Transfer, 118 (2018), pp. 480-491
- Zokri, S. M., et al., Influence of Viscous Dissipation on the Flow and Heat Transfer of a Jeffrey Fluid towards Horizontal Circular Cylinder with Free Convection: A Numerical Study, Malaysian Journal of Fundamental and Applied Sciences, 14 (2018), 1, pp. 40-47
- Hayat, T., et al., Mixed Convection Flow of Viscoelastic Nanofluid over a Stretching Cylinder, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37 (2015), 3, pp. 849-859
- Dalir, N., Numerical Study of Entropy Generation for Forced Convection Flow and Heat Transfer of a Jeffrey Fluid over a Stretching Sheet, Alexandria Engineering Journal, 53 (2014), 4, pp. 769-778
- Hayat, T., et al., Unsteady Flow and Heat Transfer of Jeffrey Fluid over a Stretching Sheet, Thermal Science, 18 (2014), 4, pp. 1069-1078
- Narayana, P. V. S., Babu, D. H., Numerical Study of MHD Heat and Mass Transfer of a Jeffrey Fluid over a Stretching Sheet with Chemical Reaction and Thermal Radiation, Journal of the Taiwan Institute of Chemical Engineers, 59 (2016), 2016, pp. 18-25
- Ojjela, O., et al., Influence of Thermophoresis and Induced Magnetic Field on Chemically Reacting Mixed Convective Flow of Jeffrey Fluid between Porous Parallel Plates, Journal of Molecular Liquids, 232 (2017), pp. 195-206
- Hayat, T., et al., Cattaneo-Christov Double-Diffusion Model for Flow of Jeffrey Fluid, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39 (2017), 12, pp. 4965-4971
- Hayat, T., et al., Effect of Cattaneo-Christov Heat Flux on Jeffrey Fluid Flow with Variable Thermal Conductivity, Results in Physics, 8 (2018), pp. 341-351
- Choi, S. U., Eastman, J. A., Enhancing Thermal Conductivity of Fluids with Nanoparticles, Report no. 84938, San Francisco, CA (United States), 1995
- Buongiorno, J., Convective Transport in Nanofluids, Journal of Heat Transfer, 128 (2006), 3, pp. 240-250
- Eastman, J. A., et al., Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-based Nanofluids Containing Copper Nanoparticles, Applied Physics Letters, 78 (2001), 6, pp. 718-720
- Choi, S., et al., Anomalous Thermal Conductivity Enhancement in Nanotube Suspensions, Applied Physics Letters, 79 (2001), 14, pp. 2252-2254
- Khan, W., Pop, I., Boundary-layer Flow of a Nanofluid past a Stretching Sheet, International Journal of Heat and Mass Transfer, 53 (2010), 11, pp. 2477-2483
- Makinde, O. D., Aziz, A., Boundary Layer Flow of a Nanofluid past a Stretching Sheet with a Convective Boundary Condition, International Journal of Thermal Sciences, 50 (2011), 7, pp. 1326-1332
- Ibrahim, W., Makinde, O., Magnetohydrodynamic stagnation point flow of a power-law nanofluid towards a convectively heated stretching sheet with slip, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 230 (2016), 5, pp. 345-354
- Shehzad, S. A., et al., Thermally Radiative Three-dimensional Flow of Jeffrey Nanofluid with Internal Heat Generation and Magnetic Field, Journal of Magnetism and Magnetic Materials, 397 (2016), pp. 108-114
- Avinash, K., et al. Non-Uniform Heat Source/Sink Effect on Liquid Film Flow of Jeffrey Nanofluid over a Stretching Sheet, Diffusion Foundations, 2017, Vol. 11, pp. 72-83.
- Qayyum, S., et al., Magnetohydrodynamic (MHD) Nonlinear Convective Flow of Jeffrey Nanofluid over a Nonlinear Stretching Surface with Variable Thickness and Chemical Reaction, International Journal of Mechanical Sciences, 134 (2017), pp. 306-314
- Abbasi, F., et al., Mixed Convection Flow of Jeffrey Nanofluid with Thermal Radiation and Double Stratification, Journal of Hydrodynamics, Ser. B, 28 (2016), 5, pp. 840-849
- Dhanai, R., et al., MHD Mixed Convection Nanofluid Flow and Heat Transfer over an Inclined Cylinder due to Velocity and Thermal Slip Effects: Buongiorno's Model, Powder Technology, 288 (2016), pp. 140-150
- Sakiadis, B., Boundary‐layer Behavior on Continuous Solid Surfaces: I. Boundary‐layer Equations for Two‐dimensional and Axisymmetric Flow, AIChE Journal, 7 (1961), 1, pp. 26-28
- Crane, L. J., Flow past a Stretching Plate, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 21 (1970), 4, pp. 645-647
- Makinde, O., et al., MHD Flow of a Variable Viscosity Nanofluid over a Radially Stretching Convective Surface with Radiative Heat, Journal of Molecular Liquids, 219 (2016), pp. 624-630
- Salleh, M. Z., et al., Boundary Layer Flow and Heat Transfer over a Stretching Sheet with Newtonian Heating, Journal of the Taiwan Institute of Chemical Engineers, 41 (2010), 6, pp. 651-655
- Mamatha, S., et al. Effect of Convective Boundary Condition on MHD Carreau Dusty Fluid over a Stretching Sheet with Heat Source, Defect and Diffusion Forum, 2017, Vol. 377, pp. 233-241.
- Hsiao, K.-L., Stagnation Electrical MHD Nanofluid Mixed Convection with Slip Boundary on a Stretching Sheet, Applied Thermal Engineering, 98 (2016), pp. 850-861
- Reddy, P. B. A., Magnetohydrodynamic Flow of a Casson Fluid over an Exponentially Inclined Permeable Stretching Surface with Thermal Radiation and Chemical Reaction, Ain Shams Engineering Journal, 7 (2016), 2, pp. 593-602
- Afridi, M. I., et al., Entropy Generation in Magnetohydrodynamic Mixed Convection Flow over an Inclined Stretching Sheet, Entropy, 19 (2016), 1, pp. 10
- Sravanthi, C., Homotopy Analysis Solution of MHD Slip Flow past an Exponentially Stretching Inclined Sheet with Soret-Dufour Effects, Journal of the Nigerian Mathematical Society, 35 (2016), 1, pp. 208-226
- Thumma, T., et al., Numerical Study of Heat Source/Sink Effects on Dissipative Magnetic Nanofluid Flow from a Non-linear Inclined Stretching/Shrinking Sheet, Journal of Molecular Liquids, 232 (2017), pp. 159-173
- Gupta, S., et al., MHD Mixed Convective Stagnation Point Flow and Heat Transfer of an Incompressible Nanofluid over an Inclined Stretching Sheet with Chemical Reaction and Radiation, International Journal of Heat and Mass Transfer, 118 (2018), pp. 378-387
- Soundalgekar, V., Viscous Dissipation Effects on Unsteady Free Convective Flow past an Infinite, Vertical Porous Plate with Constant Suction, International Journal of Heat and Mass Transfer, 15 (1972), 6, pp. 1253-1261
- Yirga, Y., Shankar, B., Effects of Thermal Radiation and Viscous Dissipation on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Nanofluid towards a Stretching Sheet, Journal of Nanofluids, 2 (2013), 4, pp. 283-291
- Mohamed, M. K. A., et al., Effects of Viscous Dissipation on Free Convection Boundary Layer Flow towards a Horizontal Circular Cylinder, ARPN Journal of Engineering and Applied Sciences, 11 (2016), 11, pp. 7258-7263
- Mohamed, M. K. A., et al., The Viscous Dissipation Effects on The Mixed Convection Boundary Layer Flow on a Horizontal Circular Cylinder, Jurnal Teknologi, 78 (2016), 4-4, pp. 73-79
- Besthapu, P., et al., Mixed Convection Flow of Thermally Stratified MHD Nanofluid over an Exponentially Stretching Surface with Viscous Dissipation Effect, Journal of the Taiwan Institute of Chemical Engineers, 71 (2017), pp. 307-314
- Hussain, A., et al., Combined Effects of Viscous Dissipation and Joule Heating on MHD Sisko Nanofluid over a Stretching Cylinder, Journal of Molecular Liquids, 231 (2017), pp. 341-352
- Kumar, R., et al., Rotating Frame Analysis of Radiating and Reacting Ferro-nanofluid Considering Joule heating and Viscous Dissipation, International Journal of Heat and Mass Transfer, 120 (2018), pp. 540-551
- Mahanthesh, B., Gireesha, B. J., Scrutinization of Thermal Radiation, Viscous Dissipation and Joule Heating Effects on Marangoni Convective Two-phase Flow of Casson Fluid with Fluid-particle Suspension, Results in Physics, 8 (2018), pp. 869-878
- Makinde, O., Olanrewaju, P., Buoyancy Effects on Thermal Boundary Layer over a Vertical Plate with a Convective Surface Boundary Condition, Journal of Fluids Engineering, 132 (2010), 4, pp. 044502
- Makinde, O. D., Similarity Solution for Natural Convection from a Moving Vertical Plate with Internal Heat Generation and a Convective Boundary Condition, Thermal Science, 15 (2011), suppl. 1, pp. 137-143
- Afridi, M. I., et al., Entropy Generation in Hydromagnetic Boundary Flow under the Effects of Frictional and Joule Heating: Exact Solutions, The European Physical Journal Plus, 132 (2017), 9, pp. 404
- Rauf, A., et al., MHD Stagnation Point Flow of Micro Nanofluid towards a Shrinking Sheet with Convective and Zero Mass Flux Conditions, Bulletin of the Polish Academy of Sciences Technical Sciences, 65 (2017), 2, pp. 155-162
- Chaudhary, R. C., Jain, P., An Exact Solution to the Unsteady Free-convection Boundary-layer Flow past an Impulsively Started Vertical Surface with Newtonian Heating, Journal of Engineering Physics and Thermophysics, 80 (2007), 5, pp. 954-960
- Reddy, P. S., et al., MHD Heat and Mass Transfer Flow of a Nanofluid over an Inclined Vertical Porous Plate with Radiation and Heat Generation/Absorption, Advanced Powder Technology, 28 (2017), 3, pp. 1008-1017