**ABSTRACT**

The motion of non-Newtonian fluid with heat and mass transfer through porous medium past a shrinking plate is discussed. The fluid obeys Casson model, heat generation, viscous dissipation, thermal diffusion, and chemical reaction are taken in our considered. The motion is modulated mathematically by a system of non-linear PDE which describe the continuity, momentum, heat, and mass equations. These system of non-linear equations are transformed into ODE by using a suitable transformations. These equations are solved numerically by using MATHEMATICA package. The numerical distributions of the velocity, temperature, and concentration are obtained as a functions of the physical parameters of the problem. Moreover, the effects of these parameters on these solutions are discussed numerically and illustrated graphically through some figures. It is clear that these parameters play an important role to control the velocity, temperature, and concentration of the fluid motion. It is found that the fluid velocity deceases with the increasing of electric parameter while it increases as the magnetic Hartman parameter increases, these results is good agreement with the physical situation. Also, the fluid temperature decreases and increases as the Prandtl number and Eckert number increases, respectively. At least the fluid concentration decreases with both of Soret and Schimdt numbers.

**KEYWORDS**

PAPER SUBMITTED: 2019-04-18

PAPER REVISED: 2019-10-12

PAPER ACCEPTED: 2019-10-19

PUBLISHED ONLINE: 2019-11-17

**THERMAL SCIENCE** YEAR

**2021**, VOLUME

**25**, ISSUE

**Issue 1**, PAGES [257 - 265]

- Pramanik, S., Casson Fluid Flow and Heat Transfer past an Exponentially Porous Stretching Sheet in Presence of Thermal Radiation, Ain Shams Engineering Journal, 5 (2014), 1, pp. 205-212
- Ellahi, R., et al., Convective Radiative Plane Poiseuille Flow of Nanofluid through Porous Medium with Slip: An Application of Stefan Blowing, Journal of Molecular Liquids, 273 (2019), Jan., pp. 292-304
- Akbar, N., Influence of Magnetic Field on Peristaltic Flow of a Casson Fluid in an a Symmetric Channel: Application in Crude Oil Refinement, Journal of Magnetism and Magnetic Materials, 378 (2015), Mar., pp. 463-468
- Ellahi, R., et al., Mixed Convection Flow and Heat Transfer in Ferromagnetic Fluid over a Stretching Sheet with Partial Slip Effects, Thermal Science, 22 (2018), 6A, pp. 2515-2526
- Hussanan, A., et al., Unsteady Boundary-layer Flow and Heat Transfer of a Casson Fluid past an Oscillating Vertical Plate with Newtonian Heating, Plos One, 9 (2014), 10, e108763
- Abou-Zeid, M. Y., Effects of Thermal-Diffusion and Viscous Dissipation on Peristaltic Flow of Micropolar Non-Newtonian Nanofluid: Application of Homotopy Perturbation Method, Results in Physics, 6 (2016), Aug., pp. 481-495
- El-Dabe, N. T., Abou-Zeid M. Y., The Wall Properties Effect Peristaltic Transport Micropolar Non-Newtonian Fluid with Heat and Mass Transfer, Mathematical Problems in Engineering, 2010 (2010), ID 898062
- Hassan, M., et al., Convection Heat Transfer Flow of Nanofluid in a Porous Medium over Wavy Surface, Physics Letters A, 382 (2018), 38, pp. 2749-2753
- Abou-Zeid, M. Y., Homotopy Perturbation Method for MHD Non-Newtonian Nanofluid Flow through a Porus Medium in Eccentric Annuli in Peristalsis, Thermal Science, 21 (2017), 5, pp. 2069-2080
- El-Dabe, N. T., et al., Magnetohydrodynamic Peristaltic Flow of Jeffry Nanofluid with Heat Transfer through a Porous Medium in a Vertical Tube, Applied Mathematics and Information Sciences, 11 (2017), 4, pp. 1097-1103
- Kataria, H. R., Patel, H. R., Heat and Mass Transfer in Magnetohydrodynamic (MHD) Casson Fluid Flow past over an Oscillating Vertical Plate Embedded in Porous Medium with Ramped Wall Temperature, Propulsion and Power Research, 7 (2018), 9, pp. 257-267
- Shaaban, A. A., Abou-Zeid, M. Y., Effects of Heat and Mass Transfer on MHD Peristaltic Flow of a NonNewtonian Fluid through a Porous Medium between Two Coaxial Cylinders, Mathematical Problems in Engineering, 2013 (2013), ID 819689
- Ellahi, R., A Study on the Mixed Convection Boundary-layer Flow and Heat Transfer over a Vertical Slender Cylinder, Thermal Science, 18 (2014), 4, pp. 1247-1258
- Raju, C. S. K., et al., Heat and Mass Transfer in Magnetohydrodynamic Casson Fluid over an Exponentially Permeable Stretching Surface, Engineering Science and Technology, an International Journal, 19 (2015), 1, pp. 45-52
- Shehzad, S. A., et al., Effects of Mass Transfer on MHD Flow of Casson Fluid with Chemical Reaction and Suction, Brazilian Journal of Chemical Engineering, 30 (2013), 1, pp. 187-195
- El-Dabe, N. T., et al., Magnetohydrodynamic Non-Newtonian Nanofluid Flow over a Stretching Sheet through a Non-Darcy Porous Medium with Radiation and Chemical Reaction, Journal of Computational and Theoretical Nanoscience, 12 (2015), 12, pp. 5363-5371
- Alamri, S. Z., et al., Effects of Mass Transfer on MHD Second Grade Fluid towards Stretching Cylinder: A Novel Perspective of Cattaneo-Christov Heat Flux Model, Physics Letters A, 383 (2019), 2-3, pp. 276-281
- Yousif , M. A., et al., Numerical Study of Momentum and Heat Transfer of MHD Carreau Nanofluid over Exponentially Stretched Plate with Internal Heat Source/Sink and Radiation, Heat Transfer Research, 50 (2019), 7, pp. 649-658
- Hassan, M., et al., A Comparative Study of Magnetic and Non-Magnetic Particles in Nanofluid Propagating over a Wedge, Canadian Journal of Physics, 97 (2019), 3, pp. 277-285
- Chirkov, V., et al., The Dependence of the Efficiency of Electrohydrodynamic Heat Exchanger on the Electric Conductivity of Liquid, IEEE Transactions on Industry Applications, 53 (2017), 3, pp. 2440-2445
- Kuzko, A. E., Electrohydrodynamic Flows and Heat Transfer in the Blade-Plane Elecrode System, Fluid Dynamics, 48 (2013), 3, pp. 310-320
- Abou-Zeid, M. Y., Magnetohydrodynamic Boundary-Layer Heat Transfer to a Stretching Sheet Including Viscous Dissipation and Internal Heat Generation in a Porous Medium, Journal of porous Media, 14 (2011), 11, pp. 1007-1018
- Pal, D., Mondal, H., Hydromagnetic Non-Darcy Flow and Heat Transfer over a Stretching Sheet in the Presence of Thermal Radiation and Ohmic Dissipation, Communication in Nonlinear Science and Numerical Simulation, 15 (2010), 5, pp. 1197-1209
- Mohamed, M. A., Abou-Zeid, M. Y., MHD Peristaltic Flow of Micropolar Casson Nanofluid through a Porous Medium between Two Co-Axial Tubes, Journal of Porous Media, 22 (2019), 9, pp. 1079-1093
- Abou-Zeid, M. Y.,et al., Numerical Treatment and Global Error Estimation of Natural Convective Effects on Gliding Motion of Bacteria on a Power-Law Nanoslime through a Non-Darcy Porous Medium, Journal of Porous Medium, 18 (2015), 11, pp. 1091-1106
- Abou-Zeid, M. Y., Mohamed, M. A., Homotopy Perturbation Method for Creeping Flow of Non-Newtonian Power-Law Nanofluid in a Nonuniform Inclined Channel with Peristalsis, Zeitschrift fur Naturforschung – Section A Journal of Physical Sciences, 72 (2017), 10a, pp. 899-907