## THERMAL SCIENCE

International Scientific Journal

### EFFECTS OF HALL CURRENTS WITH HEAT AND MASS TRANSFER ON THE PERISTALTIC TRANSPORT OF A CASSON FLUID THROUGH A POROUS MEDIUM IN A VERTICAL CIRCULAR CYLINDER

**ABSTRACT**

In the current paper, the peristaltic transport of a non-Newtonian fluid obeying a Casson model with heat and mass transfer inside a vertical circular cylinder is studied. The considered system is affected by a strong horizontal uniform magnetic field together with the heat radiation and the Hall current. The problem is modulated mathematically by a system of PDE that describe the basic behavior of the fluid motion. The boundary value problem is analytically solved with the appropriate boundary conditions in accordance with the special case, in the absence of the Eckert number. The solutions are obtained in terms of the modified Bessel function of the first kind. Again, in the general case, the system is solved by means of the homotopy perturbation and then numerically through the Runge-Kutta Merson with a shooting technique. A comparison is done between these two methods. Therefore, the velocity, temperature and concentration distributions are obtained. A set of diagrams are plotted to illustrate the influence of the various physical parameters in the forgoing distributions. Finally, the trapping phenomenon is also discussed.

**KEYWORDS**

PAPER SUBMITTED: 2018-02-22

PAPER REVISED: 2018-05-18

PAPER ACCEPTED: 2018-06-04

PUBLISHED ONLINE: 2018-09-29

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 2**, PAGES [1067 - 1081]

- Hina, S., et al., Influence of Compliant Walls on Peristaltic Motion with Heat/Mass Transfer and Chemical Reaction, International Journal of Heat and Mass Transfer, 55 (2012), pp. 3386-3394.
- Noreen, S., Qasim, M., Peristaltic Flow with Inclined Magnetic Field and Convective Boundary Conditions, Applied Bionics and Biomechanics, 11 (2014), pp.61-67.
- El-Dabe, N. T., et al., Magneto Hydrodynamic Peristaltic Flow of Jeffery Nanofluid with Heat Transfer through a Porous Medium in a Vertical Tube, Applied Mathematics and Information Sciences, 11 (2017), 4, pp.1097-1103.
- Shaaban, A. A., Abou-zeid, M. Y., Effects of Heat and Mass Transfer on MHD Peristaltic Flow of a Non-Newtonian Fluid through a Porous Medium between Two Coaxial Cylinders, Mathematical Problems in Engineering, 2013 (2013), pp.1-11.
- Hayat, T., et al., Peristaltic Flow of Sutterby Fluid Channel with Radiative Heat Transfer and Compliant Walls: A numerical study, Results in Physics, 6 (2016), pp. 805-810.
- Nadeem, S., Akram, S., Heat Transfer in a Peristaltic Flow of MHD Fluid with Partial Slip, Commun Nonlinear Sci Numer Simulat, 15 (2010), pp. 312-321.
- Hayat, T., et al., Effects of Hall Current on Unsteady Flow of a Second Grade Fluid in a Rotating System, Chemical Engineering Communications, 192 (2005), pp. 1272-1284.
- Mehmood, O.U., et al., Non-Linear Peristaltic Flow of Walter's B Fluid in an Asymmetric Channel with Heat Transfer and Chemical Reactions, Thermal Sci., 18(2014), 4, pp.1065-1107.
- Eldabe, N. T., et al., Hall Effects on the Peristaltic Transport of Williamson Fluid through a Porous Medium with Heat and Mass Transfer, Applied Mathematical Modelling, 40 (2016), pp. 315-328.
- El Koumy, S. R., et al., Hall and Porous Boundaries Effects on Peristaltic Transport Through Porous Medium of a Maxwell Model, Transport Porous Medium, 94 (2012), pp.643-658.
- Akbar, N. S., et al., MHD Dissipative Flow and Heat Transfer of Casson Fluids due to Metachronal Wave Propulsion of Beating Cilia with Thermal and Velocity Slip Effects Under an Oblique Magnetic Field, Acta Astronautica, 128 (2016), pp. 1-12.
- Arthur, E. M., et al., Analysis of Casson Fluid Flow Over a Vertical Porous Surface with Chemical Reaction in the Presence of Magnetic Field, Journal of Applied Mathematics and Physics, 3(2015), pp. 713-723.
- Ali, K., et al., On Combined Effect of Thermal Radiation and Viscous Dissipation in Hydromagnetic Micropolar Fluid Flow Between two Stretchable Disks, Thermal Sci.,21(2017), 5, pp. 2155-2166.
- Elbashbeshy, E. M. A., et al., Effects of Pressure Stress Work and Thermal Radiation on Free Convection Flow around a Sphere Embedded in a Porous Medium with Newtonian Heating, Thermal Sci., 22 (2018), 1B, pp. 401-412.
- Eldabe, N., Abou-zeid, M., Radially Varying Magnetic Field Effect on Peristaltic Motion with Heat and Mass Transfer of a Non-Newtonian Fluid between Two Co-Axial Tubes, Thermal Sci., 2016, pp. 1-13, DOI No. (10.2298).
- Vasudev, C., et al., Peristaltic Flow of a Newtonian Fluid through a Porous Medium in a Vertical Tube under the Effect of a Magnetic Field. International Journal of Current Scientific Research, 1 (2011), 3, pp. 105-110.
- He, J. H., Homotopy Perturbation Technique, Computer Methods in Applied Mechanics and Engineering, 178 (1999), 3, pp. 257-262.
- Kumar. H., Homotopy Perturbation Method Analysis to MHD Flow of a Radiative NanoFluid with Viscous Dissipation and Ohmic Heating over a Stretching Porous Plate, Thermal Sci., 22(2018), 1B, pp. 413-422.
- Rajeev, Homotopy Perturbation Method for a Stefan Problem with Variable Latent Heat, Thermal Sci., 18 (2014), pp. 391-398.
- Abou-zeid, M.,Homotopy Perturbation Method to MHD Non-Newtonian NanoFluid Flow through a Porous Medium in Eccentric Annuli with Peristalsis, Thermal Sci.,21(2017), 5, pp. 2069-2080.
- Abou-zeid, M., 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), pp. 481-495.
- 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 Media, 18 (2015), 11, pp. 1091-1106
- Hayat, T., et al., Heat and Mass Transfer Effects on Peristaltic Flow of an Oldroyd-B Fluid in a Channel with Compliant Walls, Heat Transfer-Asian Research, 41 (2012), 1, pp. 63-83.
- Ali, N., et al., Slip Effects on the Peristaltic Flow of a Third Grade Fluid in a Circular Cylindrical Tube, Journal of Applied Mechanics, 76 (2009), pp. 1-10
- Noreen, S., Mixed Convection Peristaltic Flow of Third Order Nanofluid with an Induced Magnetic Field, PLOS ONE, 8 (2013), 11, pp. 1-15.
- Akbar, N. S., et al., Nano Fluid Flow in Tapering Stenosed Arteries with Permeable Walls, International Journal of Thermal Sci., 85 (2014),pp. 54-61.