A mathematical study of magnetohydrodynamic Casson fluid via special functions with heat and mass transfer embedded in porous plate

Authors

  • Kashif Ali Abro Department of Basic Science and Related Studies, Mehran University of Engineering Technology, Jamshoro, Pakistan
  • Hina Saeed Shaikh Federal Government College, Karachi
  • Norzieha Mustapha Universiti Teknologi MARA
  • Ilyas Khan Majmaah University
  • Asifa Tassaddiq Majmaah University

DOI:

https://doi.org/10.11113/mjfas.v14n1.731

Keywords:

Special functions, Caputo Fractional differentiation, Rheological Impacts and Graphical illustrations.

Abstract

This article is proposed to investigate the impacts of heat and mass transfer in magnetohydrodynamic casson fluid embedded in porous medium. The generalized solutions have been traced out for the temperature distribution, mass concentration and velocity profiles under the existence and non-existence of transverse magnetic field, permeability and porosity. The corresponding solutions of temperature distribution and mass concentration, velocity profiles are expressed in terms of newly defined generalized Robotnov-Hartley function, wright function and Mittage-Leffler function respectively. All the corresponding solutions fulfill necessary conditions (initial, natural and boundary conditions) as well. Caputo Fractionalized solutions have been converted for ordinary solutions by substituting . Some similar solutions for the temperature distribution, mass concentration and velocity profiles have been particularized form generalized solutions. Owing to the rheology of problem, graphical illustrations of distinct parameters are discussed in detail by depicting figures using Mathcad software (15).

Author Biographies

Kashif Ali Abro, Department of Basic Science and Related Studies, Mehran University of Engineering Technology, Jamshoro, Pakistan

Lecturer at Department of Basic Science and Related Studies,

Norzieha Mustapha, Universiti Teknologi MARA

Fakulti Sains Komputer dan Matematik

Ilyas Khan, Majmaah University

Basic Engineering Sciences Department

Asifa Tassaddiq, Majmaah University

College of Computer and Information Sciences

References

I. Khan, A. Farhad, S. Sharidan, M Qasim, Unsteady free convection flow in a Walters-B fluid and heat transfer analysis, Bulletin of the Malaysian Mathematical Sciences Society 37 (2014), 437–448.

I. Khan, K. Fakhar, MI.Anwar, Hydromagnetic rotating flows of an Oldroyd-B fluid in a porous medium, Special Topics and Review in Porous Media 3 (2012), 89–95.

M. Qasim, Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink, Alexandria Engineering Journal 52 (2013), 571–575.

J. Kleppe, WJ. Marner Transient free convection in a Bingham plastic on a vertical flat plate. Journal of Heat Transfer 25 (1972), 371–376.

BI. Olajuwon, Flow and natural convection heat transfer in a power law fluid past a vertical plate with heat generation, International Journal of Nonlinear Science, 7 (2009) 50–56.

MN. Zakaria, H. Abid, I. Khan, S. Sharidan, The effects of radiation on free convection flow with ramped wall temperature in Brinkman type fluid. Jurnal Teknologi, 62 (2013), 33–39.

MA. Hassan, M. Pathak, MK. Khan, Natural convection of viscoplastic fluids in a square enclosure. Journal of Heat Transfer, 135 (2013), 122501–12.

A. A. Kashif, A. A. Shaikh, I. A. Junejo, Analytical Solutions Under No Slip Effects for Accelerated Flows of Maxwell Fluids, Sindh Univ. Res. Jour. (Sci. Ser.), 47 (2015) 613-618.

A. A Kashif, A. A. Shaikh, Exact analytical solutions for Maxwell fluid over an oscillating plane, Sci.Int.(Lahore) 27 (2015) 923–929.

A. A. Kashif, Porous Effects on Second Grade Fluid in Oscillating Plate, J. Appl. Environ. Biol. Sci., 6 (2016), 71-82.

N. Casson, A flow equation for pigment oil suspensions of the printing ink type. In: Rheology of disperse systems. Mill CC (Ed.) Pergamon Press, Oxford 22 (1959), 84–102.

MY. Malik, M. Naseer, S. Nadeem, A. Rehman, The boundary layer flow of Casson nanofluid over a vertical exponentially stretching cylinder, Applied Nanoscience, (2013), doi 10.1007/s13204-013-0267-0.

J. Venkatesan, DS. Sankar, K. Hemalatha, Y. Yatim, Mathematical analysis of Casson fluid model for blood rheology in stenosed narrow arteries, Journal of Applied Mathematics 44 (2013), 1–11.

T. Gul, S. Islam, K. khan, M. A. Khan, R. A. Shah, A. Gul, Muradullah, Thin Film Flow Analysis of a MHD Third Grade Fluid on a Vertical Belt With no-slip Boundary Conditions, J. Appl. Environ. Biol. Sci., 4 (2014), 71-84.

S. Abid, S. Islam, T. Gul, M. A. Khan, S. Nasir, A. Gul, Magnetic hydrodynamic flow of unsteady second grade fluid between two vertical plates with oscillating boundary conditions, J. Appl. Environ. Biol. Sci., 4 (2014), 1-10.

H. Rasheed, T. Gul, S.Islam, S. Nasir, M. A. Khan, A. Gul, Study of couette and poiseuille flows of an unsteady MHD third grade fluid, J. Appl. Environ. Biol. Sci., 4 (2014), 12-21.

A. A. Kashif, Porous Effects on Second Grade Fluid in Oscillating Plate, J. Appl. Environ. Biol. Sci., 6 (2016), 71-82.

A. A Kashif, M. Hussain, M. M. Baig, Impacts of Magnetic Field on Fractionalized Viscoelastic Fluid, J. Appl. Environ. Biol. Sci., 6 (2016), 84-93.

N. Casson, A flow equation for the pigment oil suspension of the printing ink type. In: Rheology of Disperse Systems, Pergamon, New York 15 (1959), 84-102.

N. A. Shah, I. Khan, Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives, Eur. Phys. J. C., (2016), 1-11, DOI 10.1140/epjc/s10052-016-4209-3.

. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999).

C. Stankovi, On the function of E. M. Wright. Publ. Inst. Math. (Belgr.) 10 (1970), 113-124.

R. Gorenflo, Y. Luchko, F. Mainardi, Analytical properties and applications of Wright function, Fract. Calc. Appl. Anal. 2 (1999) 383-414.

Downloads

Published

08-03-2018

Issue

Vol. 14 No. 1 (2018): January - March

Section

Article