# Mixed Convection in a Casson Fluid Flow towards a Heated Shrinking Surface

• Haider Ali Department of Mathematics, Institute of Southern Punjab, Multan, Pakistan
• Ghulam Shabir Department of Mathematics, University of Agriculture, Faisalabad, Pakistan
• Yasir Qayyum Department of Mathematics, Institute of Southern Punjab, Multan, Pakistan
• Ather Qayyum Department of Mathematics, Institute of Southern Punjab, Multan, Pakistan
Keywords: stagnation flow, heat transfer, Casson fluid, shrinking sheet

### Abstract

In this paper, an extensive analysis of mixed convection effects on steady two-dimensional stagnation point flow of a Casson fluid over a heated horizontal sheet has been numerically investigated. The governing Navier-Stokes equations of the present problem are transformed into nonlinear ordinary differential equations by applying a similarity transformation. A numerical solution of the problem has been obtained by employing the linearization technique along with the finite difference discretization. The impact of the Casson fluid parameter, the thermo-radiative parameter, the mixed convection parameter, the slip parameter, and the Prandtl number on the fluid motion and temperature is studied through graphical data. The convection parameter, the slip parameter and the Casson fluid parameter tends to accelerate the flow. The temperature distribution is however reduced by the convection parameter, slip parameter, thermal radiation and the Prandtl number.

This work is based on [25] in which micropolar fluid flow over a heated surface was investigated by using the homotopy analysis method. We have extended the problem by considering the combined impact of mixed convection and thermal radiation on the Casson fluid flow towards a heated shrinking sheet, by using a numerical method.

### References

K. Rohlf and G. Tenti, The role of the Womersley number in pulsatile blood flow: a theoretical study of the Casson model, Journal of Biomechanics 34(1) (2001), 141-148. https://doi.org/10.1016/s0021-9290(00)00103-2

A. Mernone, V. J. N. Mazumdar and S. K. Lucas, A mathematical study of peristaltic transport of a Casson fluid, Mathematical and Computer Modelling 35(7-8) (2002), 895-912. https://doi.org/10.1016/s0895-7177(02)00058-4

Donald D. Joye, Shear rate and viscosity corrections for a Casson fluid in cylindrical (Couette) geometries, Journal of Colloid and Interface Science 267(1) (2003), 204-210. https://doi.org/10.1016/j.jcis.2003.07.035

R. R. Huilgol and Z. You, Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschelâ€“Bulkley fluids, Journal of Non-Newtonian Fluid Mechanics 128(2-3) (2005), 126-143. https://doi.org/10.1016/j.jnnfm.2005.04.004

Adebowale Martins Obalalu, Adebayo Olusegun Ajala, Akintayo Oladimeji Akindele et al., Unsteady squeezed flow and heat transfer of dissipative casson fluid using optimal homotopy analysis method: An application of solar radiation, Partial Differential Equations in Applied Mathematics 4 (2021), 100146. https://doi.org/10.1016/j.padiff.2021.100146

J. V. Ramana Reddy, V. Sugunamma and N. Sandeep, Enhanced heat transfer in the flow of dissipative non-Newtonian Casson fluid flow over a convectively heated upper surface of a paraboloid of revolution, Journal of Molecular Liquids 229 (2017), 380-388. https://doi.org/10.1016/j.molliq.2016.12.100

I. Sarah Oyelakin, Sabyasachi Mondal and Precious Sibanda, Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions, Alexandria Engineering Journal 55 (2016) 1025-1035. https://doi.org/10.1016/j.aej.2016.03.003

O. Daniel Makinde, Imran Ullah, Sharidan Shafie and Ilyas Khan, Unsteady MHD Falkner-Skan flow of Casson nanofluid with generative/destructive chemical reaction, Chemical Engineering Science 172 (2017), 694-706. https://doi.org/10.1016/j.ces.2018.09.011

J. Rahimi, D.D. Ganji, M. Khaki and Kh. Hosseinzadeh, Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet by collocation method, Alexandria Engineering Journal 56 (2017), 621-627. https://doi.org/10.1016/j.aej.2016.11.006

A. A. Joneidi, D. D. Ganji and M. Babaelahi, Micropolar flow in a porous channel with high mass transfer, International Communications in Heat and Mass Transfer 36 (2009), 1082-1088. https://doi.org/10.1016/j.icheatmasstransfer.2009.06.021

M. Sheikholeslami and D. D. Ganji, Numerical approach for magnetic nanofluid flow in a porous cavity using CuO nanoparticles, Materials and Design 120 (2017), 382-393. https://doi.org/10.1016/j.matdes.2017.02.039

M. Sheikholeslami, Z. Ziabakhsh and D. D. Ganji, Transport of magnetohydrodynamic nanofluid in a porous media, Colloids and Surfaces A: Physicochemical and Engineering Aspects 520 (2017), 201-212. https://doi.org/10.1016/j.colsurfa.2017.01.066

M. Sheikholeslami and D. D. Ganji, Impact of electric field on nanofluid forced convection heat transfer with considering variable properties, Journal of Molecular Liquids 229 (2017), 566-573. https://doi.org/10.1016/j.molliq.2016.12.107

M. Sheikholeslami and D. D. Ganji, Free convection of Fe3O4-water nanofluid under the influence of an external magnetic source, Journal of Molecular Liquids 229 (2017), 530-540. https://doi.org/10.1016/j.molliq.2016.12.101

M. Sheikholeslami and D. D. Ganji, Transportation of MHD nanofluid free convection in a porous semi annulus using numerical approach, Chemical Physics Letters 669 (2017), 202-210. https://doi.org/10.1016/j.cplett.2016.12.045

M. Fakour, A. Vahabzadeh, D. D. Ganji and M. Hatami, Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls, Journal of Molecular Liquids 204 (2015), 198-204. https://doi.org/10.1016/j.molliq.2015.01.040

S. Nadeem, Rashid Mehmood and S. S. Motsa, Numerical investigation on MHD oblique flow of Walters B type nanofluid over a convective surface, International Journal of Thermal Sciences 92 (2015), 162-172. https://doi.org/10.1016/j.ijthermalsci.2015.01.034

K. Ramesh and M. Devakar, Some analytical solutions for flows of Casson fluid with slip boundary conditions, Ain Shams Engineering Journal 6 (2015), 967-975. https://doi.org/10.1016/j.asej.2015.02.007

D. McDonald, Blood Flows in Arteries, 2nd edition, Arnold, London, UK, 1974.

E. Magyari and B. Keller, Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface, J. Phys. Appl. Phys. 32 (1999), 577-585. https://doi.org/10.1088/0022-3727/32/5/012

S. Pramanik, Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation, Ain Shams Engineering Journal 5 (2014), 205-212. https://doi.org/10.1016/j.asej.2013.05.003

K. Bhattacharya, K. Vajravelu and T. Hayat, Slip effect on parametric space and the solution for the boundary layer flow of Casson fluid over a non-porous stretching/shrinking sheet, International Journal of Fluid Mechanics Research 40 (2013), 482-493. https://doi.org/10.1615/interjfluidmechres.v40.i6.20

K. Ali, S. Ahmad and M. Ashraf, Numerical simulation of flow and heat transfer in hydromagnetic micropolar fluid between two stretchable disks with viscous dissipation effects, Journal of Theoretical and Applied Mechanics 54 (2016), 633-643. https://doi.org/10.15632/jtam-pl.54.2.633

S. Ahmad, K. Ali and M. Ashraf, Heat and mass transfer analysis of MHD micropolar fluid in a channel with chemical reaction, UPB Scientific Bulletin, Series D: Mechanical Engineering 78(1) (2016), 131-146.

M. M. Rashidi, Muhammad Ashraf, Behnam Rostami, M. T. Rastegari and S. Bashir, Mixed convection boundary-layer flow of a micro polar fluid towards a heated shrinking sheet by homotopy analysis method, Thermal Science 20(1) (2016), 21-34. https://doi.org/10.2298/tsci130212096r

Published
2023-08-09
How to Cite
Ali, H., Shabir, G., Ahmad, Z., Qayyum, Y., & Qayyum, A. (2023). Mixed Convection in a Casson Fluid Flow towards a Heated Shrinking Surface. Earthline Journal of Mathematical Sciences, 13(2), 413-429. https://doi.org/10.34198/ejms.13223.413429
Section
Articles