Quadratic Thermal Convection in Magneto-Casson Fluid Flow Induced by Stretchy Material with Tiny Particles and Viscous Dissipation Effects

E. O. Fatunmbi *

Department of Mathematics and Statistics, Federal Polytechnic, Ilaro, Nigeria.

O. A. Agbolade

Department of Mathematics and Statistics, Federal Polytechnic, Ilaro, Nigeria.

*Author to whom correspondence should be addressed.


This investigation is based on the phenomenon of quadratic thermal convection in Magneto-Casson fluid flow induced by stretchy material with tiny particles and viscous dissipation effects. The study aims to understand and optimize the complex behaviour of fluid flow and heat transfer in this system, which has significant implications for engineering and industrial applications. The Magneto-Casson fluid, characterized by its non-Newtonian behaviour and yield stress, interacts with stretchy material and tiny particles, introducing unique flow characteristics and thermal properties. Viscous dissipation, resulting from internal friction, further influences the convective heat transfer process. Mathematical models are developed and solved by employing a numerical technique through the Runge-Kutta Fehlberg scheme coupled with the shooting method to investigate these phenomena comprehensively. The results are deliberated using several graphs on the dimensionless profiles. The results showed that there is a decline in the momentum boundary film as the magnetic field improves due to the effect of the Lorentz force. Also, an increase in the Casson fluid term raises the viscosity and thereby resists the fluid motion.

Keywords: Magneto-Casson fluid, viscous dissipation, quadratic convection, stretching sheet

How to Cite

Fatunmbi , E. O., & Agbolade , O. A. (2023). Quadratic Thermal Convection in Magneto-Casson Fluid Flow Induced by Stretchy Material with Tiny Particles and Viscous Dissipation Effects. Physical Science International Journal, 27(4), 1–11. https://doi.org/10.9734/psij/2023/v27i4795


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Gbadeyan JA, Titiloye EO, Adeosun AT. Effect of variable thermal conductivity and viscosity on casson nanofluid flow with convective heating and velocity slip, Heliyon. 2020;6:e03076.

Fatunmbi EO, Okoya SS. Heat transfer in boundary layer magneto-micropolar fluids with temperature-dependent material properties over a stretching sheet. Advances in Materials Science and Engineering. 2020:1-11.

DOI: 10.1155/2020/5734979

Rajput GR, Shamshuddin MD, Salawu SO. Thermo solutal convective non-newtonian radiative casson fluid transport in a vertical plate propagated by arrhenius kinetics with heat source/sink. Heat Transfer. 2020;20:1ֲ0.

Khan MI, Waqas M, Hayat T, Alsaedi A. Colloidal study of Casson fluid with homogeneous-heterogeneous reactions. Colloid Interface Sci., 2017;498, 85ֹ0.

Fatunmbi EO, Adeosun AT, Salawu SO. Entropy analysis of nonlinear radiative casson nanofluid transport over an electromagnetic actuator with temperature-dependent properties. Partial Differential Equations in Applied Mathematics. 2021;4:100152.

Mukhopadhyay S, Bhattacharyya PRK. Casson fluid flow over an unsteady stretching surface. Ain Shams Eng. J. 2014;4(4):933ֹ-938.

Casson N. Rheology of Disperse Systems. Pergamon. 1959:84-02.

Reza M, Chahal R, Sharma N. Radiation effect on MHD Casson fluid flow over a power-law stretching sheet with chemical reaction. World Academy of Science, Engineering and Technology, International Journal of Chemical, Molecular, Nuclear, Materials and Metallurgical Engineering. 2016;10(5):566-571.

Qing J, Bhatti MM, Abbas MA, Rashidi MM, Ali ME. Entropy generation on MHD casson nanofluid flow over a porous stretching/shrinking surface, Entropy. 2016;18:1-14.

Sohail M, Shah Z, Tassaddiq A, Kumam P, Roy P. Entropy generation in MHD casson fuid fow with variable heat conductance and thermal conductivity over non-linear bi-directional stretching surface, Scientific. 2020;10:1-16.

DOI: 10.1038/s41598-020-69411-2

Omotola OE, Fatunmbi EO. Dynamics of multiple slip and thermal radiation on hydromagnetic casson nanofluid flow over a nonlinear porous stretchable surface. Physical Science International Journal. 2021;25(4):1-14.

Rashidi MM, Ganesh NV, Abdul AK, Ganga HB. Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation. Journal of Molecular Liquids. 2014;198:234-238.

Babu MJ, Sandeep N. Effect of nonlinear thermal radiation on non-aligned bio-convective stagnation point flow of a magnetic-nanofluid over a stretching sheet. Alexandria Engineering Journal. 2016;55(3):1931-1939.

Fatunmbi EO, Adeosun AT, Salawu SO. Irreversibility Analysis for Eyringאowell Nanoliquid Flow Past Magnetized Riga Device with Nonlinear Thermal Radiation, Fluids. 2021;6:1-22416.


Mishra S, Pal D, Mondal H, Sibanda P. On radiative-magnetoconvective heat and mass transfer of a nanofluid past a non-linear stretching surface with ohmic heating and convective surface boundary condition. Propulsion and Power Research; 2016.


Mondal H, Mishra SPK, Kundu Sibanda P. Entropy generation of variable viscosity and thermal radiation on magneto nanofluid flow with dusty fluid. J. Appl. Comput. Mech. 2020;6(1):171-182

DOI: 10.22055/JACM.2019.28273.1473

Kumar MA, Reddy WD, Rao VS, Goud BS. Thermal radiation impact on MHD heat transfer natural convective nano fluid flow over an impulsively started vertical plate. Case Studies in Thermal Engineering. 2021;24: 1-10.

Fatunmbi EO, Ramonu OJ, Salawu SO. Analysis of heat transfer phenomenon in hydromagnetic micropolar nanoliquid over a vertical stretching material featuring convective and isothermal heating conditions. Waves in Random and Complex Media; 2023.

DOI: 10.1080/17455030.2023.2173494

Thriveni K, Mahanthesh B. Optimization and sensitivity analysis of heat transport of hybrid nanoliquid in an annulus with quadratic Boussinesq approximation and quadratic thermal radiation. Eur. Phys. J. Plus. 2020;135:1–22.

Fatunmbi EO, Okoya SS. Quadratic mixed convection stagnation-point flow in hydromagnetic casson nanofluid over a nonlinear stretching sheet with variable thermal conductivity. Defect and Diffusion. 2020;409:95-109.

Kameswaran PK, Sibanda P, Partha MK, Murthy PVSN. Thermophoretic and nonlinear convection in a non-darcy porous medium. J. Heat Transf. 2014;136(4): 042601.

Jha BK, Gwandu BJ. MHD free convection in a vertical slit microchannel with super-hydrophobic slip and temperature jump: Non-linear Boussinesq approximation approach. SN Appl. Sci. 2019;1(6): 603.

RamReddy C, Naveen P, Srinivasacharya D. Influence of non-linear Boussinesq approximation on natural convective flow of a power-law fluid along an inclined plate under convective thermal boundary condition. Nonlinear Eng. 2019;8(1): 94ֱ06.

Sajjan K, Shah NA, Ahammad NA, Raju CSK, Kumar MD, Weera W. Nonlinear boussinesq and rosseland approximations on 3D flow in an interruption of ternary nanoparticles with various shapes of densities and conductivity properties. AIMS Mathematics. 2022;7(10): 18416ֱ8449.

DOI: 10.3934/math.20221014

Mahanthesh B, Mackolil J, Radhika M, Al-Kouz W, Siddabasappa M. Significance of quadratic thermal radiation and quadratic convection on boundary layer two-phase flow of a dusty nanoliquid past a vertical plate. International Communications in Heat and Mass Transfer. 2020:105029.


Ali ME. Heat transfer characteristics of a continuous stretching surface. Warme-und Stoffubertragung. 1994;29(4):227-234.

Attili BS, Syam ML. Efficient shooting method for solving two point boundary value problems. Chaos, Solitons and Fractals. 2008;35(5):895-903.

Mahanthesh B, Gireesha BJ, Gorla RSR, Makinde OD. Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: A numerical study. Neural Computing and Applications. 2018;30(5): 1557-1567.

Grubka LJ, Bobba KM. Heat transfer characteristics of a continuous, stretching surface with variable temperature. Heat Transfer. 1985;107:1-3.