• MomohJimoh Avidime Shied Department of Mathematics, Federal University Lokoja, Nigeria
  • Anselm Oyem Federal University Lokoja
  • Sheidu O. Momoh Department of Mathematics, Federal University Lokoja, Nigeria
  • Felix Tega Onojovwo Department of Mathematics, Federal University Lokoja, Nigeria
Keywords: Fluid flow, Nanoparticles, Sherwood number, Skin-friction coefficient, Thermophysical parameters, Vertical Plate


This paper considers the Casson nanofluid flow of a free convective heat transfer with heat source over a vertical plate and its thermophysical properties. The governing partial differential equations were reduced to couple nonlinear ordinary differential equations using similarity variables. The couple nonlinear ordinary differential equations were solved numerically using Runge-Kutta fourth order method with shooting technique and implemented using MatLab. The effects of various non-dimensional governing parameter namely, Prandtl number, Biot number, Grashof number, heat source parameter, skin-friction coefficient, Nusselt number and Sherwood number is analysed for Casson nanofluid flow, discussed and presented graphically. The result showed that heat source parameter increases in skin-friction coefficient, velocity and temperature profiles but, decreases in concentration profiles and Nusselt number.


Anwar R.K., Misiran M.I., Khan M.I., Alharbi S.O., Thounthong P. and Nisar K. S. (2019): Numerical solution of Casson nanofluid flow over a nonlinear inclined surface with soret and dufour effects by Keller-box method. Journal of Frontier Physics, https://dx.doi:10.3389/fphy.2019.00139 DOI:

Anwar T., Kumam P., and Watthayu W. (2021): Unsteady mhd natural convection flow of Casson fluid incorporating thermal radiative flux and heat injection/suction mechanism under variable wall conditions. Scientific Reports, 11(1), 4275. DOI:

Arthur E.M., Seini I.Y. and Bortteir L.B. (2015): 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(6), DOI:

Blair, G. W. S. (1959). An equation for the flow of blood, plasma and serum through glass capillaries. Nature, 183, 613–614. DOI:

Choi S.U.S. and Eastman J.A. (1995): Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exposition, San Francisco, 12–17

Dawar A., Shah Z., Islam S., Idress M. and Khan W. (2018): Magnetohydrodynamic CNTs Casson nanofluid and radiative heat transfer in a rotating channel. Int. Journal Phys. Res Appl., 1, 017-032. DOI:

Faraz F., Haider S. and Imran S.M. (2019): Study of magnetohydrodynamics impacts on an axisymmetric Casson nanofluid flow and heat transfer over unsteady radially stretching sheet. SN Applied Sciences, 2(14). DOI:

Gbadeyan J.A., Titiloye E.O., and Adeosun A.T. (2020): Effect of variable thermal conductivity and viscosity on Casson nanofluid flow with convective heating and velocity slip. Heliyon, 6(1), e03076. DOI:

Hayat T. and Nadeem S. (2017): Heat transfer enhancement with Ag–CuO/water hybrid nanofluid. Results in Physics, 7, 2317–2324. DOI:

Hussain T., Shehzad S.A., Alsaedi A., Hayat T., Ramzan M., (2015): Flow of Casson nanofluid with viscous dissipation and convective conditions: a mathematical model. Journal of Central South University, 22, 1132-1140. DOI:

Khan H., Ali F., Khan N., Khan I. and Mohamed A. (2022): Electromagnetic flow of Casson nanofluid over a vertical Riga plate with ramped wall conditions. Front. Phys., 10. DOI:

Kigio J.K., Mutuku, N.W., and Oke S.A. (2021): Analysis of volume fraction and convective heat transfer on mhd Casson nanofluid over a vertical plate. Fluid Mechanics, 7(1), 1–8. DOI:

Koriko O.K., Oreyeni T., and Oyem O.A. (2018): On the analysis of variable thermophysical properties of thermophoretic viscoelastic fluid flow past a vertical surface with nth order of chemical reaction. OALib, 05(6), 1–17. DOI:

Meng G., Chen G., Tan Z., and Wang Z. (2022): Fluid flow and heat transfer of carbon nanotubes- or graphene nano platelets-based nanofluids in a channel with micro-cylinders: an experimental study. Heat and Mass Transfer, 58(12), 2221–2234. DOI:

Muthukumar S., Sureshkumar S., El-Sapa S., and Chamkha A.J. (2022): Impacts of uniform and sinusoidal heating in a nanofluid saturated porous chamber influenced by the thermal radiation and the magnetic field. Numerical Heat Transfer, Part A: Applications, 1–19. DOI:

Mutuku W.N. and Oyem A.O. (2021): Casson fluid of a stagnation-point flow (spf) towards a vertical shrinking/stretching sheet. FUDMA Journal of Sciences, 5(1), 16-26. DOI:

Oke A.S., Mutuku W.N., Kimathi M., and Animasaun, I.L. (2020): Insight into the dynamics of non-Newtonian Casson fluid over a rotating non-uniform surface subject to Coriolis force. Nonlinear Engineering, 9(1), 398–411. DOI:

Okello J.A., Oyem A.O., and Mutuku W.N. (2021): Examination of Engin oil-based (MWCNTs-TiO_2, MWCNTs-Al_2 O_3, MWCNTs-Cu) hybrid nanofluids for optimal nanolubricant. IOSR Journal of Mathematics, 17(2), 24-38.

Oyem O.A., (2015): Effects of thermophysical properties on free convective heat and mass transfer flow over a vertical plate. PhD thesis (unpublished), Department of Mathematical Science, FUTA. Nigeria.

Pramanik S. (2014): Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation. Ain Shams Engineering Journal, 5(1):205–212. DOI:

Qin Y., Shang L., Zhou L., Zhu J., Yuan S., Zang, C., Ao D., and Li Z. (2022): Application of nanofluids in rapid methane hydrate formation. A Review Energy Fuels, 36(16), 8995–9013. DOI:

ShanthaSheela J., Gururaj A. D. M., Ismail M. and Dhanasekar, S (2021). Review on magnetohydrodynamic flow of nanofluids past a vertical plate under the influence of thermal radiation. IOP Conf. Series: Earth and Environmental Science, 850 012037, https://dx.doi:10.1088/1755-1315/850/1/012037 DOI:

Sivashanmugam (2012). Application of nanofluids in heat transfer. Open Science. DOI:

Swarnalathamma B.V. (2018): Heat and mass transfer on mhd flow of nanofluid with thermal slip effects. Int. Journal of Applied Engineering Research, 13(18), 13705 – 13726

Ullah I., Khan I. and Shafie S. (2016): Mhd natural convection flow of Casson nanofluid over nonlinearly stretching sheet through porous medium with chemical reaction and thermal radiation. Nanoscale Research Letters, 11:527. https://dx.doi.10.1186/s11671-016-1745-6 DOI:

Vijayaragavan R. and Kavitha M.A. (2017): Chemical reacting radiative Casson fluid flow over a vertical plate in the presence of heat source/sink and aligned magnetic field. Chemical Process Engineering Research, 49, 14-31

Yun-Xiang Li, Israr Ur Rehman M., Wen-Hua Huang, Ijaz Khan M., Sami Ullah Khan, and Ronnason Chinram, Kadry S., (2022): Dynamics of casson nanoparticles with non-uniform heat source/sink: a numerical analysis. Ain Shams Engineering Journal, 13(1), DOI:

How to Cite