Engineering Transactions, 0, 0, pp. , 0

Numerical Analysis of the Transient and Non-Isothermal Channel Flow of a Third-Grade Fluid with Convective Cooling

University of Cape Town
South Africa

Oluwole Daniel MAKINDE
Stellenbosch University
South Africa

We investigate the unsteady, non-isothermal, pressure driven channel flow of a third grade liquid subject to exothermic reactions. We assume temperature dependent fluid viscosity and also that the flow is subjected to convective cooling at the channel walls. The exothermic reactions are modelled via Arrhenius kinetics and the convective heat exchange with the ambient at the channel walls follows Newton’s law of cooling. The time-dependent, coupled, and nonlinear partial differential equations governing the flow and heat transfer problem are solved numerically using efficient, semi-implicit finite difference algorithms. The sensitivity of the fluid flow and heat transfer system to the various embedded parameters is explored.
Keywords: unsteady channel flow; third grade fluid; variable viscosity; exothermic kinetics; convective cooling; finite difference method
Full Text: PDF


Truesdell C., Noll W., The non-linear field theories of mechanics, Vol. 111/3: Handbuch der Physik/Encyclopedia of Physics, S. Flügge [Ed.], Springer, Berlin 1965, doi: 10.1007/978-3-642-46015-9.

Rajagopal K.R., On boundary conditions for fluids of the differential type: Navier-Stokes equations and related non-linear problems, Plenum Press, New York 1995, doi: 10.1007/978-1-4899-1415-6_22.

Salawu S.O., Oke S.I., Inherent irreversibility of exothermic chemical reactive thirdgrade Poiseuille flow of a variable viscosity with convective cooling, Journal of Applied and Computational Mechanics, 4(3): 167–174, 2018, doi: 10.22055/jacm.2017.22933.1144.

Adesanya S.O., Falade J.A., Jangili S., Anwar Bég O., Irreversibility analysis for reactive third-grade fluid flow and heat transfer with convective wall cooling, Alexandria Engineering Journal, 56(1): 153–160, 2017, doi: 10.1016/j.aej.2016.09.017.

Chinyoka T., Makinde O.D., Buoyancy effects on unsteady mhd flow of a reactive third-grade fluid with asymmetric convective cooling, Journal of Applied Fluid Mechanics, 8(4): 931–941, 2015,

Chinyoka T., Makinde O.D., Unsteady hydromagnetic flow of a reactive variable viscosity third-grade fluid in a channel with convective cooling, International Journal for Numerical Methods in Fluids, 69: 353–365, 2012, doi: 10.1002/fld.2562.

Makinde O.D., Chinyoka T., Numerical study of unsteady hydromagnetic generalized Couette flow of a reactive third-grade fluid with asymmetric convective cooling, Computers & Mathematics with Applications, 61(4): 1167–1179, 2011, doi: 10.1016/j.camwa.2010.12.066.

Chinyoka T., Makinde O.D., Analysis of transient generalized Couette flow of a reactive variable viscosity third-grade liquid with asymmetric convective cooling, Mathematical and Computer Modelling, 54(1–2): 160–174, 2011, doi: 10.1016/j.mcm.2011.01.047.

Siddiqui A.M., Mahmood R., Ghori Q.K., Thin film flow of a third grade fluid on a moving belt by He’s homotopy perturbation method, International Jornal of Non-Linear Science Numerical Simulation, 7(1): 1–8, 2006, doi: 10.1515/IJNSNS.2006.7.1.7.

Fosdick R.L., Rajagopal K.R., Thermodynamics and stability of fluids of third grade, Proceedings of the Royal Society of London. A: Mathematical and Physical Sciences, 369(1738): 351–377, 1980, doi: 10.1098/rspa.1980.0005.

Yürüsoy M., Pakdemirli M., Approximate analytical solutions for the flow of a third grade fluid in a pipe, International Journal of Non-Linear Mechanics, 37(2): 187–195, 2002, doi: 10.1016/S0020-7462(00)00105-0.

Massoudi M., Christe I., Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe, International Journal of Non-Linear Mechanics, 30(5): 687–699, 1995, doi: 10.1016/0020-7462(95)00031-I.

Frank-Kamenetskii D.A., Diffusion and heat transfer in chemical kinetics, Plenum Press, New York, 1969,

Chinyoka T., Computational dynamics of a thermally decomposable viscoelastic lubricant under shear, ASME Journal of Fluids Engineering, 130(12): 121201 (7 pages), 2008, doi: 10.1115/1.2978993.

Chinyoka T., Renardy Y.Y., Renardy M., Khismatullin D.B., Two-dimensional study of drop deformation under simple shear for Oldroyd-B liquids, Journal of Non-Newtonian Fluid Mechanics, 130(1): 45–56, 2005, doi: 10.1016/j.jnnfm.2005.07.005.

Ireka I.E., Chinyoka T., Analysis of shear banding phenomena in non-isothermal flow of fluids governed by the diffusive Johnson-Segalman model, Applied Mathematical Modelling, 40(5–6): 3843–3859, 2016, doi: 10.1016/j.apm.2015.11.005.

DOI: 10.24423/engtrans.1182.20200720

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland