Irreversibility Analysis of MHD Buoyancy-Driven Variable Viscosity Liquid Film along an Inclined Heated Plate Convective Cooling

Document Type : Research Paper


1 Mathematics Department, Namibia University of Science and Technology, Windhoek, 9000, Namibia

2 Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa


Analysis of intrinsic irreversibility and heat transfer in a buoyancy-driven changeable viscosity liquid along an incline heated wall with convective cooling taking into consideration the heated isothermal and isoflux wall is investigated. By Newton’s law of cooling, we assumed the free surface exchange heat with environment and fluid viscosity is exponentially dependent on temperature. Appropriate governing model equations for momentum and energy balance with volumetric entropy generation expression are obtained and then transformed using dimensionless variables to form set of nonlinear boundary valued problem. Using shooting method with Runge-Kutta-Fehlberg integration scheme, the model is numerically tackled. Pertinent results for the fluid velocity, temperature, skin friction, Nusselt number, entropy generation rate and Bejan number are obtained and discussed.


Main Subjects

[1] Thiele, U., Knobloch, E., Thin liquid films on a slightly inclined heated plate. Physica D, 190 (2004) 213–248.
[2] Ern, A., Joubaud, R., Lelièvre, T., Numerical study of a thin liquid film flowing down an inclined wavy plane. Physica D, 240 (2011) 1714–1723.
[3] Ghiasy, D., Boodhoo, K.V.K., Tham, M.T., Thermographic analysis of thin liquid films on a rotating disc: Approach and challenges. Applied Thermal Engineering, 44 (2012) 39-49.
[4] Makinde, O.D., Hermite–Pade´ approximation approach to steady flow of a liquid film with adiabatic free surface along an inclined heat plate. Physica A, 381 (2007) 1–7.
[5] Sadiq, I.M.R., Usha, R., Linear instability in a thin viscoelastic liquid film on an inclined, non-uniformly heated wall. International Journal of Engineering Science, 43 (2005) 1435–1449.
[6] Makinde, O.D., Laminar falling liquid film with variable viscosity along an inclined heated plate. Applied Mathematics and Computation, 175 (2006) 80–88.
[7] Sekhar, G.N., Jayalatha, G., Elastic effects on Rayleigh-Benard convection in liquids with temperature-dependent viscosity. International Journal of Thermal Sciences, 49 (2010) 67–75.
[8] Nonino, C., Del Giudice, S., Savino, S., Temperature dependent viscosity effects on laminar forced convection in the entrance region of straight ducts. International Journal of Heat and Mass Transfer, 49 (2006) 4469–4481.
[9] Hooman, K., Gurgenci, H., Effects of temperature-dependent viscosity on Be´nard convection in a porous medium using a non-Darcy model. International Journal of Heat and Mass Transfer, 51 (2008) 1139–1149.
[10] Kabova, Y.O., Kuznetsov, V.V., Kabov, O.A., Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film. International Journal of Heat and Mass Transfer, 55 (2012) 1271–1278.
[11] Eegunjobi, A.S., Makinde, O.D., Entropy generation analysis in transient variable viscosity Couette ow between two concentric pipes. Journal of Thermal Science and Technology, 9(2), 2014, 8p.
[12] Vishnu Ganesha, N., Al-Mdallalb, Q.M., Chamkhac, A.J., A numerical investigation of Newtonian fluid flow with buoyancy, thermal slip of order two and entropy generation. Case Studies in Thermal Engineering, 13 (2019) 100376.
[13] Eegunjobi A.S., Makinde, O.D., MHD Mixed Convection Slip Flow of Radiating Casson Fluid with Entropy Generation in a Channel Filled with Porous Media. Defect and Diffusion Forum, 374 (2017) 47-66.
[14] Sourtiji, E., Gorji-Bandpy, M., Ganji, D.D., Seyyedi, S.M., Magnetohydrodynamic buoyancy-driven heat transfer in a cylindrical–triangular annulus filled by Cu–water nanofluid using CVFEM. Journal of Molecular Liquids, 196 (2014) 370-380.
[15] Parmar, L., Kulshreshtha, S.B., Singh, D.P., The role of magnetic field intensity in blood flow through overlapping stenosed artery: A Herschel-Bulkley fluid model. Advances in Applied Science Research, 4(6) (2013) 318-328.
[16] Astarita, G.M., Palumbo, G., Non-Newtonian gravity flow along inclined plane surfaces, Industrial & Engineering Chemistry Fundamentals, 3(4) (1964) 333-339.
[17] Makinde, O.D., Laminar falling liquid film with variable viscosity along an inclined heated plate, Applied Mathematics and Computation, 175 (2006) 80-88.
[18] Makinde, O.D., Thermodynamic second law analysis for a gravity-driven variable viscosity liquid film along an inclined heated plate with convective cooling. Journal of Mechanical Science and Technology, 24(4) (2010) 899-908.
[19] Saouli, S., Aiboud-Saouli, S., Second law analysis of laminar falling liquid film along an inclined heated plate. International Communications in Heat and Mass Transfer, 31 (2004) 879-886.
[20] Cebeci, T., Bradshaw. P., Physical and Computational Aspects of Convective Heat Transfer, Springer: New York, NY, USA, 1988.
[21] Afridi, M.I., Qasim, M., Khan, N.I., Makinde, O.D., Minimization of Entropy Generation in MHD Mixed Convection Flow with Energy Dissipation and Joule Heating: Utilization of Sparrow-Quack-Boerner Local Non-Similarity Method, Defect and Diffusion Forum, 387 (2018) 63-77.
[22] Khan, N.A., Naz, F., Sultan, F., Entropy generation analysis and effects of slip conditions on micropolar fluid flow due to a rotating disk, Open Engineering, 7 (2017) 185–198.