Thermodynamic Second Law Analysis of Hydromagnetic Gravity-Driven Two-step Exothermic Chemical Reactive Flow with Heat Absorption Along a Channel

Document Type: Original Article


1 Department of Mathematics, Landmark University, Omu-aran, Nigeria

2 Department of Mathematics and Computer Science, Federal University of Petroleum Resources, Effurun, Nigeria


This study examines the second law of thermodynamic gravity-driven viscous combustible fluid flow of two-step exothermic chemical reaction with heat absorption and convective cooling under bimolecular kinetic. The flow is acted upon by periodic changes in the axial pressure gradient and time along the axis of the channel with the existence of magnetic field. The heat convection at the channel surfaces with the environment is the same and satisfies the Newtons law of cooling. The dimensionless main equations of the flow are solved using a convergent and stable semi-implicit finite difference method. The effect of some fluid parameters associated with the problem on momentum and temperature are obtained. The expression for irreversibility ratio, volumetric entropy generation and Bejan number along with the graphical results are presented and quantitatively discussed.


  1. Bejan, A. 1994, Entropy Generation Through Heat and Fluid Flow, John Wiley & Sons, New York, p. 98 (Chapter 5).
  2. Bejan, A, 1996. Entropy Generation Minimization, CRC Press, Boca Raton, Florida.
  3. Adesanya, S.O., Makinde, O.D. 2015, Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface. Physica A 432, 222-229.
  4. Adesanya, S.O., Falade, J.A., Srinivas Jangili, c., Anwar Beg, O. 2017, Irreversibility analysis for reactive third-grade fluid flow and heat transfer with convective wall cooling. Alexandra Engineering Journal. 56, 153-160.
  5. Makinde, O.D. 2006, Irreversibility analysis for gravity driven non-Newtonian liquid film along an inclined isothermal plate. Physica Scripta, 74, 642-645.
  6. Aziz, A. 2003, Entropy generation in pressure gradient assisted Couette flow with different thermal boundary conditions. Entropy. 5, 271-312.
  7. Narusawa, U. 2001, The second law analysis of mixed convection in rectangular ducts. Heat Mass Transfer. 37, 197-203.
  8. Salawu, S.O., Fatunmbi, E.O. 2017, Inherent irreversibility of hydromagnetic third-grade reactive poiseuille flow of a variable viscosity in porous media with convective cooling. Journal of the Serbian Society for Computational Mechanics, 11, 46-58.
  9. Srinivas, J., Ramana Murthy, J.V. 2016, Second law analysis of the flow of two immiscible micropolar fluids between two porous beds. Journal of Engineering Thermophysics, 25, 126-142.
  10. Srinivas, J., Ramana Murthy, J.V., Chamkha, A.J. 2016, Analysis of entropy generation in an inclined channel flow containing two immiscible micropolar fluids using HAM. Int. J. Numer. Meth. Heat Fluid Flow. 23, 1027-1049.
  11. Tasnim, S.H., Mahmud, S. 2002, Entropy generation in a vertical concentric channel with temperature dependent viscosity. Int. Commun. Heat Mass Transfer. 29, 907-918.
  12. Taufiq, B.N., Masjuki, H.H., Mahlia, T.M.I., Saidur, R., Faizul, M.S., Mohamad, E.N. 2007, Second law analysis for optimal thermal design of radial fin geometry by convection. Applied Thermal Engineering, 27, 1363-1370.
  13. Anwar, M.I., Rodkiewicz, C.M. 1972, Nonuniform magnetic field effects in MHD slider bearings. ASME Journal of Lubrication Technology, 94, 101-105.
  14. Ariel, P.D. 2002, On computation of MHD flow near a rotating disk, Zeitschrift fitr Angewandte Mathematik and Mechanik, 82, 235-246.
  15. Dada, M.S., Salawu, S.O. 2017, Analysis of heat and mass transfer of an inclined magnetic field pressure-driven flow past a permeable plate. Applications and Applied Mathematics: An International Journal (AAM). 12, 189-200.
  16. Das, S., Jana, R.N. 2012, Entropy generation due to MHD flow in a porous channel with Navier slip. Ain Shams Engineering Journal, 5, 575-584.
  17. Dimian, M.F., Essawy, A.H. 2000, Magnetic field effects on mixed convection between rotating coaxial disk. Journal of Engineering Physics and Thermophysics. 73, 1082-1091.
  18. Lu, R.F., Chien, R.D., Lin, J.R. 2006, Effects of fluid inertia in magneto-hydrodynamic annular squeeze films. Tribology International. 39, 221-226.
  19. Reddy Gorla, R.S., Byrd, L.W., Pratt, D.M. 2007, Second law analysis for microscale flow and heat transfer. Applied Thermal Engineering. 27, 1414-1423.
  20. Salawu, S.O. and Dada, M.S. 2016, Radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic feld with dissipation in a non-Darcy medium. Journal of the Nigerian Mathematical Society. 35, 93-106
  21. Szabo, Z.G. 1964, Advances in kinetics of homogeneous gas reactions, Methusen and Co Ltd, Great Britain
  22. Makinde, O.D., Olanrewaju, P.O., Titiloye, E.O., Ogunsola, A.W. 2013, On thermal stability of a two-step exothermic chemical reaction in a slab. Journal of Mathematical sciences. 13, 1-15.
  23. Kareem, R.A., Gbadeyan, J.A. 2016, Unsteady radiative hydromagnetic internal heat generation fluid flow through a porous channel of a two-step exothermic chemical reaction. Journal of the Nigerian Association of Mathematical Physics, 34, 111-124.
  24. Chinyoka, T., Renardy, Y.Y., Renardy, M., Khismatullin, D.B. 2005, Two-dimensional study of drop deformation under simple shear for Oldroyd-B liquids. Journal of Non-Newton Fluid Mechanics, 31, 45-56.
  25. Chinyoka, T. 2008, Computational dynamics of a thermally decomposable viscoelastic lubricant under shear. Trans. ASME, Journal of Fluids Engineering, 130, 121201. doi:10.1115/1.2978993