Effects of Viscous Dissipation and Wall Conduction on Steady Mixed Convection Couette Flow of Heat Generating/Absorbing Fluid
More details
Hide details
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Online publication date: 2019-12-04
Publication date: 2019-12-01
International Journal of Applied Mechanics and Engineering 2019;24(4):12-35
This article theoretically investigated mixed convection flow of heat generating/absorbing fluid in the presence of viscous dissipation and wall conduction effects. The flow is considered to be steady in a vertical channel with some boundary thickness. One of the plates is heated while the other is kept at ambient temperature. The governing flow equations were solved analytically using Homotopy Perturbation Method (HPM). The influences of the governing parameters were captured in graphs, tables and a table was constructed for validation of the work. It is worthwhile to stress that, both the velocity and temperature profiles decrease near the heated plate with an increase in boundary thickness (d) while the reverse cases were observed toward the cold plate. The velocity profile increases near the heated plate with increase in mixed convection parameter (Gre) and decreases towards the cold plate. Rate of heat transfer has been observed to decrease with increase in boundary plate thickness (d) while the critical value of (Gre) increases with growing boundary plate thickness. The study therefore established the importance of boundary plate thickness in mixed convection investigation.
Kevin D.C. and Barbaros C. (2011): The effects of axial conduction on heat transfer in a liquid microchannel flow.– International Journal of Heat and Mass Transfer, vol.54, No.11-12, pp.2542-2549.
Michael J.S. and Dimos P. (2005): Effect of microreactor wall conduction on the reforming process of methane. –Chemical Engineering Science, vol.60, pp.6983-6997.
Hassab M.A., Khamis M.M. and Shawky I.M. (2013): The effect of axial wall conduction on heat transfer parameters for a parallel-plate channel having a step change boundary conditions.– Numerical Heat Transfer: Part A, vol.63, pp.430-451.
Ates A., Darici S. and Bilir S. (2007): Transient conjugated heat transfer in thick walled pipes with uniform heat flux boundary conditions. – 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, HEFAT.
Mei L., Wang Q.W. and Zhixiong G. (2016): Investigation on evaluation criteria of axial wall heat conduction under two classical thermal boundary conditions.– Applied Energy, vol.162, pp.1662-1669.
Moukalled F., Darwish M. and Acharya S. (1995): Influence of wall conduction on mixed convection heat transfer in externally finned pipes.– Numerical Heat Transfer, Part A: Application, vol.28, No.2, pp.157-173.
Hamid N. and Behnam R. (2012): Mixed convective slip in a vertical plate microchannel with symmetric and asymmetric wall heat fluxes. –Transaction of the Canadian Society for Mechanical Engineering, vol.36, No.3, pp.207-218.
Ajibade O.A. and Thomas U.O. (2017): Entropy generation and irreversibility analysis due to steady mixed convection flow in a vertical porous channel. – International Journal of Heat and Technology, vol.35, No.3, pp.433-446.
Swati M. (2012): Mixed convection boundary layer flow along a stretching cylinder in porous medium. – Journal of Petroleum Science and Engineering, vol.76-97, pp.73-78.
Jha K.B., Debora D. and Ajibade O.A. (2015): Mixed convection in an inclined channel filled with porous material having time periodic boundary conditions.– Transport in Porous Media, vol.109, No.1, DOI 10.1007/s11242-015-0533-6.
Mehdi M. and Mohsen S. (2015): MHD mixed convection slip flow in a vertical parallel plate microchannel heated at asymmetric and uniform heat flux. – Journal of Mechanical Science and Technology, vol.29, No.7, pp.1-8.
Jha K.B., Debora D. and Ajibade O.A. (2013): Steady fully developed mixed convection flow in a vertical parallel plate microchannel with bilateral heating and filled with porous material. – Journal of Process Mechanical Engineering, vol.227, No.1, pp.56-66.
Jha K.B. and Babatunde A. (2014): Mathematical modeling and exact solution of steady fully developed mixed convection flow in a vertical micro-porous-annulus. – Afrika Matematika, DOI 10.1007/s13370-014-0277-4.
Dileep S.C. and Vikas K. (2011): Radiation effects on mixed convection ow and viscous heating in a vertical partially filled with a porous medium. – Tankang Journal of Science and Engineering, vol.14, No.2, pp.97-106.
Joseph K.M., Peter A. and Abubakar S.M. (2017): Effect of Brinkman number and magnetic field on Laminar convection in a vertical plate channel. – Science World Journal, vol.12, No.4, pp.58-62.
Pranab K.M. and Sanchayan M. Viscous dissipation effects on the limiting value of Nusselt numbers for a shear driven flow between two asymmetrically heated parallel plates. – Frontiers in Heat and Mass Transfer, 3(033004), (212).
Jha K.B. and Ajibade O.A. (2010): Unsteady free convective Couette flow of heat generating/absorbing fluid. – International Journal of Energy and Technology, vol.2, No.12, pp.1-9.
Jha B.K., Michael O.O. and Babatunde A. (2016): Steady fully developed mixed convection flow in a vertical micro-concentric annulus with heat generating/absorbing fluid: an exact solution. – Ain Shams Engineering Journal, DOI.org/10.1016/j.asej.2016.08.005.
Vajravelu K. and Sastri K.S. (1978): Laminar free convection heat transfer of a viscous in-compressible heat generating fluid flow past a vertical porous plate in the presence of free-stream oscillations I. – Acta Mechanica, vol.31, pp.71-87.
Vajravelu K. and Sastri K.S. (1978): Laminar free convection heat transfer of a viscous incompressible heat generating fluid flow past a vertical porous plate in the presence of free-stream oscillations II. – Acta Mechanica, vol.31, pp.80-100.
Vajravelu K. (1979): Natural convection at a heated semi infinite vertical plate with temperature dependent heat sources or sinks. – Proceeding of the Indian Academy of Sciences, vol.88, No.4, pp.369-376.
Moalem D. (1976): Steady-state heat transfer within porous medium with temperature dependent heat generation. – International Journal of Heat and Mass Transfer, vol.19, pp.529-537.
Foraboschi F.P. and Federico I.Di. (1964): Heat transfer in Laminar flow of non-Newtonian heat generating fluids. – International Journal of Heat and Mass Transfer, vol.7, No.3, pp.315-318.
Jafar B. and Hossein A. (2009): Study of convergence of Homotopy Perturbation Method for systems of partial differential equations. – Computer and Mathematics with Application, vol.58, pp.2221-2230.
Asma A.E., Adem K. and Bachok M.T. (2014): Note on the convergence analysis of Homotopy Perturbation Method for fractional partial differential equations. – Abstract and Analysis, ID803902:8 pages.
Elsayed A.M.A., Elkalla I.L. and Hammad D. (2012): A homotopy perturbation technique for solving partial differential equations of fractional order in infinite domains. – Applied Mathematics and Computation, pp.8329-8340.
Jafar H., Alipour A. and Tajadodi H. (2012): Convergence of homotopy perturbation method for solving integral equations. – Thai Journal of Mathematics, vol.8, No.3, pp.511-520.
He J.H. (1999): Homotopy perturbation technique. – Computer Methods in Applied Mechanics and Engineering, vol.178, pp.257-262.
He J.H. (2000): A coupling method of a homotopy perturbation technique for non-linear problems. – Journal of Non-Linear Mechanics, vol.35, pp.37-43.
He J.H. (2003): Homotopy perturbation method: a new nonlinear analytical technique. – Applied Mathematics and Computation, vol.135, pp.73-79.
He J.H. (2006): Homotopy perturbation method for solving boundary value problems. – Physics Letters A, vol.350, pp.87-88.
Journals System - logo
Scroll to top