Impact of Thermal Stratification on Unsteady Natural Convection Couette Flow Formation in a Vertical Channel Filled with Anisotropic Porous Material

Abstract:

Recently, heat transfer problems where anisotropic porous medium or stably stratified fluid are taken into account have been separately studied. Developing a mathematical model that combines these physical quantities naturally results to complex coupled differential equations. In this paper, a fully developed time dependent natural convection Couette flow of stably stratified fluid between vertical parallel channels filled with anisotropic porous material is investigated. The governing partial differential equations are transformed into ordinary differential equations using Laplace transform techniques and then decoupled using D’Alembert method. Exact solutions in Laplace domain for the velocity and temperature equations are then obtained. A numerical method: Riemann-sum approximation is then used to invert the expressions for the velocity and temperature profiles, as well as the resulting skin friction, rate of heat transfer and volumetric mass flow rate into their corresponding time domain. The research establishes that both the anisotropic and the stratification parameters aid in regulating the fluid temperature and velocity. The research further reveals that the fluid velocity attains its maximum (or minimum) velocity when θ = 90⁰ (or θ = 0⁰) for k^*<1 and when k^*>1, the fluid velocity is least (or maximum) when θ = 90⁰ (or θ = 0⁰).

• Periodical: Defect and Diffusion Forum (Volume 408)
• Pages: 67-82
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.408.67
• Online since: April 2021
• Authors: Basant Kumar Jha, Muhammad Kabir Musa*, Abiodun O. Ajibade
• Keywords: Anisotropic Porous Medium, Couette Flow, D’Alembert Method, Riemann Sum Approximation, Stably Stratified Fluid

References

[1] J. Yovogan, J. Degan, Effect of anisotropic permeability on convective heat transfer through a porous riverbed underlying a fluid layer, J. Eng Math. 18 (2013) 127-140.

DOI: 10.1007/s10665-012-9605-6

[2] P. Bera, A. Khalili, Double-diffusive natural convection in an anisotropic porous cavity with opposing buoyancy forces: multi-solutions and oscillations. Int. J. of Heat and Mass Transfer 45 (2002) 3205-3222.

DOI: 10.1016/s0017-9310(02)00024-8

[3] T. Karmakar, G.P.R. Sekhar, Effect of anisotropic permeability on fluid flow through composite porous channel, Jr. Eng. Math. 100 (2016) 33-51.

DOI: 10.1007/s10665-015-9831-9

[4] G. Degan, S. Zohoun, P. Vasseur, Forced convection in horizontal porous channels with hydrodynamic anisotropy. International Journal of Heat and Mass Transfer 45 (2002) 3181- 3188.

DOI: 10.1016/s0017-9310(02)00032-7

[5] P.A. Selkin, J.S. Gee, L. Tauxe, W.P. Meurer, A.J. Newell, The effect of remanence anisotropy on Paleointensity estimate: a case study from the Archean Stillwater Complex. Earth and Planetary Science Latters 183 (2000) 403-416.

DOI: 10.1016/s0012-821x(00)00292-2

[6] T. Nilsen, L. Storesletten, An analytical study on natural convection in isotropic and anisotropic porous channels, J. of Heat Transfer 112 (1990) 396-401.

DOI: 10.1115/1.2910390

[7] M. Mobedi, O. Cekmer, I. Pop, Forced convection heat transfer inside an anisotropic porous channel with oblique principal axes. Effect of viscous dissipation, International Journal of Thermal Science, 49 (2010) 1984 - (1993).

DOI: 10.1016/j.ijthermalsci.2010.06.002

[8] A. Shapiro, E. Fedorovich, Natural convection in a stably stratified fluid along vertical plates and cylinders with temporally periodic surface temperature variation, J. Fluid Mech 546 (2006) 295-311.

DOI: 10.1017/s0022112005007159

[9] R. K. Deka, A. Paul, Convectively driven flow past an infinite moving vertical cylinder with thermal and mass stratification, Pramana Journal of Physics 81(4) (2013) 641-665.

DOI: 10.1007/s12043-013-0604-6

[10] A. Shapiro, E. Fedorovich, Prandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid. Int. Journal of Heat and Mass Transfer 47 (2004) 4911-4927.

DOI: 10.1016/j.ijheatmasstransfer.2004.04.035

[11] A. Shapiro, E. Fedorovich, Unsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid. Journal of fluid mech. 498 (2004) 333-352.

DOI: 10.1017/s0022112003006803

[12] R. K. Deka, A. Paul, Transient free convection flow past an infinite moving vertical cylinder in a stably stratified fluid. Journal of heat transfer 134 (2012) 1-8.

DOI: 10.1115/1.4005205

[13] E. Magyari, I. Pop, B. Keller, Unsteady free convection along an infinite vertical flat plate embedded in a stably stratified fluid-saturated porous medium, Transport in porous media 62 (2006) 233-249.

DOI: 10.1007/s11242-005-1292-6

[14] G. Degan, P. Vasseur, Aiding mixed convection through a vertical anisotropic porous channel with oblique principal axes, Int. Journal of Engr. Scie. 40 (2002) 193-209.

DOI: 10.1016/s0020-7225(01)00012-x

[15] R. K. Deka, A. Bhattacharya, Magneto-hydrodynamic (MHD) flow past an infinite vertical plate immersed in a stably stratified fluid, International Journal of the Physical Sciences,6(24) (2011) 5831-5836.

[16] A.R.A. Khaled, K. Vafai, The role of porous media in modeling flow and heat transfer in biological tissues, International Journal of Heat and Mass Transfer 46 (2003) 4989–003.

DOI: 10.1016/s0017-9310(03)00301-6

[17] A. C. Liakopoulos, Darcy's coefficient of permeability as symmetric tensor of second rank, Hydrological Sciences Journal, 10(3) (1965) 41-48.

[18] R. Ziyaddin, K. Huseyin, Two-phase steady flow along a horizontal glass pipe in the presence of the magnetic and electrical fields, Int Journal of heat and fluid flow 29 (2007) 263-268.

DOI: 10.1016/j.ijheatfluidflow.2007.09.003

[19] B. K. Jha, S. Isa, Computational treatment of MHD transient natural convection flow in a vertical channel due to symmetric heating in the presence of induced magnetic field, Journal of the physical society of Japan, 82 (2013) 1-9.

DOI: 10.7566/jpsj.82.084401

[20] B. K. Jha, M. K. Musa, Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material, Appl. Math. Mech.-Engl. Ed, 33(3) (2012) 303–314.

DOI: 10.1007/s10483-012-1551-8

[21] B. C. Prasannakumara, B.J. Gireesha, M.R. Krishnamurthy, K. Ganesh Kumar, MHD flow and nonlinear radiative heat transfer of Sisko nanofluid over a nonlinear stretching sheet, Informatics in Medicine Unlocked, 9 (2017) 123–132.

DOI: 10.1016/j.imu.2017.07.006

[22] B.J. Gireesha, K. Ganesh Kumar, G.K. Ramesh, B.C. Prasannakumara, Nonlinear convective heat and mass transfer of Oldroyd-B nanofluid over a stretching sheet in the presence of uniform heat source/sink, Results in Physics, 9 (2018) 1555–1563.

DOI: 10.1016/j.rinp.2018.04.006

[23] M. M. Nandeppanavar, B.C. Prasannakumara, J. M. Shilpa, Journal nano fluids, 7(4) (2018) 635 - 645.