Unsteady Natural Convection Couette Flow of Heat Generating/Absorbing Fluid Between Vertical Parallel Plates Filled With Porous Material

Basant K.Jha; Muhammad K.Musa

doi:10.3879/j.issn.1000-0887.2012.03.003

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Basant K.Jha, Muhammad K.Musa. Unsteady Natural Convection Couette Flow of Heat Generating/Absorbing Fluid Between Vertical Parallel Plates Filled With Porous Material[J]. Applied Mathematics and Mechanics, 2012, 33(3): 292-302. doi: 10.3879/j.issn.1000-0887.2012.03.003

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Unsteady Natural Convection Couette Flow of Heat Generating/Absorbing Fluid Between Vertical Parallel Plates Filled With Porous Material

doi: 10.3879/j.issn.1000-0887.2012.03.003

Basant K.Jha^1,2,
Muhammad K.Musa¹

¹Department of Mathematics, Ahmadu Bello University, Zaria 234, Nigeria;²Mathematics Unit, School of Basic and Remedial Studies, Ahmadu Bello University, Funtua 6007, Nigeria

Received Date: 2010-12-31
Rev Recd Date: 2011-11-18
Publish Date: 2012-03-15

Abstract

Abstract

The extended Brinkman Darcy model for momentum equation, and an energy equation were used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel (formed by two infinite vertical parallel plates) filled with fluidsaturated porous medium. The flow was triggered by the asymmetric heating and the acceleration motion of one of the bounding plates. The governing equations were simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain closed form solutions for the velocity and temperature profiles. Then the skin friction as well as the rate of heat transfer were consequently derived. It is noticed that at different sections within the vertical channel, the fluid flow as well as the temperature profile increase with time and are both higher near the moving plate.In particular, increasing the gap between the plates increases the velocity and the temperature of the fluid, however, reduces the skin friction and the rate of heat transfer.
- heat generating/absorbing fluid,
- natural convection flow,
- porous material,
- acceleration motion,

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References(13)

References

[1]	Schlichting H. Boundary Layer Theory[M]. New York: McGraw-Hill, 1968: 75-78.
[2]	Ishigaki H. An exact periodic solution of the energy equation[J]. Journal of Fluid Mechanics, 1971, 50(4): 657-668.
[3]	Singh A K. Natural convection in unsteady Couette motion[J]. Defense Science Journal, 1988, 38(1): 35- 41.
[4]	Jha B K, Ajibade A O. Unsteady free convection Couette flow of heat generating/absorbing fluid[J]. International Journal of Energy and Technology, 2010, 2(12): 1-9.
[5]	Jha B K, Ajibade A O. Free convective flow of heat generating/absorbing fluids between vertical porous plates with periodic heat input[J]. International Communication in Heat and Mass Transfer, 2009, 36(6): 624-631.
[6]	Jha B K. Transient free-convective flow in a vertical channel with heat sink[J]. International Journal of Applied Mechanics and Engineering, 2003, 8(3): 497-502.
[7]	Jha B K, Ajibade A O. Transient natural convection flow between vertical parallel plates with temperature dependent heat sources/sinks[J]. Journal of Heat Technology, 2009, 27(2): 87-94.
[8]	Ingham D B, Merkin J A, Pop I. Flow past a suddenly cooled vertical flat surface in a saturated porous medium[J]. International Journal of Heat and Mass Transfer, 1982, 25: 1916-1919.
[9]	Hong J T, Yamada Y, Tien C L. Effects of non-Darcian and non-uniform porosity on vertical-plate natural convective in porous media[J]. ASME Journal of Heat Transfer, 1987, 109(2): 356-362.
[10]	Cheng P, Hsu C T. Fully developed forced convection flow through an annular packed-sphere bed with wall effects[J]. International Journal of Heat and Mass Transfer, 1986, 29(12): 2373-2383.
[11]	Cheng P, Hsu C T. Effects of radial thermal dispersion on fully developed forced convection in a cylindrical tube[J]. International Journal of Heat and Mass Transfer, 1987, 30(11): 1843-1853.
[12]	Cheng P, Vortmeyer D. Transverse thermal dispersion and wall channeling in a packed bed with forced convection flow[J]. Chemical Engineering Science, 1988, 43: 2523-2532.
[13]	Jha B K. Transient natural convection through vertical porous stratum[J]. Heat and Mass Transfer, 1997, 33(3): 261-263.