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## International Journal of Applied Mechanics and Engineering

2016 | Vol. 21, no. 4 | 891--904
Tytuł artykułu

### Unsteady Hartmann two-phase flow: the Riemann-sum approximation approach

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We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparisons with the closed form solutions obtained for steady states which have been derived separately and also by the implicit finite difference method. The variation of velocity, mass flow rate and skin-friction on both plates for various physical parameters involved in the problem are reported and discussed with the help of line graphs. It was found that the effect of changes of the electric load parameter is to aid or oppose the flow as compared to the short-circuited case.
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891--904
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Bibliogr. 13 poz., wykr.
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Bibliografia
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• [8] Umavathi J.C., Chamkha A.J., Mateen A. and Al-Mudhaf A. (2005): Unsteady two-fluid flow and heat transfer in a horizontal channel. – Heat and Mass Transfer, vol.422, pp.81-90.
• [9] Umavathi J.C., Mateen A., Chamkha A.J. and Mudhaf A.A. (2006): Oscillatory Hartmann two-fluid flow and heat transfer in a horizontal channel. – International Journal of Applied Mechanics and Engineering, vol.11, No.1, pp.155-178.
• [10] Umavathi J.C., Chamkha A.J., Mateen A. and Kumar J.P. (2008): Unsteady magnetohydrodynamic two-fluid flow and heat transfer in a horizontal channel. – Heat and Technology, vol.262, pp.121-133.
• [11] Linga Raju T. and Nagavalli M. (2014): MHD two -layered unsteady fluid flow and heat transfer through a horizontal channel between parallel plates in a rotating system. – Int. J. of Applied Mechanics and Engineering, vol.19, No.1, pp.97-121.
• [12] Jha B.K. and Apere C.A. (2010): Unsteady MHD Couette flow in an annuli: the Riemann-sum approximation approach. – J. Phys. Soc. Jpn., vol.79, 124403.
• [13] Tzou D.Y. (1997): Macro to Microscale Heat Transfer: The Lagging Behaviour. – Taylor and Francis.
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