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Research Papers: Forced Convection

Analytical Analysis of Magneto-hydrodynamic (MHD) Transient Flow Past a Suddenly Started Infinite Vertical Plate With Thermal Radiation and Ramped Wall Temperature

[+] Author and Article Information
N. Ahmed

Department of Mathematics,
Gauhati University Institute of Science
and Technology,
Guwahati 781014, Assam, India
e-mail: saheel_nazib@yahoo.com

M. Dutta

Department of Mathematics,
Gauhati University Institute of Science
and Technology,
Guwahati 781014, Assam, India
e-mail: manasdutta@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 24, 2012; final manuscript received November 13, 2013; published online January 31, 2014. Assoc. Editor: He-Ping Tan.

J. Heat Transfer 136(4), 041703 (Jan 31, 2014) (8 pages) Paper No: HT-12-1461; doi: 10.1115/1.4026052 History: Received August 24, 2012; Revised November 13, 2013

An exact solution to the problem of a magnetohydrodynamic viscous, incompressible free convective flow of an electrically conducting, Newtonian non-Gray fluid past a suddenly started infinite vertical plate with ramped wall temperature in presence of appreciable radiation heat transfer and uniform transverse magnetic field is presented. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The resulting system of the equations governing the flow is solved by adopting Laplace Transform technique in closed form. Detailed computations of the influence of Hartmann number, radiation conduction parameter Q, Reynolds number Re and time t on the variations in the fluid velocity, fluid temperature, and skin friction and Nusselt number at the plate are demonstrated graphically. The results show that the imposition of the transverse magnetic field retards the fluid motion and causes the viscous drag at the plate to fall. The investigation simulates that the fluid temperature drops and the rate of heat transfer from the plate to the fluid gets increased for increasing Reynolds number.

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References

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Figures

Grahic Jump Location
Fig. 1

Velocity distribution versus y for Gr = 30, Re = 10, Pr = 0.71, Q = 5, t = 0.5

Grahic Jump Location
Fig. 2

Velocity distribution versus y for Gr = 30, Re = 10, Pr = 0.71, Q = 5, t = 2

Grahic Jump Location
Fig. 3

Velocity distribution versus y for Gr = 30, M = 5, Pr = 0.71, Q = 5, t = 0.5

Grahic Jump Location
Fig. 4

Velocity distribution versus y for Gr = 30, M = 5, Pr = 0.71, Q = 5, t = 2

Grahic Jump Location
Fig. 5

Velocity distribution versus y for Gr = 30, Re = 7, M = 5, Pr = 0.71, t = 0.5

Grahic Jump Location
Fig. 6

Velocity distribution versus y for Gr = 30, Re = 7, M = 5, Pr = 0.71, t = 2

Grahic Jump Location
Fig. 7

Temperature distribution versus y for Pr = 0.71, Q = 5, t = 0.5

Grahic Jump Location
Fig. 8

Temperature distribution versus y for Pr = 0.71, Q = 5, t = 2

Grahic Jump Location
Fig. 9

Temperature distribution versus y for Re = 10, Pr = 0.71, t = 0.5

Grahic Jump Location
Fig. 10

Temperature distribution versus y for Re = 10, Pr = 0.71, t = 2

Grahic Jump Location
Fig. 11

Skin friction τ versus time t for Gr = 30, Re = 10, Pr = 0.71, Q = 5

Grahic Jump Location
Fig. 12

Nusselt number Nu versus time t for Pr = 0.71, Q = 5

Grahic Jump Location
Fig. 13

Nusselt number Nu versus time t for Re = 10, Pr = 0.71

Grahic Jump Location
Fig. 14

(Fig. 7 of Das et al. [21]) temperature profiles for variations in Ra (radiation) when Pr = 0.71 and τ (time) = 0.5

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