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Fully developed magneto convection flow in a vertical rectangular duct

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Abstract

An analysis is performed to study the MHD free convection flow in a vertical rectangular duct for laminar and fully developed regime taking into consideration the effects of Ohmic heating and viscous dissipation. Numerical solutions are found using finite difference method of second-order accuracy. The effects of various physical parameters such as Hartmann number, aspect ratio, buoyancy parameter and circuit parameter are presented graphically. It is found that as Hartmann number, buoyancy parameter and aspect ratio increase, the upward and downward flow rates are increased for open circuit but decrease for short circuit.

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Abbreviations

B 0 :

Magnetic field strength

E 0 :

Electric field

g :

Acceleration due to gravity

k :

Thermal conductivity of the fluid

M :

Hartmann number

N :

Buoyancy parameter

T :

Fluid temperature

T 0 :

Reference temperature

T1, T2:

Temperatures of the walls of the duct

W :

Velocity in the Z-direction

X, Y, Z:

Cartesian coordinates

β T :

Coefficient of thermal expansion

σ e :

Electrical conductivity

ρ 0 :

Density of the fluid

ν :

Kinematic viscosity

μ :

Viscosity

θ :

Dimensionless temperature

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Authors and Affiliations

  1. Department of Mathematics, Gulbarga University, Gulbarga, 585 106, Karnataka, India

    J. Prathap Kumar

  2. Department of Civil Engineering, National Chi Nan University, 1 University Rd, Puli, 545, Nantou, Taiwan, ROC

    J. C. Umavathi & I. C. Liu

  3. Faculty of Mathematics, University of Cluj, CP 253, 3400, Cluj, Romania

    I. Pop

Authors
  1. J. C. Umavathi
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  2. I. C. Liu
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  3. J. Prathap Kumar
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  4. I. Pop
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Correspondence to J. C. Umavathi.

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Umavathi, J.C., Liu, I.C., Prathap Kumar, J. et al. Fully developed magneto convection flow in a vertical rectangular duct. Heat Mass Transfer 47, 1–11 (2011). https://doi.org/10.1007/s00231-010-0650-2

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  • DOI: https://doi.org/10.1007/s00231-010-0650-2

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