Abstract
Abstract Aim of the paper is to investigate the effects of linearly varying thermal conductivity, viscous dissipation and Ohmic heating on steady free convection flow of a viscous incompressible electrically conducting liquid having low Prandtl number along an inclined isothermal non-conducting porous plate in the presence of transverse magnetic field. The governing equations of continuity, momentum and energy are transformed into ordinary differential equations using similarity transformation. The resulting coupled and non-linear ordinary differential equations are solved using Runge-Kutta fourth order method and shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and Nusselt number at the plate are derived, discussed and their numerical values for various values of physical parameters are presented through tables.
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Abbreviations
- g :
-
Acceleration due to gravity of the Earth
- x,y:
-
Cartesian coordinates
- f :
-
dimensionless stream function
- Gr :
-
Grashof number {=g β(T w −T ∞)x 3/ν 2}
- f w :
-
injection/suction parameter \(\{=-\frac{v_{w}x}{3\nu}(\frac{\mathit{Gr}}{4})^{-1/2}\}\)
- B o :
-
magnetic field intensity
- M :
-
magnetic parameter \(\{=\frac{\sigma B_{o}^{2}x^{2}}{\mu}(\frac{\mathit{Gr}}{4})^{-1/2}\}\)
- Nu :
-
Nusselt number
- Pr :
-
Prandtl number (=μ C p /κ)
- C f :
-
skin-friction coefficient
- C p :
-
specific heat at constant pressure
- T :
-
temperature of the fluid
- T w :
-
temperature of the plate
- T ∞ :
-
temperature of fluid far from plate
- u,v:
-
velocity components along x- and y-directions, respectively
- E :
-
viscous dissipation parameter {=4g β x/C p }
- β :
-
Coefficient of thermal expansion
- μ :
-
coefficient of viscosity
- θ :
-
dimensionless temperature {=(T−T ∞)/(T w −T ∞)}
- σ :
-
electrical conductivity
- γ :
-
inclination angle from the vertical direction
- ν,ρ:
-
kinematic viscosity (=μ/ρ), fluid density, respectively
- η :
-
similarity variable
- ψ :
-
stream function
- κ*,κ:
-
variable thermal conductivity, thermal conductivity, respectively
- ′:
-
differentiation with respect to η
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Sharma, P.R., Singh, G. Effects of variable thermal conductivity, viscous dissipation on steady MHD natural convection flow of low Prandtl fluid on an inclined porous plate with Ohmic heating. Meccanica 45, 237–247 (2010). https://doi.org/10.1007/s11012-009-9240-0
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DOI: https://doi.org/10.1007/s11012-009-9240-0