Abstract
The combined effects of the permeability of the medium, magnetic field, buoyancy forces and dissipation on the unsteady mixed convection flow over a horizontal cylinder and a sphere embedded in a porous medium have been studied. The nonlinear coupled partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The skin friction, heat transfer and mass transfer increase with the permeability of the medium, magnetic field and buoyancy parameter. The heat and mass transfer continuously decrease with the stream-wise distance, whereas the skin friction increases from zero, attains a maximum and then decreases to zero. The skin friction, heat transfer and mass transfer are significantly affected by the free stream velocity distribution. The effect of dissipation parameter is found to be more pronounced on the heat transfer than on the skin friction and mass transfer.
Zusammenfassung
Untersucht wurden kombinierte Effekte der Permeabilität des Mediums, des magnetischen Feldes, der Auftriebskräfte und der Dissipation auf die instationäre Mischkonvektions-Strömung über einen horizontalen Zylinder und eine Kugel, die in einem porösen Medium eingebettet sind. Die nichtlinearen gekoppelten partiellen Differentialgleichungen mit drei unabhängigen Variablen wurden numerisch unter Benutzung eines impliziten Finite-Differenzen-Verfahrens in Verbindung mit der Quasi-Linearisierungstechnik gelöst. Die Oberflächenreibung und die Wärme- und Stoffübertragung steigen mit der Permeabilität des Mediums, dem magnetischen Feld und dem Auftriebsparameter an. Die Wärme- und Stoffübertragung fällt stetig in Strömungsrichtung ab, wohingegen die Oberflächenreibung von Null ansteigt, ein Maximum erreicht und wieder auf Null abfällt. Die Oberflächenreibung und die Wärme- und Stoffübertragung werden signifikant von der Verteilung der Freistromgeschwindigkeit beeinfluβt. Es wurde festgestellt, das der Dissipations-Parameter stärker die Wärmeübertragung als die Oberflächenreibung und die Stoffübertragung beeinfluβt.
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Abbreviations
- B o :
-
magnetic field
- c p :
-
specific heat at a constant pressure
- C :
-
concentration or species mass fraction
- C f :
-
skin friction coefficient
- D :
-
binary diffusion coefficient
- E :
-
Eckert number
- f :
-
dimensionless stream function
- F :
-
constant in the second order resistance
- g :
-
acceleration due to gravity
- G, H :
-
dimensionless temperature and concentration, respectively
- Gr, Gr c :
-
Grashof numbers
- Ha :
-
Hartmann number
- k :
-
thermal conductivity
- K :
-
dimensionless permeability parameter
- K 1 :
-
dimensional permeability parameter
- L, M :
-
characteristic length and magnetic parameter, respectively
- N i (i=1 to 6):
-
functions of ξ (or\(\bar x\))
- Nu, Sh :
-
Nusselt number and Sherwood number, respectively
- Pr, Sc :
-
Prandtl number and Schmidt number, respectively
- r :
-
radial distance from a surface element to the axis of symmetry
- R :
-
radius of the cylinder or the sphere
- Re L ,Re R :
-
Reynolds numbers defined with respect toL andR, respectively
- t, t*:
-
dimensional and dimensionless times, respectively
- T :
-
dimensional temperature
- u, v :
-
velocity components alongx andy directions, respectively
- x, y :
-
distances along and perpendicular to the surface
- \(\bar x\) :
-
dimensionless distance along streamwise direction
- α, α 1 :
-
ratio of Grashof number and Reynolds number squared
- β, β*:
-
coefficients of thermal expansion and expansion with mass fraction, respectively
- ε :
-
porosity
- ε 1,ε 2 :
-
constants
- ξ, η :
-
transformed coordinates
- ν :
-
kinematic viscosity
- ϱ, σ :
-
density and electrical conductivity, respectively
- ζ w :
-
shear stress at the wall
- ϕ, ϑ :
-
function oft* and angle ofy axis with respect to the vertical respectively
- ψ :
-
dimensional stream function
- ω*:
-
frequency parameter
- j :
-
index
- ′:
-
prime denotes derivatives with respect to η
- e :
-
conditions at the edge of the boundary layer
- i :
-
initial conditions (i.e., conditions att = 0)
- s :
-
steady state
- t, t*:
-
derivatives with respect tot andt*, respectively
- w :
-
conditions at the wall
- x, y, ξ :
-
derivatives with respect tox, y andξ, respectively
- ∞ :
-
free stream conditions
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Kumari, M., Nath, G. Unsteady mixed convection with double diffusion over a horizontal cylinder and a sphere within a porous medium. Wärme- und Stoffübertragung 24, 103–109 (1989). https://doi.org/10.1007/BF01786443
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DOI: https://doi.org/10.1007/BF01786443