The Influence of Injection or Withdrawal of Fluid on Free Convection About a Vertical Cylinder in a Porous Medium

Abstract

Free convection about a vertical cylinder in a porous medium subject to constant wII tempemmre or conxtant wall heat flux is considered. The influence of uniform bteml m a flux on the boundary4ayer transport ic studied. Numerrerrcal results for heat transfer along the boundary and tempemtwe profiles are presented for various wlues of the pammeter w which is a measure of the effect of injection or withdiowl of fluid as compared to the combined transverse eurvahre and bteml mass f i x effects.

Effect of Thermal Radiation on Non-Darcy Natural Convection From a Vertical Cylinder Embedded in a Nanofluid Porous Media

“…The accuracy of the aforementioned numerical method was validated by direct comparisons with the numerical results reported earlier by Yücel (1984), Bassom and Rees (1996), Yih (1999), and EL-Hakiem and Rashad (2007) for various values of ξ in the absence of thermal radiation effects and inertia effects of the porous medium (R d → ∞, Er = 0) for a regular Newtonian fluid (ϕ = 0.0). Table 1 presents the results of this comparison.…”

“…The system of equations (10) and (11) with the boundary conditions (12) reduces to the equations of a Darcy free convection flow of Newtonian fluid over an isothermal vertical cylinder saturated porous medium, when R d → ∞, ϕ = 0, and Er = 0; this case has been studied by Yücel (1984) and Bassom and Rees (1996). The nondimensional equations (10) and (11) with the boundary conditions (12) when ϕ = 0 and Er = 0 reduce to the equations of a Darcy free convection flow of Newtonian fluid over an isothermal vertical cylinder saturated porous medium in the presence of radiation interaction, which has been investigated by Yih (1999) and when ϕ = 0 (regular Newtonian fluid), this case has been studied by EL-Hakiem and Rashad (2007).…”

Heat and mass transfer by non‐Darcy free convection from a vertical cylinder embedded in porous media with a temperature‐dependent viscosity

“…The step sizes employed were arrived at after performing numerical experimentations to assess grid independence and ensure accuracy of the results. The accuracy of the aforementioned numerical method was validated by direct comparisons with the numerical results reported earlier by Minkowycz (1976), Yücel (1984), Bassom and Rees (1996), Yih (1999) and EL-Hakiem and Rashad (2007) in the absence of inertial coefficient, constant viscosity, thermal radiation and concentration buoyancy effects. Table I presents the results of these various comparisons.…”

“…It may be remarked that the system of equations ( 10)-( 12) with the boundary conditions ( 15) reduce to the equations of a Darcy free convection flow over an isothermal vertical cylinder saturated porous medium, when R d ,u r ! 1 and Er ¼ 0, this case has been studied by Minkowycz (1976), Yücel (1984) and Bassom and Rees (1996). It may also be remarked that the non-dimensional equations ( 13)-( 14) with the boundary conditions ( 12) when u r !…”

“…Minkowycz (1976) was the first author to present free convection about a vertical cylinder embedded in a porous medium with a variable wall temperature. Yücel (1984) employed an implicit finite-difference method to examine free convection about a vertical cylinder in a porous medium. Bassom and Rees (1996) investigated the variable wall temperature case on free convection from an isothermal vertical cylinder embedded in a saturated porous medium.…”