Similarity analysis for natural convection from a vertical plate with distributed wall concentration

Abstract

Abstract. Steady laminar natural convection flow over a semi-infinite vertical plate is examined in this paper. It is assumed that the concentration of a species along the plate follows some algebraic law with respect to chemical reaction. Similarity solutions may then be obtained for different orders of reaction. The fundamental parameters of this problem are the Schmidt number, Sc, and reaction order, n. Numerical results, based on the fourth order Runge-Kutta method, for Schmidt number ranging from 0.0 to 100.0 and reaction order from 0.0 to 1.5 are presented. When chemical reaction occurs, diffusion and velocity domains are seen to expand out from the plate. For large values of n, one may expect a smaller diffusion layer which, at fixed Schmidt number, is associated with increased velocity and reduced convection-layer.

Effects of Chemical Reaction and Double Dispersion on Non-Darcy Free Convection Heat and Mass Transfer

“…The wall is maintained at constant temperature and concentration, T w and C w , respectively. The governing equations for the steady state scenario [as given by Mulolani and Rahman (2000) and El-Amin (2004)] may be presented as: Mass:…”

“…They stated that the presence of pure air or water is impossible in nature and that some foreign mass may be present either naturally or mixed with air or water. Mulolani and Rahman (2000) studied laminar natural convection flow over a semi-infinite vertical plate under the assumption that the concentration of species along the plate follows some algebraic law with respect to chemical reaction. They obtained similarity solutions for different order of reaction rates and Schmidt number Sc.…”

Solute Transport With Chemical Reaction in Singleand Multi-Phase Flow in Porous Media

“…The wall is maintained at constant temperature and concentration, T w and C w , respectively. The governing equations for the steady state scenario [as given by (Mulolani & Rahman, 2000;El-Amin, 2004) may be presented as: Momentum:…”

“…With analogy to (Mulolani & Rahman, 2000;Aissa & Mohammadein, 2006), we define Gc to be the modified Grashof number, Re x is local Reynolds number, Sc and λ are Schmidt number and non-dimensional chemical reaction parameter defined as Gc = β * * g(C w − C ∞ ) 2 x 3 /ν 2 , Re x = u r x/ν, Sc = ν/D and λ = K 0 αd(C w − C ∞ ) n−3 /Kgβ * * , where the diffusivity ratio Le (Lewis number) is the ratio of Schmidt number and Prandtl number, and u r = gβ * d(T w − T ∞ ) is the reference velocity as defined by (Elbashbeshy, 1997). Eq.…”

Boundary-Layer Flow in a Porous Medium of a Nanofluid Past a Vertical Cone

“…The natural convection on vertical surfaces in porous media has been studied used Darcy's law by a number of authors [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Boundary layer analysis of natural convection over a cone has been investigated by Yih [21][22][23][24].…”