Increasing the convergence modulus of an asymptotic expansion: an algorithm for numerical differentiation

1990 ◽  
pp. 387-394
Author(s):  
G. Walz
Keyword(s):  
Asymptotic Expansion ◽  
Numerical Differentiation

Influence of free convection on the diffusion current to a sphere in a laminar forced flow regime

1985 ◽  
Vol 50 (12) ◽  
pp. 2697-2714
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Asymptotic Expansion ◽  
Free Convection ◽  
Boundary Value Problem ◽  
Concentration Gradient ◽  
Empirical Formula ◽  
Convective Diffusion ◽  
Forced Flow ◽  
Diffusion Current ◽  
Wide Range ◽  
Free And Forced Convection

The formulation and solution of a boundary value problem is presented, describing the influence of the free convective diffusion on the forced one to a sphere for a wide range of Rayleigh, Ra, and Peclet, Pe, numbers. It is assumed that both the free and forced convection are oriented in the same sense. Numerical results obtained by the method of finite differences were approximated by an empirical formula based on an analytically derived asymptotic expansion for Pe → ∞. The concentration gradient at the surface and the total diffusion current calculated from the empirical formula agree with those obtained from the numerical solution within the limits of the estimated errors.

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