New methods of the mass and heat transfer theory—II. The methods of asymptotic interpolation and extrapolation

On the onset of natural convection of Bingham liquid in rectangular enclosures

“…In order to obtain an approximation valid for the entire range of aspect ratio we use the interpolation method proposed in [13], i.e., we write down the formula, which fits the asymptotes (7) and (10) smoothly. The simplest expression, which satisfies these conditions reads…”

“…cations. In order to estimate the critical temperature gradient in a cavity with an arbitrary aspect ratio we combine the method of asymptotic interpolation [13] with numerical modelling. The obtained approximation formula is in good agreement with the numerical results over the entire range of the aspect ratio.…”

Enhancement of mass transfer from particles by local shear‐rate and correlations with application to drug dissolution

“…The 1968 and 1971 theoretical studies above established the basis for the future studies on this subject. Using an advanced interpolation method, Polyanin and Dil'man developed the following approximate correlation for shear‐induced enhancement to the Sherwood number at Re S = 0 (Stokes flow) as an interpolation between the Frankel and Acrivos S * → 0 result and the approximate finite S * → ∞ limit of Acrivos: For small Peclet numbers Sh 0 ≈ 1 + 0.26 S *1/2 , close to the Frankel and Acrivos formula at small S * but slightly higher than Acrivos in the limit S * → ∞.…”

Wave resistance of an air-cushion vehicle in unsteady motion over an ice sheet

“…The interpolation formula for the quantity M (κ) in the region 0 κ < ∞ is constructed by asymptotic interpolation [8,9]. According to this method, the quantity M (κ) is sought in the form…”

“…The function Ψ(κ) is specified a priori and depends on several parameters, which are chosen so that the approximate formula (2.16) yields a correct asymptotic representation of specified accuracy for the other limiting case as κ → ∞. In the particular case where only the higher-order term of the asymptotic representation M (κ) is known for κ → ∞, this function is taken to be the function Ψ(κ) = (1 + Cκ l ) m [8,9]. For m = −1, passing to the limit as κ → ∞ and comparing expressions (2.15) and (2.16), we obtain Ψ(κ) = (1 + k 4 κ) −1 and, hence, M (κ) = (1 + k 4 κ) −1 .…”