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- W2034757662 abstract "This paper presents a theoretical investigation on the solidification of a low Peclet number fluid flow in the thermal entrance region of a round pipe. The velocity is assumed laminar and fully developed throughout the pipe and the fluid temperature is taken to be uniform at X = −∞. The pipe wall is adiabatic at X ≤ 0 and is cooled convectively at X ≥ 0. The exact solution in the liquid and solid phase are obtained by using the method of separation of variables and constructing two sets of orthonormal functions from the nonorthogonal eigenfunctious at X = ± 0. The solutions including temperature distributions, liquid-solid interfaces and Nusselt numbers for the parameters, Bi = 20, 4, 0.4, 0.04, Pe = 1, 3, 5, 10, 20, 30, ∞ and the superheat ratios, ξ = (1 − θf)/θf, θf= 0.1, 0.2, …, 0.9 are presented in this paper. The length of ice-free zone xf corresponding to Pe = ∞ are in excellent agreement with the existing solution. On présente une étude théorique de la solidification d'un écoulement de fluide à faible nombre de Péclet, dans la zone d'échange thermique sur un tube a section circulaire. On suppose que la vitesse est laminaire, que l'écoulement est totalement développé d'un bout à l'autre du tube et que la température du fluide est uniforme à X = − ∞. La paroi du tuyau est adiabatique à X ≤ 0 et elle est refroidie par convection à X ≥ 0. On obtient les solutions exactes, dans les phases liquide et solide, en employant la méthode de séparation des variables et en construisant deux séries de fonctions orthonormales à partir des fonctions propres non orthogonales à X = ± 0. On présente les solutions, incluant les distributions des températures, les aires d'interfaces entre liquide et solide et les nombres de Nusselt, pour les paramètres Bi = 20, 4, 0.4, 0.04, et Pe = 1, 3, 5, 10, 20, 30, ∞, ainsi que pour les rapports de surchauffe ξ = (1 − θf)/θf, θf, = 0.1, 0.2 …, 0.9. La longueur Xf de la zone exempte de glace, qui correspond à Pe = ∞, concorde très bien avec la solution existante." @default.
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- W2034757662 date "1980-04-01" @default.
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- W2034757662 title "Solidification of a low peclet number fluid flow in a round pipe with the boundary condition of the third kind" @default.
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- W2034757662 doi "https://doi.org/10.1002/cjce.5450580207" @default.
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