Journal ArticleDOI
Perturbation solution for spherical and cylindrical solidification by combined convective and radiative cooling
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TLDR
In this paper, the problem of inward solidification of a liquid in cylindrical and spherical geometries is considered and the results are compared with a numerical solution, obtained by using the enthalpy method, for various values of the Stefan number.About:
This article is published in International Journal of Heat and Fluid Flow.The article was published on 1990-06-01. It has received 17 citations till now. The article focuses on the topics: Stefan number & Radiative transfer.read more
Citations
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Journal ArticleDOI
Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body
TL;DR: In this article, an analytic approach based on the homotopy analysis method is proposed to solve a nonlinear model of combined convective and radiative cooling of a spherical body, and an explicit series solution is given, which agrees well with the exact or numerical solutions.
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A note on the solution of singular boundary value problems arising in engineering and applied sciences: Use of OHAM
TL;DR: The effectiveness of the OHAM has been evaluated by successfully solving two SBVPs given in recent literature as well a SBVP related to the reaction–diffusion process in a spherical catalyst, showing an excellent agreement when compared with the numerical/exact/available solutions.
Journal ArticleDOI
Freezing of a supercooled spherical droplet with mixed boundary conditions
TL;DR: In this article, the freezing of a supercooled droplet is modelled by a mixed boundary condition on the outer surface of the droplet, and a novel asymptotic solution is developed for a small Stefan number and an arbitrary Biot number.
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Simplified analysis of heat and mass transfer model in droplet evaporation process
TL;DR: In this article, a simplified model on single droplet evaporation into a stagnant gas space is established based on molecule diffusion on the droplet surface subjected to boundary conditions of constant temperature and conduction heat transferring on the external surface of the spherical droplet.
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Numerical prediction of phase-change heat conduction of injection-molded high density polyethylene thick-walled parts via the enthalpy transforming model with mushy zone
TL;DR: In this article, the enthalpy transforming scheme proposed by Cao and Faghri, which could handle the Stefan problems for generalized multidimensional phase-change structures, is applied coupled with the control-volume/finite-difference techniques.
References
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Book
Perturbation Methods in Applied Mathematics
TL;DR: In this paper, limit process expansions applied to Ordinary Differential Equations (ODE) are applied to partial differential equations (PDE) in the context of Fluid Mechanics.
Book
Free and moving boundary problems
TL;DR: In this paper, a front-tracking method is used to solve moving boundary problems and an analytical solution of seepage problems is proposed. But this method is not suitable for solving free boundary problems.
Journal ArticleDOI
Implicit Finite—difference Solutions of the Enthalpy Formulation of Stefan Problems
Journal ArticleDOI
Inward spherical solidification—solution by the method of strained coordinates
R.I. Pedroso,G. A. Domoto +1 more
TL;DR: In this paper, the method of strained coordinates is applied to obtain a perturbation solution for spherical solidification of a saturated liquid and the solution is uniformly valid and can be applied as the freezing front approaches the center where the regular-perturbation solutions are found to diverge.
Journal ArticleDOI
Mathematical analysis of bubble dissolution
J. L. Duda,James S. Vrentas +1 more
TL;DR: In this article, a perturbation series solution is derived for isothermal bubble dissolution and bubble growth from an initially finite size, which is superior in several aspects to the quasi-stationary and quasi-steady state approximations derived previously.