An accurate numerical solution for the transient heating of an evaporating spherical droplet |
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Authors: | SL Mitchell M VynnyckyIG Gusev SS Sazhin |
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Institution: | a Mathematics Application Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland b Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Computing, Engineering and Mathematics, University of Brighton, BN2 4GJ, UK |
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Abstract: | A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is extended for the purposes of solving a moving boundary problem for the transient heating of an evaporating spherical droplet. The Keller box finite-difference scheme is used, in tandem with the so-called boundary immobilization method. An important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space - an issue not previously discussed in relation to this widely-used scheme. In addition, we demonstrate that our solution is in close agreement with the solution obtained using an alternative numerical scheme that employs an analytic solution of the heat conduction equation inside the droplet, for which the droplet radius was assumed to be a piecewise linear function of time. The advantages of the new method are discussed. |
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Keywords: | Droplets Diesel fuel Heating Evaporation Stefan problem Keller box scheme |
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