Ahmed, S. G. An approximate method for oxygen diffusion in a sphere with simultaneous absorption. (English) Zbl 0969.76083 Int. J. Numer. Methods Heat Fluid Flow 9, No. 6, 631-642 (1999). Summary: The oxygen diffusion problem is usually formulated in two stages: first, the steady state stage, and second, the moving boundary stage. In this paper, we consider the solution of the second stage, for which a new semi-analytical method is developed. The method starts by assuming a polynomial representing the profile of oxygen concentration, and then by some mathematical manipulation a system of linear equations is obtained. Numerical solution for the system with a simple scheme relating the moving boundary and its velocity leads to the unknown functions in the assumed polynomial. Cited in 4 Documents MSC: 76R50 Diffusion 76M25 Other numerical methods (fluid mechanics) (MSC2010) Keywords:polynomial representation of oxygen concentration; oxygen diffusion; moving boundary stage; semi-analytical method; system of linear equations PDF BibTeX XML Cite \textit{S. G. Ahmed}, Int. J. Numer. Methods Heat Fluid Flow 9, No. 6, 631--642 (1999; Zbl 0969.76083) Full Text: DOI References: [1] Ahmed, S.G. (1997), ”A new numerical technique developed for polymer processing problems”, the 3rd International Conference on Engineering Mathematics and Physics, Cairo. · Zbl 0902.65070 [2] Ahmed, S.G. and Wrobel, L.C. (1995), ”Numerical solution of solidification problems using integral equations”, in 3rd International Conference of Free and Moving Boundary, Bled. [3] DOI: 10.1137/0712049 · Zbl 0317.65032 [4] DOI: 10.1093/imamat/10.1.19 · Zbl 0247.65064 [5] Crank, J. and Gupta, R.S. (1972b), J. Inst. Maths Applics, Vol. 10, pp. 269-304. [6] DOI: 10.1093/imamat/26.4.411 · Zbl 0468.65063 [7] DOI: 10.1016/0017-9310(89)90227-5 [8] DOI: 10.1016/0307-904X(90)90044-6 · Zbl 0701.65084 [9] DOI: 10.1016/0017-9310(81)90033-8 · Zbl 0462.76095 [10] DOI: 10.1093/imamat/13.3.385 [11] DOI: 10.1093/imamat/22.4.467 · Zbl 0394.65032 [12] Murray, W.D. andLandis, F. (1959), ”Numerical and machine solutions of transient heat conduction problems involving melting and freezing”, J. Heat Transfer, Vol. 81, pp. 106-12. [13] DOI: 10.1002/nme.1620350708 · Zbl 0788.73079 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.