Find out how to access previewonly content
Moving boundaries due to distributed sources in a slab
 S. C. Gupta
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Analytical and numerical solutions have been obtained for some moving boundary problems associated with Joule heating and distributed absorption of oxygen in tissues. Several questions have been examined which are concerned with the solutions of classical formulation of sharp melting front model and the classical enthalpy formulation in which solid, liquid and mushy regions are present. Thermal properties and heat sources in the solid and liquid regions have been taken as unequal. The shorttime analytical solutions presented here provide useful information. An effective numerical scheme has been proposed which is accurate and simple.
 Crowley, A. B., Ockendon, J. R. (1977) A Stefan problem with a nonmonotone boundary. J. Inst. Maths. Applics. 20: pp. 269281
 Atthey, D. R. (1974) A finite difference scheme for melting problems. J. Inst. Maths. Applics. 13: pp. 353366
 Crank, J., Gupta, R. S. (1972) A moving boundary problem arising from the diffusion of oxygen in absorbing tissue. J. Inst. Maths. Applics. 10: pp. 1933
 Lacey, A. A., Shillor, M. (1983) The existence and stability of regions with superheating in the classical twophase onedimensional Stefan problem with heat sources. IMA Journal of Applied Mathematics 30: pp. 215230
 Primicerio, M. Mushy region in phase change problems. In: Gorenflo, , Hoffmann, eds. (1982) Applied NonLinear Functional Analysis. Lang, Frankfurt (Main), pp. 251269
 Atthey, D. R., D.Phil. thesis, University of Oxford (1972).
 Lacey, A. A., Tayler, A. B. (1983) A mushy region in Stefan problem. IMA Journal of Applied Mathematics 30: pp. 303313
 Ughi, M. (1984) A melting problem with a mushy region: Qualitative properties. IMA Journal of Applied Mathematics 33: pp. 135152
 Rogers, J. C. W. (1977) A free boundary problem as diffusion with nonlinear absorption. J. Inst. Maths. Applics. 20: pp. 261268
 Hansen, E., Hougaard, P. (1974) On a moving boundary problem from biomechanics. J. Inst. Maths. Applics. 13: pp. 385398
 Crank, J., Gupta, R. S. (1972) A method for solving moving boundary problems in heat flow using cubic splines or polynomials. J. Inst. Maths. Applics. 10: pp. 296304
 Dahmardah, H. O., Mayers, D. F. (1983) A Fourierseries solution of the CrankGupta equation. IMA Journal of Numerical Analysis 3: pp. 8185
 Carslaw, H. S., Jaeger, J. C. (1959) Conduction of Heat in Solids. Clarendon Press, Oxford
 Gupta, S. C. (1985) Axisymmetric solidification in a long cylindrical mold. Applied Scientific Research 42: pp. 229244
 Rubinstein, L. I., Crystallization of a binary alloy. In:The Stefan Problem. American Mathematical Society (1967) pp. 52–60.
 Fasano, A., Primicerio, M. (1977) General free boundary problems for the heat equation. J. Math. Anal. Appl. I 57: pp. 694723
 Murray, W. D., Landis, F. (1959) Numerical and machine solutions of transient heat conduction problems involving melting or freezing. ASME J. Heat Transfer 81: pp. 106112
 Gupta, S. C. (1990) Numerical and analytical solutions of one dimensional freezing of dilute binary alloys with coupled heat and mass transfer. Int. J. Heat Mass Transfer 33: pp. 393602
 Title
 Moving boundaries due to distributed sources in a slab
 Journal

Applied Scientific Research
Volume 54, Issue 2 , pp 137160
 Cover Date
 19950301
 DOI
 10.1007/BF00864370
 Print ISSN
 00036994
 Online ISSN
 15731987
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 moving boundary
 mushy region
 weak enthalpy formulation
 oxygendiffusion model
 Industry Sectors
 Authors

 S. C. Gupta ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India