Author
Dhirendra Kumar
Bio: Dhirendra Kumar is an academic researcher. The author has contributed to research in topics: Mechanics & Boundary value problem. The author has an hindex of 4, co-authored 6 publications receiving 175 citations.
Papers
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TL;DR: In this paper, the variable time step method introduced by Douglas and Gallie for solving a one-dimensional Stefan problem with constant heat flux at the fixed end is extended to cover a more general boundary condition.
84 citations
TL;DR: In this article, a modified version of the variable time step method is proposed and the results computed from various methods clearly show the superiority of the present method over the others. And the numerical results are also compared with those obtained from the integral method and are found to be in very good agreement.
61 citations
TL;DR: In this paper, the authors proposed a variable time step method for the diffusion of oxygen in absorbing tissue, which requires a smaller number of time steps than do the other methods, and the numerical results compare extremely well with those due to earlier authors.
22 citations
9 citations
TL;DR: In this paper , the authors investigated the MHD flow of Williamson fluid through a non-Darcy porous medium with micro-rotation, and the governing equations were first converted into a coupled system of ODEs with initial and boundary conditions.
8 citations
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TL;DR: The major methods of mathematical modelling of solidification and melting problems are reviewed in this article, where basic guidelines are outlined to choose a correct mathematical formulation for solving solidification or melting problems.
Abstract: The major methods of mathematical modelling of solidification and melting problems are reviewed in this paper. Different analytical methods, nowadays still used as standard references to validate numerical models, are presented. Various mathematical formulations to numerically solve solidification and melting problems are categorized. Relative merits and disadvantages of each formulation are analysed. Recent advances in modelling solidification and melting problems associated with convective motion of liquid phase are discussed. Based on this comprehensive survey, basic guidelines are outlined to choose a correct mathematical formulation for solving solidification and melting problems.
427 citations
TL;DR: The use of the Monte Carlo method in radiative heat transfer is reviewed in this paper, where surface-surface, enclosure, and participating media problems are considered, as well as the effects of using parallel algorithms.
Abstract: The use of the Monte Carlo method in radiative heat transfer is reviewed. The review covers surface-surface, enclosure, and participating media problems. Discussio. is included of research on the fundamentals of the method and on applications to surface-surface interchange in enclosures, exchange between surfaces with roughness characteristics, determination of configuration factors, inverse design, transfer through packed beds and fiber layers, participating media, scattering, hybrid methods, spectrally dependent problems including media with line structure, effects of using parallel algorithms, practical applications, and extensions of the method. Conclusions are presented on needed future work and the place of Monte Carlo techniques in radiative heat transfer computations
331 citations
TL;DR: Theoretical treatments of the dynamics of a single bubble in a pressure field have been undertaken for many decades as mentioned in this paper, and there now exists a solid theoretical basis for the dynamic dynamics of the single bubble.
249 citations
TL;DR: Tarzia et al. as discussed by the authors presented a bibliografía on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems, which contains 5869 titles referring to 588 scientific journals, 122 books, 88 symposia, 30 collections, 59 thesis and 247 technical reports.
Abstract: We present a bibliography on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems. It contains 5869 titles referring to 588 scientific Journals, 122 books, 88 symposia (having at least 3 contributions on the subject), 30 collections, 59 thesis and 247 technical reports. It tries to give a comprehensive account of the western existing mathematicalphysical-engineering literature on this research field. RESUMEN Se presenta una bibliografía sobre problemas de frontera móvil y libre para la ecuación del calor-difusión, en particular sobre el problema de Stefan y problemas relacionados. Contiene 5869 títulos distribuidos en 588 revistas científicas, 122 libros, 88 simposios (teniendo al menos 3 contribuciones en el tema), 30 colecciones, 59 tesis y 247 informes técnicos o prepublicaciones. Se da un informe amplio de la bibliografía matemática, física y de las ingenierías existente en occidente sobre este tema de investigación. Primary Mathematics Subject Classification Number (*): 35R35, 80A22 Secondary Mathematics Subject Classification Number (*): 35B40, 35C05, 35C15, 35Kxx, 35R30, 46N20, 49J20, 65Mxx, 65Nxx, 76R50, 76S05, 76T05, 93C20. (*) Following the 1991 Mathematics Subject Classification compiled by Mathematical Reviews and Zentralblatt fur Mathematik. Primary key words: Enthalpy formulation or method, Filtration, Free boundary problems, Freezing, Melting, Moving boundary problems, Mushy region, Phase-change problem, Solidification, Stefan problem. Secondary key words: Continuous mechanics, Diffusion process, Functional analysis, Heat conduction, Mathematical methods, Numerical methods, Partial differential equations, Variational inequalities, Weak solutions. Palabras claves primarias: Método o formulación en entalpía, Filtración, Problemas de frontera libre, Congelación, Derretimiento, Problemas de frontera móvil, Región pastosa, Problema de cambio de fase, Solidificación, Problema de Stefan. Palabras claves secundarias: Mecánica del continuo, Procesos difusivos, Análisis funcional, Conducción del calor, Métodos matemáticos, Métodos numéricos, Ecuaciones diferenciales a derivadas parciales, Inecuaciones variacionales, Soluciones débiles. El manuscrito fue recibido y aceptado en octubre de 1999. D.A. Tarzia, A bibliography on FBP. The Stefan problem, MAT Serie A, # 2 (2000). 3
224 citations
TL;DR: In this article, a mathematical model for exergy loss analysis of a freeze-drying process was established to evaluate the exergy losses in individual operations and the distribution of exery losses in a freeze dryer.
125 citations