FRACTIONAL HEAT CONDUCTION WITH FINITE WAVE SPEED IN A THERMO-VISCO-ELASTIC SPHERICAL SHELL

Authors

  • MRIDULA KANORIA DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY OF CALCUTTA
  • ABHIK SUR DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY OF CALCUTTA

Keywords:

GENERALIZED THERMO-ELASTICITY, THREE-PHASE-LAG MODEL, FRACTIONAL ORDER HEAT EQUATION, EIGEN VALUE APPROACH, VECTOR-MATRIX DIFFEREN-TIAL EQUATION, STEP INPUT TEMPERATURES.

Abstract

THIS PROBLEM DEALS WITH THE THERMO-VISCO-ELASTIC INTERACTION DUE TO STEP INPUT OF TEMPERATURE ON THE STRESS FREE BOUNDARIES OF A HOMOGENEOUS VISCO-ELASTIC ISOTROPIC SPHERICAL SHELL IN THE CONTEXT OF A NEW CONSIDERATION OF HEAT CONDUCTION WITH FRACTIONAL ORDER GENERALIZED THERMOELASTICITY. USING THE LAPLACE TRANSFORMATION, THE FUNDAMENTAL EQUATIONS HAVE BEEN EXPRESSED IN THE FORM OF A VECTOR-MATRIX DIFFERENTIAL EQUATION WHICH IS THEN SOLVED BY EIGEN VALUE APPROACH. THE INVERSION OF THE TRANSFORMED SOLUTION IS CARRIED OUT BY APPLYING A METHOD OF BELLMAN ET AL (1966). NUMERICAL ESTIMATES FOR THERMOPHYSICAL QUANTITIES ARE OBTAINED FOR COPPER LIKE MATERIAL FOR WEAK, NORMAL AND STRONG CONDUCTIVITY AND HAVE BEEN DEPICTED GRAPHICALLY TO ESTIMATE THE EFFECTS OF THE FRACTIONAL ORDER PARAMETER. COMPARISONS OF THE RESULTS FOR DIFFERENT THEORIES (TEWED (GN-III), THREE-PHASE-LAG MODEL) HAVE ALSO BEEN PRESENTED.

Author Biographies

MRIDULA KANORIA, DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY OF CALCUTTA

ASSOCIATE PROFESSOR, DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY OF CALCUTTA

ABHIK SUR, DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY OF CALCUTTA

DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY OF CALCUTTA, RESEARCH SCHOLAR.

Downloads

Published

2014-02-13

Issue

Vol. 11 No. 7 (2014)

Section

Articles

License

Authors who publish with this journal agree to the following terms:

 

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).