Finite Difference Schemes for the Determination of Thermal Coefficient and Analysis of its Variation with Time

M. Usman, M.O. Ahmed, Sumera. K, Mumtaz. A, M. Rafiq


In this paper, numerical solution of thermal conduction problem has been analyzed. Three Finitedifference schemes have been derived for the determination of thermal coefficient and for temperaturedistribution at different time levels. Moreover, by using derived schemes a test problem has beensolved and computed results have been compared with exact solutions for different time level, itreveals accuracy of these schemes as well as the physical behavior of the test problem. The generalpattern which has been observed is that with passage of time temperature distribution increases.

Full Text:



J.R.Cannon, 1963. Determination of an unknown coefficient in parabolic differential equation, Duke Math J 30, 313-323.

J.R.Cannon and H.M.Yin, 1990. Numerial solution of some parabolic inverse problems, Numer Methods of Partial Differential equation 2,177-191.

Mehdi Deghan, 2005. Identification of a Time –dependent Coefficient in a partial differential equation subject to an Extra Measurment, Numer Methods Partial Differential Eq 21, 611-622.

M.A.Rana, Rashid Qamar, A.A. Farooq, A.M. Siddiqui. 2011. Finite-difference analysis of natural convection flow of viscous fluid in a porous channel with constant heat source, Applied Mathematics Letters 24, 2087-2092.

A.G. Fatuallyev, 2002. Numerical procedure for the determination of an unknown coefficient in Parabolic equation, Comput Phys Commum 144(1),29-33.

P.B.Patial and U.P.Verma. 2009. “Numerical Computational Method” Revised Edition, Narsoa.

R. L. Burden and J. D. Faires, 2011. “Numerical Analysis” 8th edition, PWS, Publishing company , Bostan.

M.K.Jain, 1991. “Numerical Solution of Differential Equations” 2nd edition, Willy Estern Limited.

Copyright (c) 2016 M. Usman

Powered By KICS