Abstract
This paper introduces a procedure for solving a non-linear system of a partial differential equations of the parabolic type with random coefficients. An adaptive method transform the system into a set of ordinary differential equations which is solved after a suitable expansion of the probability density of the unknown random field in terms of orthogonal polynomials.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Adomian (1983), “Stochastic System”, Academic Press, New York.
T. T. Soong (1973), “Random Differential Equations in Science and Engineering”, Academic Press, New York.
L. Carlomusto, A. Pianese and L.M. de Socio (1989), “Heat Transfer for the Two Phases of a Porous Storage Matrix”, Energy Storage Systems, B. Kilkis and S. Kalac Eds., 721–728, Kluwer Ac. Publ. The Netherlands.
I. Bonzani and R. Riganti (to appear), “On the Probability Density of Random Fields in Continuum Mechanics”, in Non-Linear Stochastic Evolution Equations in Mathematical Physics, by N. Bellomo, L.M. de Socio and R. Monaco, World Scientific Publ. Co.
N. Bellomo, L.M. de Socio and R. Monaco (1988), “Random Heat Equation: Solutions by the Stochastic Adaptive Interpolation Method”, Comp. Math. Appl. 16, 759–766.
N. Bellomo and F. Flandoli (to appear), “Stochastic Partial Differential Equations in Continuum Physics: on the Foundations of the Stochastic Interpolation Method for Ito’s type Equations”, Math. Comput. Simul., 2nd special issue on Stochastic Systems Modeling.
L. Carlomusto, L.M. de Socio, G. Gaffuri and A. Pianese (1988), “An Efficient Method for Solving the Boundary Layer Equations”, Proc. of the 5th Int. Conf. on Boundary and Interior Layers-Computational and Asymptotic Methods, BAIL V 20-24 June 1988 Shanghai, China, 103–108.
R. Bellman and G. Adomian (1985), “Partial Differential Equations”, Reidel.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Carlomusto, L., Pianese, A., de Socio, L.M., Kotsiopoulos, P., Calderon, T. (1991). Temperature Distribution in A Porous Slab with Random Thermophysical Characteristic. In: Kakaç, S., Kilkiş, B., Kulacki, F.A., Arinç, F. (eds) Convective Heat and Mass Transfer in Porous Media. NATO ASI Series, vol 196. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3220-6_19
Download citation
DOI: https://doi.org/10.1007/978-94-011-3220-6_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5419-5
Online ISBN: 978-94-011-3220-6
eBook Packages: Springer Book Archive