A Numerical Solution for an Inverse Natural Magneto-Convection Problem

Abstract

An inverse boundary-value problem arising in natural magneto-convection is formulated and investigated numerically for the first time. The physical problem takes place in a square cavity whose boundary contains a left hostile wall on which no boundary condition can be prescribed or measured and a right accessible wall on which two boundary conditions, i.e., boundary temperature and heat flux data, are overspecified. A novel algorithm, based on a regularized dual-reciprocity boundary-element method (DRBEM), is presented. Accurate and stable numerical results at various convective Rayleigh and magnetic Hartmann numbers are reported for retrieving a discontinuous time-varying step heat flux in one example, and a uniform boundary temperature in the second example.

Acknowledgments

N. Alsoy-Akgün would like to thank the hospitality shown by the Department of Applied Mathematics at the University of Leeds, while she was a research visitor there for 6 months in 2012.