Implementation of DRBEM for the determination of the heat flux in an inverse problem

Abstract

A numerical investigation of inverse unsteady natural convection flow in a square cavity filled with C u − water nanofluid is performed. In the direct problem, the enclosure is bounded by one isothermally heated vertical wall at temperature Tm and by three adiabatic walls. In the inverse problem, the enclosure is bounded by right hostile wall on which no boundary condition can be prescribed or measured and by left accessible wall on which both the boundary temperature and heat flux data are overspecified. The dual reciprocity boundary element method (DRBEM) with the fundamental solutions of Laplace and modified Helmholtz equations is used for the solutions of direct and inverse problems. Inhomogeneities are approximated with radial basis functions. Computations are performed for several values of Rayleigh number (Ra), solid volume fraction (φ) and percentage of noise (ρ), and accurate and stable results are given for three forms of heat flux namely, steady heat flux (q=q(y)), time dependent uniform heat flux (q=q(t)) and non-uniform time dependent heat flux (q=q(y,t)).