A dual-reciprocity boundary element approach for axisymmetric nonlinear time-dependent heat conduction in a nonhomogeneous solid

Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

“…Juan et al [7] have proposed an alternative resolution for the heat transfer problem involved in direct-chill casting processes employing the EFG method. A dual-reciprocity boundary element method was used also in [30]. This numerical method was proposed to solve a unsteady axisymmetric heat conduction problem involving a non-homogeneous solid with temperature-dependent properties.…”

“…To demonstrate the efficiency and accuracy of this algorithm, two examples are discussed. In the first example, we compare the results obtained by the proposed approach, highorder homotopic continuation with the radial point interpolation method (HOHC-RPIM), with those calculated by the Newton-Raphson method [30,31]. It should be noted that the Newton-Raphson method is coupled with the RPIM for the first time.…”

The Effect of Rotation and Inhomogeneity on the Transient Magneto-Thermoviscoelastic Stresses in an Anisotropic Solid

“…This method was originally introduced by Brebbia and Nardini [18]. Interested readers can find more details in the following references: Ang et al [19], Divo and Kassab [20], Fahmy [21], Gaul et al [22], Partridge et al [23], Wrobel and Brebbia [24], Yun and Ang [25] and Zhang and Zhu [26].…”

“…and(25) in Eq. (22), we obtain the representation formula :f {q'T-rq)dC-\ {cpt -pX)rdR (26) Jc JR Let r* be the particular solution for the governing Eq.…”

A complex variable boundary element method for axisymmetric heat conduction in a nonhomogeneous solid

“…Guided by the analysis in [1] and [10], we use suitable interpolating functions to approximate certain terms in the governing partial differential equation, in order to reduce the problem to constructing an appropriate analytic complex function. The complex variable boundary element procedure presented here should provide a useful and interesting alternative to the axisymmetric boundary integral method in Brebbia et al [6] and Yun and Ang [16], which requires the computation of a rather complicated fundamental solution that is expressed in terms of complete elliptic integrals of the first and second kind. To assess the validity and the accuracy of the numerical procedure presented here, it is applied to solve some specific cases of the axisymmetric heat conduction problem.…”