A high order control volume finite element procedure for transient heat conduction analysis of functionally graded materials

An Unstructured Finite-Volume Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

“…When k ¼ 0 m À1 , time histories of temperature at three different positions are shown in Figure 10a. These results are in excellent agreement with analytical results in [23]. It is observed that the temperature field approaches steady state after t ¼ 15 s. Temperature curves along the radial direction with different values of k at t ¼ 20 s are shown in Figure 10b.…”

“…An example of a thick-wall functionally graded cylinder with infinite length [23] is studied. Due to the symmetry of the geometry and boundary conditions, only a quarter of the annulus cross section is considered, and the time step Dt ¼ 0.02 s. The Figure 9.…”

“…Yu et al [22] presented a statistical second-order twoscale method to predict heat conduction performances of FGMs with inconsistent random distributions. Charoensuk and Vessakosol [23] proposed a high-order control-volume finite-element procedure for two-dimensional transient heat conduction in FGMs based on triangular mesh.…”

“…One direction is toward high-order methods based on the triangular grid. Charoensuk and Vessakosol [23] applied the CVFEM based on a six-node triangular grid to transient heat conduction analysis. The other approach is to introduce a quadrilateral grid [25] and develop a corresponding high-order method.…”

“…Therefore, as soon as it was put forward, researchers focused attention on its application NOMENCLATURE a ij , b ij , c ij , d ij coefficients in the partial derivative of the shape function c specific heat (e x , e y ) unit normal vector outward to surface h heat transfer coefficient k, (k x , k y ) thermal conductivity L length of the line n, n 3 and development. The CVFEM and its modified forms have been demonstrated to be effective numerical approaches [23][24][25][26][27]. For 2-D problems, the CVFEM at first employed only constant strain elements viz., a three-node triangular grid.…”