Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

Abstract

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin (SUPG) method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid are performed by the Galerkin method. The second-order semiimplicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are linearized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

Design and applications of drilling trajectory measurement instrumentation in an ultra-deep borehole based on a fiber-optic gyro

“…The thermal error compensation experiments usually employ a network structure of three to four layers (Meng et al, 2009). During these experiments, we found that both fullscale design methods and orthogonal design methods were time-consuming and low in efficiency for FOG error compensation.…”

The Sardar sub-equation technique for obtaining some optical solitons of cubic nonlinear Schrödinger equation involving beta derivatives with Kerr law nonlinearity

“…and implemented in the literature to solve nonlinear fractional differential equations (NFDES) and obtain analytical traveling wave solutions, for example, the fractional differential transform method [7] , the fractional modified Kudryashov method [8] , the generalized differential transform method [9] , the fractional finite difference method [10][11][12] , the fractional finite element method [13][14][15] , the fractional boundary element method [16][17][18] , the fractional radial basis function method [19][20][21] , the fractional homotopy analysis method [22,23] , the fractional homotopy perturbation transform method [24,25] .…”