Analytically-integrated radial integration BEM for solving three-dimensional transient heat conduction problems

A triple reciprocity method in Laplace transform boundary element method for three-dimensional transient heat conduction problems

IG-DRBEM of three-dimensional transient heat conduction problems

A new general analytical PBEM for solving three-dimensional transient nonlinear heat conduction problems with spatially-varying heat generation

Three-dimensional transient heat conduction analysis by boundary knot method

Shape reconstruction in transient heat conduction problems based on radial integration boundary element method

In this paper, we consider a three-dimensional transient inverse heat conduction problem arising in pool boiling experiments, i.e., the reconstruction of the surface heat flux from pointwise temperature observations inside a heater. We show that the inverse problem is ill-posed and utilize Tikhonov regularization and conjugate gradient methods together with a discrepancy stopping rule for a stable solution. We investigate the proper choice of regularization terms, which not only affects stability of the reconstructions but also greatly influences the quality of reconstructions in the case of limited observations. For the numerical solution of the governing partial differential equation, a space-time finite element method is used. This allows us to compute exact gradients for the discretized Tikhonov functional, and enables the use of conjugate gradient methods for the solution of the regularized inverse problem. We discuss further aspects of an efficient implementation, including a multilevel optimization strategy, together with an implementable stopping criterion. Finally, the proposed algorithms are applied to the reconstruction of local boiling heat fluxes from experimental data.

The precise integration method for semi-discretized equation in the dual reciprocity method to solve three-dimensional transient heat conduction problems

RI-IGABEM based on PIM in transient heat conduction problems of FGMs

In this paper, the radial integration boundary element method is presented to analyze dynamic fracture mechanics problems of functionally gradient materials. The fundamental solutions for homogeneous, isotropic and linear elastic solids are used to derive the boundary-domain integration equations by weighted residual method and this approach leads to domain integrals appearing in the resulting integral equations. The radial integral method (RIM) is employed to transform the domain integrals into boundary integrals and thus the boundary-only integral equations formulation can be achieved. The Houbolt method is utilized to solve the resulted system of time-dependent algebraic equations from the discretization. Numerical results are given to demonstrate the efficiency and the accuracy of the present method.

The Hot Optimal Transportation Meshfree (HOTM) method for materials under extreme dynamic thermomechanical conditions

We present a fast first order explicit time integration scheme for solving parabolic problems in mechanics via standard numerical methods in space using irregular grids, such as unstructured finite element meshes, or grids containing elements or cells of very different sizes. The new scheme extends one of the explicit FIC-Time (EFT) integration methods derived by the authors in [23] that allow considerable larger time steps than the forward-Euler (FE) scheme. The new EFT scheme overcomes the limitations in the time step size of explicit time integration schemes for irregular grids containing large and small elements. A variable time step is used for eliminating the oscillations near Dirichlet boundaries when large time steps are used. The advantages of the new EFT scheme versus the FE scheme are shown in one-, two- and three-dimensional transient heat conduction problems using irregular finite element grids.

A tensor decomposition-based reduced-order BMC-ST method for analyzing three-dimensional transient heat conduction problems

Generalized Solution for Three-Dimensional Transient Heat Conduction Problems with Partial Heating

An inverse heat conduction method was used to determine the energy balance at the cutting zone in edge trimming of carbon fiber-reinforced polymer composites. Three-dimensional transient heat conduction problem was modeled and solved independently in Abaqus for both the workpiece and cutting tool. Temperatures at specific locations were also measured during cutting using thermocouples and infrared thermography. Minimizing the difference between measured and calculated temperatures allowed the estimation of the heat flux applied in each problem. The total electric power consumed in machining was also measured. The heat partition was determined from the measured and calculated energies to be 0.07, 0.56 and 0.37 for the workpiece, tool and chips, respectively. The temperature distribution in the workpiece indicated that heat penetration is shallow due to poor thermal conductivity. It was also found that the extent of estimated machining thermal damage in the workpiece is within 0.35 mm below the machined surface.

Inverse identification of boundary conditions in a scramjet combustor with a regenerative cooling system