A second-order time-accurate finite element method for analysis of conjugate heat transfer between solid and unsteady viscous flow

Abstract

A fractional four-step finite element method for analyzing conjugate heat transfer between solid and unsteady viscous flow is presented. The second-order semi-implicit Crank-Nicolson scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. The streamline upwind PetrovGalerkin method (SUPG) is applied for the weighted formulation of the Navier-Stokes equations. The method uses a three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the method presented is to consistently couple heat transfer along the fluid-solid interface. Five test cases, which are the lid-driven cavity flow, natural convection in a square cavity, transient flow over a heated circular cylinder, forced convection cooling across rectangular blocks, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the method presented.

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

“…The governing differential equations are integrated in time using the semi-implicit four-step fractional method [3,9] . The pressure gradient terms are first decoupled from the convection, diffusion, and external force terms.…”

“…Malatip et al [2] developed a combined streamline upwind PetrovGalerkin (SUPG) formulation and the segregate finite element method to analyze the steady conjugate heat transfer problems. Malatip et al [3] also developed a fractional step method to analyze the unsteady conjugate heat transfer problems. Al-Amiri et al [4] used the finite element method to study the steady-state natural convection in a fluid-saturated porous cavity of a conducting vertical wall.…”

“…The objective of this paper is to extend the fractional step finite element method [3] to analyze the fluid-thermal-structural interaction problems. The finite element method is formulated by the equal-order triangular elements for discretizing both the fluid and the solid regions.…”

Stability, convergence and optimization of interface treatments in weak and strong thermal fluid-structure interaction

“…CHT analysis can be performed in a monolithic manner in which the equations are solved simultaneously in a single solver [3] [4] but such an approach is not flexible and cannot be pursued with commercial codes. In contrast, partitioned techniques allow the direct use of a specialized solver for each subdomain, offering significant benefits in terms of efficiency and code reuse.…”