Combined Streamline Upwind Petrov Galerkin method and segregated finite element algorithm for conjugate heat transfer problems

A combined Streamline Upwind Petrov-Galerkin method (SUPG) and segregated finite element algorithm for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow is presented. The Streamline Upwind Petrov-Galerkin method is used for the analysis of viscous thermal flow in the fluid region, while the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the 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 presented method is to consistently couple heat transfer along the fluid-solid interface. Four test cases, which are the conjugate Couette flow problem in parallel plate channel, the counter-flow in heat exchanger, the conjugate natural convection in a square cavity with a conducting wall, and the conjugate natural convection and conduction from heated cylinder in square cavity, are selected to evaluate efficiency of the presented method.

[1]  Hyomin Jeong,et al.  Study on natural convection in a rectangular enclosure with a heating source , 2004 .

[2]  Myung-whan Bae,et al.  A study on natural convection from two cylinders in a cavity , 2006 .

[3]  Peng Han,et al.  A note on the solution of conjugate heat transfer problems using SIMPLE-like algorithms , 2000 .

[4]  Shaofei Dong,et al.  Conjugate of natural convection and conduction in a complicated enclosure , 2004 .

[5]  R. J. Schnipke,et al.  An equal-order velocity-pressure formulation that does not exhibit spurious pressure modes , 1986 .

[6]  C. D. Toit.  Finite element solution of the Navier-Stokes equations for incompressible flow using a segregated algorithm , 1998 .

[7]  G T Polley,et al.  Heat transfer and fluid flow , 1976 .

[8]  Michael Schäfer,et al.  Numerical simulation of coupled fluid–solid problems , 2001 .

[9]  Dipten Misra,et al.  Finite element analysis of conjugate natural convection in a square enclosure with a conducting vertical wall , 1997 .

[10]  P. Dechaumphai,et al.  Combined adaptive meshing technique and segregated finite element algorithm for analysis of free and forced convection heat transfer , 2004 .

[11]  J. Z. Zhu,et al.  The finite element method , 1977 .

[12]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[13]  Unsteady viscous flow over elliptic cylinders at various thickness with different reynolds numbers , 2005 .

[14]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[15]  Christopher Y. Choi,et al.  A numerical investigation of conjugate heat transfer from a flush heat source on a conductive board in laminar channel flow , 1995 .

[16]  An iterative FDM/BEM method for the conjugate heat transfer problem — parallel plate channel with constant outside temperature , 1995 .

[17]  Matjaž Hriberšek,et al.  Conjugate heat transfer by boundary-domain integral method , 2000 .

[18]  F. White.  Viscous Fluid Flow , 1974 .