A hybrid finite difference‐finite element method for solving the 3D energy equation in non‐isothermal flow past over a tube

Purpose – This paper aims to develop a hybrid finite difference‐finite element method and apply it to solve the three‐dimensional energy equation in non‐isothermal fluid flow past over a tube.Design/methodology/approach – To implement the hybrid scheme, the tube length is partitioned into uniform segments by choosing grid points along its length, and a plane perpendicular to the tube axis is drawn at each of the points. Subsequently, the Taylor‐Galerkin finite element technique is employed to discretize the energy equation in the planes; while the derivatives along the tube are discretized using the finite difference method.Findings – To demonstrate the validity of the proposed numerical scheme, three‐dimensional test cases have been solved using the method. The variation of L2‐norm of the error with mesh refinement shows that the numerical solution converges to the exact solution with mesh refinement. Moreover, comparison of the computational time duration shows that the proposed method is approximately ...

[1]  Giuseppe Passoni,et al.  Analysis of hybrid algorithms for the Navier–Stokes equations with respect to hydrodynamic stability theory , 2002 .

[2]  J. Cleaver,et al.  Finite element solutions of laminar flow and heat transfer of air in a staggered and an in-line tube bank , 1986 .

[3]  K. N. Seetharamu,et al.  Finite element simulation of transient laminar flow and heat transfer past an in-line tube bank , 1998 .

[4]  A three‐dimensional simulation of a steady approach flow past a circular cylinder at low Reynolds number , 1998 .

[5]  Gautam Biswas,et al.  Numerical Prediction of Flow and Heat Transfer in a Rectangular Channel With a Built-in Circular Tube , 2001, Heat Transfer: Volume 1 — Fundamentals of Heat Transfer.

[6]  P. A. Sackinger,et al.  A Finite Element Method for Free-Surface Flows of Incompressible Fluids in Three Dimensions, Part II: Dynamic Wetting Lines , 2000 .

[7]  P. A. Sackinger,et al.  A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion , 2000 .

[8]  Darrell W. Pepper,et al.  The Intermediate Finite Element Method: Fluid Flow and Heat Transfer Applications , 1999 .

[9]  A. J. Baker,et al.  A 3D incompressible Navier–Stokes velocity–vorticity weak form finite element algorithm , 2002 .

[10]  Brian Launder,et al.  The Numerical Prediction of Viscous Flow and Heat Transfer in Tube Banks , 1978 .

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

[12]  T. Sheu,et al.  ON A COMPACT MIXED-ORDER FINITE ELEMENT FOR SOLVING THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS , 1997 .

[13]  Asif Usmani,et al.  A finite element model for the simulations of mould filling in metal casting and the associated heat transfer , 1992 .

[14]  Scott J. Ormiston,et al.  Analysis of Laminar Forced Convection of Air Crossflow in In-Line Tube Banks with NonSquare Arrangements , 2005 .

[15]  T. Tezduyar,et al.  Numerical Experiments on Downstream Boundary of Flow Past Cylinder , 1991 .

[16]  Farzad Mashayek,et al.  A hybrid finite‐element–volume‐of‐fluid method for simulating free surface flows and interfaces , 1995 .