Keywords: pressure-correction, efficiency, conjugate heat transfer.

In real physical flow, many obstacles are immersed in the fluid region or the fluid region is not regular, handling it successfully or not will definitely influence the truthfulness and reliability of the simulated results because many codes are designed to simulate the whole fluid flow disregard of the immersed obstacles.

With the advance of computing practice, numerous methods have been developed ever since [1,2,3], such as VPP (vacant proportion practice), LSP (large source practice) and VCP (viscosity coefficient practice). This is done by rendering inactive, or "blocking-off" some of the control volumes of the regular grid so that the remaining active control volumes form the desired irregular domain.

In order to analyze the coupling of solid and fluid regions easily and evidently, the conjugate heat transfer problem considered in this paper. It is a closed square cavity with sides of length , within which a conducting body, with sides of length and thermal conductivity ,is centered. The left and right side walks are isothermal at temperatures of and respectively, whereas the bottom and top surfaces are thermally insulated. The gravitational acceleration acts parallel to the isothermal walls. It is assumed here the fluid properties being constant, except for the density in buoyancy term following the Boussinesq approximation. A two-dimensional,steady state,incompressible laminar flow is assumed in thepresent study.

VPP, LSP and VCP are used to deal with the coupling of solid-fluid region, i.e. the conjugate heat transfer. In these three different ways, LSP, VCP and VPP, the energy balance, i.e. continuity of temperature and heat flux, across the interface is automatically well established. Simulations shown that the three methods show similar performance in the iteration process. And here denotes that three methods are consistent if convergence were gained. The global solution procedure facilitates the code programming, making it easier to solve the conjugate heat transfer problem. But, we could discern that the inefficiency of these methods in the computation for the dealing with many independent variables, especially when the segregated method, SIMPLE is applied.

Incompressible fluid flow is characterized by a coupled set of partial differential equations for mass and momentum conservations. It is necessary for numerical solution to deal with the coupling between the velocity and pressure, and the segregated method compared to the coupled method costs less computer storage and CPU time, and gains much popularity. One of the widely used segregated methods is the pressure-based algorithm, the SIMPLE. Because there is no explicit equation for pressure [4,5], the method derives an auxiliary pressure-correction equation from the discretized continuity equation, and thus the role of the pressure-correction equation is to enforce the mass/continuity conservation. The pressure correction procedure is of great importance in the whole solution process, and usually controls and inhibits the convergence and performance of SIMPLE-like algorithms.

The governing equations are discretized using a finite volume method on a staggered Cartesian grid system. A consistent upwind scheme is employed to approximate the convection terms, and second-order central difference is used for the diffusion and source terms. The new way, noted as NLSP (New-LSP), taking into account that the iteration essence of SIMPLE method and directly involving the effects of solid into pressure-correction equation is practiced [6].

The results of the same conjugate heat transfer show that, if the outer loop time were in the same, the iteration accuracy or residuals are smaller for NSLP than that for SLP, numerically, the rate of convergence for NSLP is five times than that of SLP. Additionally, the iteration processes show that more inner loop times of step for pressure correction could reduce the outer loop times greatly for any case. Above all, the new way of coupling solid-fluid region is brief and efficient than other strategies in computational accuracy and efficiency.

1

Tao Wenquan. "Numerical heat transfer". Press of Xi'an Jiaotong University, 1988.

2

Chen X, Han P. "A note on the solution of conjugate heat transfer problems using SIMPLE-like algorithms". Int. J. Heat and Fluid Flow, 21:463-467, 2000. doi:10.1016/S0142-727X(00)00028-X

3

Polat O., Bilgen E. "Conjugate heat transfer in inclined open shallow cavities". Int. J. Heat Mass Transfer, 46:1563-1573, 2003. doi:10.1016/S0017-9310(02)00427-1

4

Desrayaud G., Fichera A. "On natural convection heat transfer in vertical channels with a single surface mounted heat-flux module". Int. J. Heat Mass Transfer, 125(4):734-739, 2003. doi:10.1115/1.1532016

5

Liaqat A., Baytas A.C. "Conjugate natural convection in a square enclosure containing volumetric sources". Int. J. Heat Mass Transfer, 44:3273-3280, 2001. doi:10.1016/S0017-9310(00)00345-8

6

Hortman M., Peric M. "Finite volume multigrid prediction of laminar natural convection:bench mark solutions". International Journal of Numerical Methods in Fluids, 11:189-207, 1990. doi:10.1002/fld.1650110206

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