1. MULTLAB FEM-UNICAMP UNICAMP LID DRIVEN CAVITY FLOW The lid-driven cavity problem has long been used a test or validation case for new codes or new solution methods. The problem geometry is simple and two- dimensional, and the boundary conditions are also simple. The standard case is fluid contained in a square domain with Dirichlet boundary conditions on all sides, with three stationary sides and one moving side (with velocity tangent to the side)

2. MULTLAB FEM-UNICAMP UNICAMP Lid Driven x Shear Driven Similar simulations have also been done at various aspect ratios, and it can also be done with the lid replaced with a moving fluid. This problem is a somewhat different situation, and is usually referred to as the shear-driven cavity. You may see the two names (lid-driven and shear-driven) used interchangeably in spite of the fact that they are distinct (and different) problems. See link on Numerical Experiments on Cavity Flows.Numerical Experiments on Cavity Flows Re = 400

3. MULTLAB FEM-UNICAMP UNICAMP Benchmark Solutions This problem has been solved as both a laminar flow and a turbulent flow, and many different numerical techniques have been used to compute these solutions. Since this case has been solved many times, there is a great deal of data to compare with. –Ghia, Ghia, and Shin (1982), "High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method", Journal of Computational Physics, Vol. 48, pp. 387-411. – Paramarne & Sharma, 2008, “Consistent Implementation and Comparison of FOU, CD, SOU, and QUICK Convection Schemes on Square, Skew, Trapezoidal, and Triangular Lid-Driven Cavity Flow”, Num Heat Transf. J, Part B Fundamentals,54:1,84 - 102Paramarne & Sharma This problem is a nice one for testing for several reasons: 1.there is a great deal of literature to compare with. 2.the (laminar) solution is steady. 3.the boundary conditions are simple and compatible with most numerical approaches

4. MULTLAB FEM-UNICAMP UNICAMP Input data for Re = 100 NX = NY = 40 XULAST=YVLAST=1m ULID = 0.0634m/s FLUID: GLYCERIN (65) Re = V.L/enul = 100 Use relax U1=V1=20 Ref Pressure Moving Lid Stationay Lids

5. MULTLAB FEM-UNICAMP UNICAMP U velocity contours X Y q1

6. MULTLAB FEM-UNICAMP UNICAMP XY PLOT FOR X/L = 0.5

7. MULTLAB FEM-UNICAMP UNICAMP Try to assembly a Triangular Cavity Use the same setting of the square cavity. Add two blockages with ‘wedge’ like shape

8. MULTLAB FEM-UNICAMP UNICAMP Conjugate Heat Transfer Ability to compute conduction of heat through solids, coupled with convective heat transfer in fluid. Example: consider the cooling of a fin when exposed at an air flow. Notice the air stream removes heat from the fin through convection while heat is conducted from the fin base. Convecção Temp. Ambiente ( T  ) Condução Fin Base T 0 Convection Environmental ( T  ) Conduction

9. MULTLAB FEM-UNICAMP UNICAMP Conjugate Heat Transfer - Example Consider a micro-chip, mounted on top a circuit board, dissipating 0,1 W on a air flow confined in a 2D channel as represented on the figure. You are asked to assembly this problem using phoenics and explore the Conjugate Heat Transfer features Air (0) Win = 0.5 m/s Tin = 20 o C Chip, P = 0,1 W Board zone– conduction only Air zone: convection only 100 mm h=4 mm h=31 mm h=6 mm

10. MULTLAB FEM-UNICAMP UNICAMP MODELS Models - Activate Velocity and Energy. Use LVEL model to turbulence Properties - choose air (0) Numeric – 300 sweeps, RELAX U1 = 100, V1 = 100 Output – Monitor IX = 1 e IZ = 3

11. MULTLAB FEM-UNICAMP UNICAMP LIST OF OBJECTCS OBJ XYZTYPEMATERIALATTRIBUTES EWALL size00.0010.1 plate h = 10 W/m2oC place0.03500 WWALL size00.0010.1 plate h = 10 W/m2oC place000 CHIP size0.0060.0010.01 blocksolid (111)Power = 0.1 W place0.00400.03 BOARD size0.0040.0010.1 blocksolid (101) place000 INLET size0.0350.0010 inlet W = 0,5 &T = 20C place000 OUT size0.0350.0010 outlet P = Patm place000.1

12. MULTLAB FEM-UNICAMP UNICAMP GRID PROPERTIES REGION X DIRECTIONZ DIRECTION CELLSPWRCELLSPWR 14-1,261 291,221 3152,5121

13. MULTLAB FEM-UNICAMP UNICAMP RESULTS The air stream does not have enough velocity to remove heat at a higher rate to diminish the chip temperature. Backelite board ( k = 0,23 W/moC) is a poor heat conductor. The fin effect is weak, the chip temperature reaches 210oC.

14. MULTLAB FEM-UNICAMP UNICAMP RESULTS Replace the board material like cooper (k = 381 W/moC) The board re-distributes the heat dissipated by the chip into the air stream reducing the max chip temperature to 68oC