1. MULTLAB FEM-UNICAMP UNICAMP SETTING STORAGE USING INFORM To get acquainted with the In-Form syntax it is introduced by means of examples. To begin with, it is shown the ways to set storage and evaluate new variables using In-Form. A sequence of workshops presents distinct features of In-Form to store auxiliary variables

2. MULTLAB FEM-UNICAMP UNICAMP SETTING STORAGE FOR AUXILIARY VARIABLES USING INFORM Auxiliary variables may be stored whole-field, and computed within the main equation-solving loop, for many purposes, including those of acting as intermediaries in the calculation of sources or fluid properties, and as references with which solved-for variables can be compared. Other auxiliary variables which In-Form can create are: single real variables, user-dimensioned real-variable arrays, and real variables having values for each cell in a patch.

3. MULTLAB FEM-UNICAMP UNICAMP SETTING STORAGE FOR AUXILIARY VARIABLES USING INFORM (STOR[ED] of Var [at PatchName] is Formula [with Options])STOR[ED] sets a account of Var variable at region described by PATCH command with PatchName name by Formula calculated. Var is any 3D-stored variable. The "with Options" element contains options which specify the action of statement:

4. MULTLAB FEM-UNICAMP UNICAMP SETTING STORAGE FOR AUXILIARY VARIABLES USING INFORM The "with Options" element contains options which specify the action of statement:with Options ZSLFIN (by default) finish of z slab ZSLSTR start of z slab SWPSTR start of sweep SWPFIN finish of sweep TSTSTR start of time step TSTFIN finish of time step RESIDU residuals CORREC corrections INFOB_n associated with an object IMAT=iprp material index IF(condition)

5. MULTLAB FEM-UNICAMP UNICAMP WORKSHOP TO PROVIDE AUXILIARY VARIABLE EVALUATION AND STORAGE USING INFORM The ‘storage’ workshops are based on a single case: heat transfer in a cylindrical pipe whose parameters are described below: The pipe radius and length are 0.05m and 7.5m with 30x30 grid. The fluid is air with constant properties (IMAT = 0). The inlet velocity and temperature is 0.15m/s and 20 o C. The north wall is held at constant temperature of 100 o C. For a ‘rescue’ situation a q1 file of this case is available for download (wksh_if_sto)wksh_if_sto

6. MULTLAB FEM-UNICAMP UNICAMP WKSH_IF_STO(1) The task of wksh_if_sto(1) is to evaluate the Fanno friction factor, Cf, for the pipe flow using In-Form. It is defined as: In terms of the grid variables, Cf is written as: Ww  North Wall where W is the averaged inlet velocity, Ww is the near wall velocity and  is the distance from the wall

7. MULTLAB FEM-UNICAMP UNICAMP WKSH_IF_STO(1) For laminar regime and fully developed flow, Cf FD is 16/Re. For comparison purposes is convenient compare the actual Cf against the fully developed one. The RCf should approach unity for the fully developed region, otherwise it is greater than one for the developing flow region.

8. MULTLAB FEM-UNICAMP UNICAMP Writing command lines using In-Form In Group 7 provide storage for RCF: STORE(RCF) In Group 19 write the lines below: inform19begin REAL(WAVG);WAVG=0.15 define the averaged velocity Evaluate ReD using Make command: (MAKE 1 OF RED IS :WAVG:*2*YVLAST/:ENUL:)MAKE Evaluate the RCF only at patch PARE using formula: (STORED RCF AT PARE is (16/RED)*2*ENUL*W1/(WAVG^2*(RV[1&NY&] - RG[1&:NY:&] )) with SWPFIN)STOREDRV[1&NY&] RG[1&:NY:&] inform19end

9. MULTLAB FEM-UNICAMP UNICAMP RESULTS WKSH_IF_STO(1) Friction Coefficient Ratio The friction coefficient ratio of wksh_if_sto(1) is on the side figure.wksh_if_sto(1) As z increases, the flow becomes fully developed and the ratio approaches 1, as expected. For z < 4, is observed a sharp increase on RCf near the entrance due to the sudden deceleration experienced by the fluid.

10. MULTLAB FEM-UNICAMP UNICAMP WKSH_IF_STO(2) The task of wksh_if_sto(2) is to evaluate the heat transfer from the wall, the pipe mixture temperature, and the pipe Nusselt number using In-Form. They are defined as: The wall heat flux: The mixture temperature The convective heat transfer coefficient The Nusselt number

11. MULTLAB FEM-UNICAMP UNICAMP WKSH_IF_STO(2) For laminar regime and thermally developed flow, Nu TD is 3.66 for constant wall temperature. For comparison purposes is convenient compare the actual Nu against the fully developed one. The RNu should approach unity for the fully developed region, otherwise it is greater than one for the developing flow region

12. MULTLAB FEM-UNICAMP UNICAMP Writing command lines using In-Form In Group 7 provide storage for RCF: STORE(RNU, TMIX,TEST,QWAL,HC) In Group 19 write the lines below: Inform19Begin REAL(TWALL);TWALL=100; define the wall temperature Evaluate wall heat flux (global variable) (STORED QWAL AT PARE is :PRNDTL(TEM1):*(TEM1-TWALL)/( RV[1&NY&] - RG[1&:NY:&] ) with SWPFIN)RV[1&NY&] RG[1&:NY:&] Evaluate mixture temperature (global variable) (STORED TMIX IS SSUM(TEST)*2/(WAVG*YVLAST^2) with SWPFIN)SSUM (STORED TEST IS (W1*TEM1*AHIGH) with SWPFIN) Evaluate heat transfer coefficient (global variable) (STORED HC AT PARE IS QWAL/(TWALL-TMIX) WITH SWPFIN) Evaluate Nusselt number ratio (global variable) (STORED RNU AT PARE IS (1/3.66)*HC*2*YVLAST/:-PRNDTL(TEM1): WITH SWPFIN) inform19end

13. MULTLAB FEM-UNICAMP UNICAMP RESULTS WKSH_IF_STO(2) The sequence of figures shows the mixture temperature ( o C), the wall heat flux (W/m 2 ) and the Nusselt number ratio against the axial pipe distance. For convenience wksh_if_sto(2) wksh_if_sto(2)

14. MULTLAB FEM-UNICAMP UNICAMP END OF THE WORKSHOP