Wall region heat and mass transfer with newtonian and viscoelastic fluids in turbulent flow

Abstract

Baton Rouge, Louisiana 70821Heat and mass transfer models that represent the experimental range of Prandtl and Schmidt numbers with turbulent flow include empirical wall region models (Churchill, 1977; Hughmark, 1975b). Shaw and Hanratty (1977) reported experimental data to rule out the plausible limiting expressions for eddy diffusivity close to a wall. Lau, Lee, and Hanratty (1977) interpret additional experimental data to indicate that the region y + < about 4 cannot be represented by a pseudo steady state assumption. Hughmark (1972Hughmark ( , 1973 analyzed experimental data to indicate that the core and transition regions can be represented by pseudo steady state models. This communication utilizes the models for the core and transition region with a range of experimental heat and mass transfer data to estimate the boundary layer contribution at the wall. Data for viscoelastic fluids in turbulent flow are also considered with respect to these models. NEWTONIAN FLUIDSThe prior work related to steady state models for the core and transition region show that eddy transport in the core of a circular pipe is represented by and for the transition region by k + E T = 0.0615 NsC-% (2) Equation (2) represents the penetration model with the contact time consistent with the wall frequency relationshipAlso, in the prior work, eddy diffusivity for heat and mass for the transition region was correlated by 2-= 0.0094 y+2 (4) V Integration of the eddy diffusivity with the upper limit as y + = 34.6 to represent the boundary with the turbulent core shows that the lower limit is y+ = 5.5 to correspond to the eddy transport of Equation (2). This is in reasonable agreement with y+ = about 4 value reported by Lau et al, as the limit of the wall boundary layer that cannot be represented by a pseudo steady state assumption.The sum of the eddy diffusivity from Equation (4) and the molecular difhsivity for heat or mass can be Figure 1 shows the data of Debrule and Sabersky (1974), Friend and Metzner (1958), Harriott and Hamilton (1965), Malina and Sparrow (1964), and Shaw and H a n r a 3 (7)which is consistent with the Shaw and Hanratty observation that the observed wall region value rules out the plausible limiting expressions for eddy dsusivity close to a wall. Figure 1 is interesting in that the Harriott and Hamilton data are correlated by Equation (7) for Nsc < 3000 but show significantly higher coefficients at the higher Schmidt numbers. The Harriott and Hamilton data were obtained by the wall solution method and the Shaw and Hanratty data by the electrochemical method. VJSCOELASTIC FLUIDSHughmark ( 1 9 7 5~) showed that the wall region frequency for a viscoelastic fluid in turbulent flow could be related to the drag reduction of the fluid with a 00w behavior index of unity fN = 0.0206 a2I3 (8) f E which corresponds to k+ET = 1.13 a-% Nsc-"~ (9) for the penetration model with this wall region frequency. The dimensionless variable a is a function of the Deborah number as shown by the reference. Similarly, the eddy diffusivity f...

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