The parameter, a$ appearing in the above equation is the turbulent Prandtl number for The value of turbulent Prandtl number is determined experimentally and is generally of the order of unity. The values of turbulent Prandtl number may also be estimated using RNG methods (Yakhot and Orszag, 1986). The Reynolds-averaged species as well as enthalpy conservation equations can be closed with the help of Eq. (3.37), provided that the closed form of the time-averaged source term is known. The modeling of time-averaged source terms for reactive flow processes will be discussed in the Chapter 5. Though it is possible to develop a transport equation for the correlation of scalar variable and fluctuating velocity by following the methods similar to those used for Reynolds stress models, gradient assumption is used in practice, for most of the engineering simulations.

The influence of a wall on the turbulent transport of scalar (species or enthalpy) at the wall can also be modeled using the wall function approach, similar to that described earlier for modeling momentum transport at the wall. It must be noted that the thermal or mass transfer boundary layer will, in general, be of different thickness than the momentum boundary layer and may change from fluid to fluid. For example, the thermal boundary layer of a high Prandtl number fluid (e.g. oil) is much less than its momentum boundary layer. The wall functions for the enthalpy equations in the form of temperature T can be written as:

(Tw - Tp) pCpC|/4kp/2 qw pypCiJ kp/ _ _ pypCiJ kp/ +

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