| (146) |
The wall laws differ only in their treatment in the buffer region; the viscous-sublayer and log-layer behaviors are identical.
The velocity distribution is modeled as:
|
| (146) |
The temperature distribution (in the absence of viscous dissipation) is modeled as:
| (147) |
The effect of viscous dissipation is introduced by the non-dimensional quantity:
| (148) |
The velocity distribution is modeled as:
| (149) |
where:
| (150) |
and the default values of the coefficients are 
= 0.42 and E = 9.0. The value of the roughness function 
in Eqn. (150) is unity for smooth walls, and for rough walls is computed according to Eqn. 165.
The temperature distribution (in the absence of viscous dissipation) is modeled as:
| (151) |
where the function P, which governs the velocity at which the logarithmic and viscous regions of the thermal profiles intersect, is by Jayatilleke [15]:
| (152) |
and 
is the molecular Prandtl number and 
is the turbulent Prandtl number.
The effect of viscous dissipation is introduced by the non-dimensional quantity:
| (153) |
where 
is a fictitious non-dimensional velocity that would occur at the intersection of the laminar and turbulent temperature profiles. It is computed from Eqn. 152 as:
| (154) |