Mean Velocity per channel:

Incompressible (constant density)

Reynolds Number: Flow will be laminar if reynolds number is less than approx.. 2300

Internal flow, based on mean velocity and hydraulic diameter, characteristic dimensions of the duct cross section

Hydraulic diameter: per: wetted perimeterwch = channel widthhch = channel height

Hydrodynamic entry length of laminar internal flow, distance required for the momentum boundary layers to join

(Nellis and Klein, 2008, pg 638)Mean velocity and cross-sectional area are constant.

k: conductivity

thermal entry length, distance required for the thermal boundary layers to join.

(Nellis and Klein, 2008, pg 647)

Ratio of thermal to hydrodynamic entry lengths

Rate of momentum to thermal boundary layer development in laminar flow is related to Prandtl number. PAO is viscous but not conductive, has a high Prandtl number. Momentum boundary layer will grow more quickly than the thermal boundary layer and the flow will become much sooner hydrodynamically fully developed than it will become thermally developed. (Nellis and Klein, 2008, pg. 647)

Thermal and momentum boundary layer growth for high Prandtl number (Nellis and Klein, 2008, pg. 648)

The roughness at the duct surface will affect the Nusselt number and friction factor for a turbulent flow but not a laminar flow (Nellis and Klein, 2008, pg. 650)

For internal flow, pressure gradient correlated using the Moody (or Darcy) friction factor.Average or apparent friction factor.

(Nellis and Klein, 2008, pg. 642)lc =length of channel

Local and average friction factor as a function of position in the entrance region of an internal flow.

The average friction factor will approach the local friction factor in the fully developed region. However, because the average friction factor has some memory of the developing region it will always be somewhat larger than the local value. Necessary to calculate average in order to solve an engineering problem, need to know the total pressure drop across a duct that must be overcome by a pump or fan.

Friction factor, laminar, fully developed region. (Nellis and Klein, 2008, pg. 652)

Average friction factor for laminar flow, rectangular ducts, approximately computed using dimensionless position L+ and this equation.

L+ dimensionless position.

(Nellis and Klein, 2008, pg. 651)

(Nellis and Klein, 2008, pg. 653)

Based off of Curr et al. (1972).

The product of the apparent friction factor in a rectangular duct and the Reynolds number as a function of L+ for two values of the aspect ratio. The results predicted by Eqs. (5-60) and (5-61) are shown, as well as the more exact solution provided by Curr et al. (1972).

Local Nusselt number for a laminar, hydrodynamically and dully developed flow in a rectangular duct exposed to unform heat flux.

AR: Aspect ratio of duct (the ratio of the minimum to the maximum dimensions)

NuDh, H, fd = 7.929

The average Nusselt number will approach the local Nusselt number in the thermally fully developed region. However, because the average Nusselt number has some memory of the developing region, it will always be somewhat larger than the local value.

Local and average heat transfer coefficient and Nusselt number as a function of position. (Nellis and Klein, 2008. 646)

Can also use EES procedure DuctFlow_N, which interpolates a table of data provided by Kakac et al. (1987) and corrects for the Prandtl number effects by applying the correction associated with a square duct, also from Kakac et al. (1987).

call DuctFlow_N(Re,Pr,LoverD_h,ALPHA_c,relRough: {Nusselt_T}, Nusselt_H, f_app)

Inputs:Re - Reynolds number based on properties evaluated at the bulk average temperaturePr - Prandtl number of the fluid evaluated at the bulk average temperatureLoverD_h - ratio of tube length to hydraulic diameter. Aspect - ratio of the minimum to maximum dimension of duct. This value should be