Let evaluate fanning friction factor. In general, this coefficient depends on channel parameters, flow character and air flow velocity.

So far as air flow in the channel is turbulent and channel section is a ring, to calculate fanning friction factor one can use Blasius equation [13]:

Nomenclature E: Energy component in energy equation F: Force component in momentum equation, N f:

Fanning friction factor g: Acceleration due to gravity, m/[s.sup.2] [k.sub.eff]: Thermal conductivity in energy equation, W/mK m: mass flow rate of fluid, kg/s Re: Reynolds number based on internal diameter of the tube, dimensionless Nu: Nusselt number, dimensionless p: Pressure component in momentum equation, N/[m.sup.2] [S.sub.m]: Accumulation of mass, Kg [S.sub.h]: Accumulation of energy, J T: Temperature, [degrees]C.

Finally, the criterial relations between Fanning friction factor f and Metzner-Reed Reynolds number [Re.sub.M] were obtained for laminar-flow and turbulent-flow regions, respectively.

Nomenclature D = inside diameter of tube f = Fanning friction factor L = length of tube [Re.sub.M] = Metzner-Reed Reynolds Number V = flow velocity Greek symbols [Y.sub.w] = shear rate on tube wall [DELTA]P = pressure drop [eta] = plastic viscosity of clathrate hydrate slurry [[mu].sub.e] = effective viscosity of clathrate hydrate slurry [[rho].sub.s] = density of clathrate hydrate slurry [[tau].sub.0] = yield shear stress of clathrate hydrate slurry [[tau].sub.w] = shear stress on tube wall [chi] = solid mass fraction

They related

fanning friction factor with generalized Reynolds number.

Ayub (2003) also proposed to evaluate evaporation pressure drop using the following correlation for Fanning friction factor:

where f is the Fanning friction factor, R = 30[degrees]/[beta], and

The average pressure loss due to friction or wall shear stress is represented by the Fanning friction factor over the one-period module of the duct, and it is determined from

This is due to the fact that even though Fanning friction factor f decreases with the increase in Re this drop is nonlinear, and the corresponding increase in Nu or is not sufficient to make the value of (j/f) large (Huzaayin et al 2009) In other words, the relative frictional penalty increases with Re to limit or reduce enhancement that would yield high area goodness factor Furthermore, as can be seen from Figure 4, (j/f) increases with the increase of period length as Case 1 outperform Cases 2 and 3: likewise.

Current Study Fanning Friction Factor Correlations Cf = C'*[Re.sup.P'] Water/Water 60/60 Plate 27/60 Plate 27/27 Plate Dynalene/Water C' 1.18 1.56 3.09 C' P' -0.10 -0.08 -0.06 P' Water/Water 60/60 Plate 27/60 Plate 27/27 Plate C' 0.57 21.40 3.15 P' 0 -0.46 -0.08 Uncertainty Analysis

The collected data were analyzed to obtain single-phase heat transfer coefficients, using modified Wilson plot method, as well as the Fanning friction factor for each plate configuration.