The film transfer coefficient, k_c, in this scenario is associated with the flow of air over the water in the pan and can be calculated using the mentioned variables. The exact formula depends on various factors including the system’s geometrical properties, the specifics of the fluid and boundary conditions.
To calculate the film-transfer coefficient, k_c, for the given scenario, we need to consider both laminar and turbulent flow cases separately.
For laminar flow over a flat plate, the film-transfer coefficient can be calculated using the following formula:
Where:
is the boundary layer thickness (meters).
is the kinematic viscosity of air (m²/s).
Sc is the Schmidt number, which is the ratio of kinematic viscosity to mass diffusivity (Sc = ν / D).
D is the mass diffusivity of water in air (m²/s).
First, let's calculate δ for laminar flow:
δ_laminar = 5.0
(
/ U)
Given:
U = 5 m/s (wind velocity)
(kinematic viscosity of air) = 1.55 x 10⁻⁵ m²/s
δ_laminar = 5.0 * (1.55 x 10⁻⁵ m²/s / 5 m/s) = 1.55 x 10⁻⁵ m
Now, calculate Sc for laminar flow:
Sc_laminar = ν / D
Given:
D (mass diffusivity of water in air) = 2.30 x 10⁻⁵ m²/s
Sc_laminar = (1.55 x 10⁻⁵ m²/s) / (2.30 x 10⁻⁵ m²/s) = 0.6739
Now, plug these values into the formula for k_c for laminar flow:
k_c_laminar = (0.664 / δ_laminar) * (ν / Sc_laminar)^(1/3)
k_c_laminar = (0.664 / 1.55 x 10⁻⁵ m) * (1.55 x 10⁻⁵ m²/s / 0.6739)^(1/3)
For turbulent flow, the calculation is more complex and involves the use of empirical correlations and coefficients. It may require additional information about the flow conditions and geometry. The formula provided here is specific to laminar flow over a flat plate.