Question

Consider two cases involving parallel flow of dry air at v = 1 m/s, T[infinity] = 45°C, and atmospheric pressure over an isothermal plate at Tₛ = 20°c. in the first case, Reₓ, = 5 × 10⁵ , while in the second case, the flow is tripped to a turbulent state at x = 0 m. at what x‐ location are the thermal boundary layer thicknesses of the two cases equal?

Answer 1

The thermal boundary layer thickness can be calculated using equations, and it can vary based on flow conditions. To find the location where the thermal boundary layer thicknesses are equal, you need to equate the expressions for laminar and turbulent flow and solve for x.

Step-by-step explanation:

The thermal boundary layer thickness in a parallel flow of dry air over an isothermal plate can be given by the equation:

δₜ = (k/ν)^(1/2)

Where, δₜ is the thermal boundary layer thickness, k is the thermal diffusivity of air, which can be calculated using the equation k = α/ρCp, ν is the kinematic viscosity of air, and α, ρ, and Cp are the thermal diffusivity, density, and specific heat capacity of air, respectively.

In the first case, since the flow is laminar, the thermal boundary layer thickness can be determined using the given parameters.

In the second case, when the flow is tripped to a turbulent state, the thermal boundary layer thickness can be determined by solving the appropriate equations for turbulent flow.

To find the x-location where the thermal boundary layer thicknesses of the two cases are equal, you need to equate the expressions for the thermal boundary layer thickness in the laminar and turbulent cases and solve for x.