Determine the nusselt number for fully developed flow and

Question

Q1. Determine the Nusselt number for fully developed flow and temperature profile in a plane duct (i.e. between two large parallel plates; see Fig. P5.2) for the case of the same constant wall heat flux in both walls

Q2. Integrate eqs. (6.253) and (6.254) within the cold boundary layer and assume second-degree polynomial velocity and temperature profiles in the cold boundary layer to show eq. (6.255).

∂3v/∂x3 + (gβ/v)(∂T/∂x)                                                               (6.253)

u(∂T/∂x) + v(∂T/∂y) = α(∂²T/∂x²)                                                  (6.254)

which can be solved by an integral method. By following the procedure similar to Bejan (1989) and Zhang and Bejan (1989), one obtains an ordinary differential equation for cold boundary layer thickness, δ

Q3. A pure vapor flows into a horizontal channel formed by two parallel plates (see Fig. P7.3) with uniform velocity (u_∞) and temperature (T_∞). The bottom plate is maintained at a temperature, T_w, below the saturation temperature, while the upper plate is adiabatic. Condensation occurs on the surface of the bottom plate, and the condensate is dragged by the vapor and flows to the positive x-direction. The thickness of the liquid film is much smaller than the distance between the two plates (δ << H ). Both velocity and temperature distribution in the liquid film can be assumed to be linear. The shear stress at the liquid-vapor interface can be estimated by τ_δ = 0.5f ρ_v(u_v - u_δ)² + m_δ(u_v - u_δ), where the fraction coefficient f = CReⁿ (C and n are constants), u_δ is the axial velocity at interface, and m_δ is rate of condensation. Obtain the ordinary differential equation that governs the liquid film thickness.

Q4. Film boiling occurs on an electrically heated 1.27 mm platinum wire placed horizontally in the water at atmospheric condition. The surface temperature of the wire is 754°C. The emissivity of the platinum wire and the liquid vapor interface can be assumed as ε_s = ε_i =1. Find the power dissipated per unit length of the wire.