Based solely on the flow correlation above and your

Question

Q1. In flow over a flat plate in laminar flow the Nusselt number correlation is Nu(x) =.332(Re_x)⁵(Pr)³³

a. Based solely on the flow correlation above and your knowledge of the structure of the laminar flow temperature boundary layer, derive the rate of growth of the boundary layer δ(x).

b. Is it possible to use a similar turbulent boundary layer Nusselt correlation for the growth of the turbulent boundary layer in (x)? Explain.

Q2. Which flat plate boundary layer grows more quickly in x, the turbulent or the laminar and explain your answer.

Q3. Which flows has the larger heat transfer coefficients- laminar or turbulent?

Q4. A simple method for measuring the surface heat transfer convection coefficient involves a thin coating material with a precise melting temperature and then measuring the time for the coating to melt through jet impingement of a hot plasma gas of known constant temperature. Now the coating material is very very thin (a few microns) and the thermal conductivity and diffusivity of the copper rod is known to be 400(W/mK), α = 10^-4(m/s²) if the time to melt is known to be 400s. Use the diffusion length approximation (L_diffusion = √(αt)) and the initial coating temperature of 300 K to determine the melting temperature. Assume a surface heat transfer coefficient of 400(W/m²K). State your assumptions clearly.

Q5. How do you explain the fact that the heat transfer coefficient of the previous problem is so much greater than the maximum value given in table 1.1 for forced convection of gasses?         

Q6. Consider a thin electrical heater attached to a plate and backed by insulation as shown in the figure. Initially the heater and the plate are at the temperature of ambient T_∞. Suddenly the power to the heater is activated producing a constant heat rate q(W/m²).

What is the temperature at x=L as t goes to ∞ in terms of the given parameters?

Now sketch the temperature distribution for the 3 times (1/τ, < 1, t/τ = 1, t/τ >> 1)

Q7. Shown above is a sketch of the temperature profiles when 2 different semi-infinite solids at different initial temperatures T_Ai, T_Bi, are forced together. Using the diffusion length approximation Ldiffusion = √(αt) derive a simple algebraic equation to calculate the contact temperature T, for any transient time t (both solids are infinite in length in the conduction direction). Assume systems A, B have different thermal diffusivities α_A, α_B.

Q8. How does your previous answer explain the phenomena of a cold bathroom floor vs a warmer bathroom rug when both are at the same temperature T_i?

Q9. What are the two conditions that make mass transfer coefficients and heat transfer coefficients analogous in boundary layer flow?

Q10. What dimensionless thermophysical property is analogous to the Schmidt number in mass transfer? And what insight does this parameter give with regards to temperature boundary layers in laminar flow?

Q11. What are the two conditions (or flow requirements) that make mass transfer coefficient and heat transfer coefficients analogous in boundary layer flow solutions?

Q12. What dimensionless thermophysical property is analogous to the Schmidt number in mass transfer problems?