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Analytical Heat Transfer
a. If the plate is placed in a hot air stream with a pressure of 1 atm,
temperature of 400 ◦ K, and velocity of 10 m/s, sketch the local
heat transfer coefficient, h x , along the plate. Also, determine
the surface heat flux at the trailing edge of the plate.
Given: air properties at 350 ◦ K, k = 30
6 2
× 10 −3 w/mk, v = 20.92 ×
10 − m /s, Pr = 0.7:
Nu x = a Re m Pr n
x
,
where a = 0.332, m = 1/2, n = 1/3 for laminar flow
a = 0.0296, m = 4/5, n = 1/3 for turbulent flow
7.25. Constant properties laminar viscous fluids (ρ, C p , K, μ = constant)
with a free-stream velocity U ∞ and temperature T ∞ move over a
flat plate at a uniform wall heat flux (q "" =
w
constant).
a. Determine the local Nusselt number (Nu x = h x · x/k) along the
plate by using the integral approximation method with the
velocity and temperature profiles across the boundary layers
as u = a + by and T = c + dy, respectively. Assume Pr = 1 for
this problem.
b. On the same plot, sketch h x , Nu x versus x for the uniform
wall heat flux (q ""
w = constant) and uniform wall temperature
(T w = constant) BCs, respectively. For the same flow velocity,
which wall BC (q ""
w or T w ) will provide a higher heat transfer
coefficient or Nusselt number? Explain why.
References
1. W. Rohsenow and H. Choi, Heat, Mass, and Momentum Transfer, Prentice-Hall, Inc.,
Englewood Cliffs, NJ, 1961.
2. F. Incropera and D. Dewitt, Fundamentals of Heat and Mass Transfer, Fifth Edition,
John Wiley & Sons, New York, NY, 2002.
3. H. Schlichting, Boundary-Layer Theory, Sixth Edition, McGraw-Hill, New York,
NY, 1968.
4. W. M. Kays and M. E. Crawford, Convective Heat and Mass Transfer, Second
Edition, McGraw-Hill, New York, NY, 1980.
5. A. Mills, Heat Transfer, Richard D. Irwin, Inc., Boston, MA, 1992.
6. E. Levy, Convection Heat Transfer, Class Notes, Lehigh University, 1973.
Analytical Heat Transfer
a. If the plate is placed in a hot air stream with a pressure of 1 atm,
temperature of 400 ◦ K, and velocity of 10 m/s, sketch the local
heat transfer coefficient, h x , along the plate. Also, determine
the surface heat flux at the trailing edge of the plate.
Given: air properties at 350 ◦ K, k = 30
6 2
× 10 −3 w/mk, v = 20.92 ×
10 − m /s, Pr = 0.7:
Nu x = a Re m Pr n
x
,
where a = 0.332, m = 1/2, n = 1/3 for laminar flow
a = 0.0296, m = 4/5, n = 1/3 for turbulent flow
7.25. Constant properties laminar viscous fluids (ρ, C p , K, μ = constant)
with a free-stream velocity U ∞ and temperature T ∞ move over a
flat plate at a uniform wall heat flux (q "" =
w
constant).
a. Determine the local Nusselt number (Nu x = h x · x/k) along the
plate by using the integral approximation method with the
velocity and temperature profiles across the boundary layers
as u = a + by and T = c + dy, respectively. Assume Pr = 1 for
this problem.
b. On the same plot, sketch h x , Nu x versus x for the uniform
wall heat flux (q ""
w = constant) and uniform wall temperature
(T w = constant) BCs, respectively. For the same flow velocity,
which wall BC (q ""
w or T w ) will provide a higher heat transfer
coefficient or Nusselt number? Explain why.
References
1. W. Rohsenow and H. Choi, Heat, Mass, and Momentum Transfer, Prentice-Hall, Inc.,
Englewood Cliffs, NJ, 1961.
2. F. Incropera and D. Dewitt, Fundamentals of Heat and Mass Transfer, Fifth Edition,
John Wiley & Sons, New York, NY, 2002.
3. H. Schlichting, Boundary-Layer Theory, Sixth Edition, McGraw-Hill, New York,
NY, 1968.
4. W. M. Kays and M. E. Crawford, Convective Heat and Mass Transfer, Second
Edition, McGraw-Hill, New York, NY, 1980.
5. A. Mills, Heat Transfer, Richard D. Irwin, Inc., Boston, MA, 1992.
6. E. Levy, Convection Heat Transfer, Class Notes, Lehigh University, 1973.