Consider a flat plate with a thickness of 1 cm, a length of 1 m, and a constant thermal conductivity of 50 W/(m·K). The
Posted: Tue Jun 07, 2022 1:44 pm
Consider a flat plate with a thickness of 1 cm, a length of
1 m, and a constant thermal
conductivity of 50 W/(m·K). The top surface of the plate is subject
to a parallel flow with a
free stream velocity of 4.5 m/s and a free stream temperature of
25°C. The bottom surface
of the plate is kept at a constant temperature of 47°C. Heat
transfer is steady on the plate.
Experiments found that the convection heat transfer on the top
surface can be correlated
by the following equation that applies to the entire length of the
plate.
0.04Re0.9 Pr1/3 x x Nu =
where x Nu is the local Nusselt number at the position x measured
from the leading edge
of the plate. (25 pts)
1. Obtain an expression for the ratio of the average Nusselt number
Nux to the local
Nusselt number x Nu . (15 pts)
2. Determine the surface heat flux at the end of the plate. The
fluid properties are given as
follows: ρ = 1000 kg/m3, μ = 9 x10-4 kg/(m·s), k = 0.6 W/(m·K), and
Pr = 6. (10 pts)
1 m, and a constant thermal
conductivity of 50 W/(m·K). The top surface of the plate is subject
to a parallel flow with a
free stream velocity of 4.5 m/s and a free stream temperature of
25°C. The bottom surface
of the plate is kept at a constant temperature of 47°C. Heat
transfer is steady on the plate.
Experiments found that the convection heat transfer on the top
surface can be correlated
by the following equation that applies to the entire length of the
plate.
0.04Re0.9 Pr1/3 x x Nu =
where x Nu is the local Nusselt number at the position x measured
from the leading edge
of the plate. (25 pts)
1. Obtain an expression for the ratio of the average Nusselt number
Nux to the local
Nusselt number x Nu . (15 pts)
2. Determine the surface heat flux at the end of the plate. The
fluid properties are given as
follows: ρ = 1000 kg/m3, μ = 9 x10-4 kg/(m·s), k = 0.6 W/(m·K), and
Pr = 6. (10 pts)