A gas at a pressure of P" = 6kN/m)and a temperature of T" = 300 °C flows over a flat plate with a velocity of u" = 20 m/s. The plate is maintained at a uniform temperature of T2 = 27°C. Solve the boundary layer fluid
flow and convective heat transfer assuming similarity solutions exist for the velocity and temperature profiles.
The gas properties: v = 5.21 x 1089m)/s, k = 36.4 x 108
(a) Plot ∞ versus C∞
(b) Plot ∞ ∗ G versus √(∞)
0
0.1
0.2
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0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10
F'
(η
)
η
F'(η) versus η
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
(v
(η
)/
U∞
)*
√x
η
(v(η)/U∞)*√x versus η
c) Attached the Excel file showing your solutions to a & b
Also – below is my hand derivation to the Falkner-Skan equations:
d) Plot (8∞)(8∞) versus C∞
e) Attached the Excel file showing your solution for (d).
Below is the hand derivation of the Falkner’s-skan solution for the convective heat transfer
portion.
0
0.1
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0.5
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0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
θ(
η)
η
θ(η) versus η
f) What is the value of QR) at x=0.5m?
g) Plot u(y) at x=0.5m.
0
2
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6
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12
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20
22
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
u(
y)
(
m
/s
)
y (m)
u(y) versus y
h) Plot v(y) at x=0.5m.
0
0.0125
0.025
0.0375
0.05
0.0625
0.075
0.0875
0.1
0.1125
0.125
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
v(
y)
(
m
/s
)
y (m)
v(y) versus y
i) What is the heat transfer rate per unit area in STU = 0.5m?

j) Plot T(y) at x=0.5m
0
25
50
75
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250
275
300
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
T(
y)
°
y (m)
T(y) versus y