1. A turbine blade 5 cm long with a cross-sectional
area A = 4.5 cm2 and a perimeter P = 12 cm is
made of a high alloy steel (k = 25 W/m K). The
temperature of the blade attachment point is
500°C, and the blade is exposed to combustion
gases at 900°C. The heat transfer coefficient
between the blade surface and the combustion
gases is 500 W/m2 K. Using the nodal network
shown in the accompanying sketch, determine
the
(a) Temperature distribution in the blade (20%)
(b) Rate of heat transfer to the blade (10%)
(c) Fin efficiency of the blade (10%)
(d) Compare the fin efficiency calculated
numerically with that calculated by the exact
method. (10%)
Hint 1: Assume that the bade has reached steady
conditions, the blade material properties are
constant and uniform, convectin at the blade tip,
and 1-D heat transfer.
Hint 2: A part of the solution is as follows:
1
2
2. Hydrogen at 15°C and a pressure of 1 atm is flowing along a flat plate at a velocity of 3 m/s.
If the plate is 0.3-m wide and at 71°C, calculate the following quantities at x= 0.3 m and at the
distance corresponding to the transition point, i.e., Rex = 5×105 (use properties at 43°C):
(a) Hydrodynamic boundary layer thickness, in cm (5%)
(b) Thickness of thermal boundary layer, in cm (5%)
(c) Local friction coefficient, dimensionless (5%)
(d) Average friction coefficient, dimensionless (5%)
(e) Drag force, in N (5%)
(f) Local convection heat transfer coefficient, in W/m2°C (10%)
(g) Average convection heat transfer coefficient, in W/m2°C (10%)
(h) Rate of heat transfer, in W (5%)
Hint 1: Assume steady conditions, 2D, constant and uniform properties, low disturbances are
present in the mainstream.
Hint 2: The properties should be found at film temperature (𝑇𝑇∞ − 𝑇𝑇𝑠𝑠 )/2 = 43℃.
3