The products of combustion from a burner are routed to an industrial application through a thin-walled metallic duct of diameter
Di=1 m and length L=100 m. The gas enters the duct at atmospheric pressure and a mean temperature and velocity of Tm,i=1600 K and Um,i=10 m/s, respectively. It must exit the duct at a temperature that is no less than Tm,o=1400 K. What is the minimum thickness of an alumina-silica insulation (Kins=0.125 W/m*K) needed to meet the outlet requirement under worst case conditions for which the duct is exposed to ambient air at T[infinity]=250 K and a cross-flow velocity of V=15 m/s? The properties of the gas may be approximated as those of air, and as a first estimate, the effect of the insulation thickness on the convection coefficient and the thermal resistance associated with the cross flow may be neglected.
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Complete question:
A structural component in the form of a wide plate is to be fabricated from a steel alloy that has a plane strain fracture toughness of 98.9 MPa root m (90 ksi root in.) and a yield strength of 860 MPa (125,000 psi). The flaw size resolution limit of the flaw detection apparatus is 3.0 mm (0.12 in.). If the design stress is one-half of the yield strength and the value of Y is 1.0, determine whether or not a critical flaw for this plate is subject to detection.
Answer:
Since the flaw 17mm is greater than 3 mm the critical flaw for this plate is subject to detection
so that critical flow is subject to detection
Explanation:
We are given:
Plane strain fracture toughness K
Yield strength Y = 860 MPa
Flaw detection apparatus = 3.0mm (12in)
y = 1.0
Let's use the expression:
We already know
K= design
a = length of surface creak
Since we are to find the length of surface creak, we will make "a" subject of the formula in the expression above.
Therefore
Substituting figures in the expression above, we have:
= 0.0168 m
= 17mm
Therefore, since the flaw 17mm > 3 mm the critical flow is subject to detection