Problem 93
A metallic airfoil of elliptical cross section has a mass of $50 \mathrm{~kg}\(, surface area of \)12 \mathrm{~m}^{2}$, and a specific heat of \(0.50 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\). The airfoil is subjected to airflow at \(1 \mathrm{~atm}\), \(25^{\circ} \mathrm{C}\), and $5 \mathrm{~m} / \mathrm{s}$ along its 3 -m-long side. The average temperature of the airfoil is observed to drop from \(160^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\) within 2 min of cooling. Assuming the surface temperature of the airfoil to be equal to its average temperature and using the momentum-heat transfer analogy, determine the average friction coefficient of the airfoil surface. Evaluate the air properties at \(25^{\circ} \mathrm{C}\) and 1 atm. Answer: \(0.000363\)
Problem 95
The electrically heated \(0.6\)-m-high and \(1.8\)-m-long windshield of a car is subjected to parallel winds at \(1 \mathrm{~atm}, 0^{\circ} \mathrm{C}\), and \(80 \mathrm{~km} / \mathrm{h}\). The electric power consumption is observed to be \(70 \mathrm{~W}\) when the exposed surface temperature of the windshield is \(4^{\circ} \mathrm{C}\). Disregarding radiation and heat transfer from the inner surface and using the momentum-heat transfer analogy, determine drag force the wind exerts on the windshield. Evaluate the air properties at \(2^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).
Problem 96
A \(5-\mathrm{m} \times 5-\mathrm{m}\) flat plate maintained at a constant temperature of \(80^{\circ} \mathrm{C}\) is subjected to parallel flow of air at \(1 \mathrm{~atm}, 20^{\circ} \mathrm{C}\), and \(10 \mathrm{~m} / \mathrm{s}\). The total drag force acting on the upper surface of the plate is measured to be \(2.4 \mathrm{~N}\). Using the momentum-heat transfer analogy, determine the average convection heat transfer coefficient and the rate of heat transfer between the upper surface of the plate and the air. Evaluate the air properties at \(50^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).
Problem 97
Air ( \(1 \mathrm{~atm}, 5^{\circ} \mathrm{C}\) ) with free stream velocity of \(2 \mathrm{~m} / \mathrm{s}\) is flowing in parallel to a stationary thin \(1-\mathrm{m} \times 1-\mathrm{m}\) flat plate over the top and bottom surfaces. The flat plate has a uniform surface temperature of $35^{\circ} \mathrm{C}\(. If the friction force asserted on the flat plate is \)0.1 \mathrm{~N}$, determine the rate of heat transfer from the plate. Evaluate the air properties at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).
Problem 99
The upper surface of an ASME SB-96 coppersilicon plate is subjected to convection with hot air flowing at \(6.5 \mathrm{~m} / \mathrm{s}\) parallel over the plate surface. The plate is square with a length of \(1 \mathrm{~m}\), and the temperature of the hot air is \(200^{\circ} \mathrm{C}\). The ASME Boiler and Pressure Vessel Code (ASME BPVC.IV-2015, HF-300) limits equipment constructed with ASME SB-96 plate to be operated at a temperature not exceeding \(93^{\circ} \mathrm{C}\). From a wind tunnel experiment, the average friction coefficient for the upper surface of the plate was found to be \(0.0023\). In the interest of designing a cooling mechanism to keep the plate surface temperature from exceeding \(93^{\circ} \mathrm{C}\), determine the minimum heat removal rate required to keep the plate surface from going above \(93^{\circ} \mathrm{C}\). Use the following air properties for the analysis: $c_{p}=1.016 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}, k=0.03419 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\(, \)\mu=2.371 \times 10^{-5} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\(, and \)\rho=0.8412 \mathrm{~kg} / \mathrm{m}^{3}$.
Problem 100
Air at \(1 \mathrm{~atm}\) is flowing over a flat plate with a free stream velocity of \(70 \mathrm{~m} / \mathrm{s}\). If the convection heat transfer coefficient can be correlated by $\mathrm{Nu}_{x}=0.03 \operatorname{Re}_{x}^{08} \operatorname{Pr}^{1 / 3}$, determine the friction coefficient and wall shear stress at a location \(2 \mathrm{~m}\) from the leading edge. Evaluate air properties at \(20^{\circ} \mathrm{C}\) and $1 \mathrm{~atm}$.
Problem 103
Using a cylinder, a sphere, and a cube as examples, show that the rate of heat transfer is inversely proportional to the nominal size of the object. That is, heat transfer per unit area increases as the size of the object decreases.
Problem 104
Determine the heat flux at the wall of a microchannel of width $1 \mu \mathrm{m}\( if the wall temperature is \)50^{\circ} \mathrm{C}$ and the average gas temperature near the wall is \(100^{\circ} \mathrm{C}\) for the cases of (a) $\sigma_{T}=1.0, \gamma=1.667, k=0.15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \lambda / \mathrm{Pr}=0.5$ (b) $\sigma_{T}=0.8, \gamma=2, \mathrm{k}=0.1 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \lambda / \mathrm{Pr}=5$
Problem 106
Evaluate the Prandtl number from the following data: $c_{p}=0.5 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R}, k=2 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot \mathrm{R}, \mu=0.3 \mathrm{lbm} / \mathrm{ft} \cdot \mathrm{s}$.
Problem 108
Consider a fluid flowing over a flat plate at a constant free stream velocity. The critical Reynolds number is \(5 \times 10^{5}\), and the distance from the leading edge at which the transition from laminar to turbulent flow occurs is \(x_{c r}=7 \mathrm{ft}\). Determine the characteristic length \(\left(L_{c}\right)\) at which the Reynolds number is \(1 \times 10^{5}\).
