Problem 11
What does the friction coefficient represent in flow over a flat plate? How is it related to the drag force acting on the plate?
Problem 12
Consider laminar flow over a flat plate. Will the friction coefficient change with distance from the leading edge? How about the heat transfer coefficient?
Problem 13
How are the average friction and heat transfer coefficients determined in flow over a flat plate?
Problem 18
Engine oil at \(85^{\circ} \mathrm{C}\) flows over a \(10-\mathrm{m}\)-long flat plate whose temperature is \(35^{\circ} \mathrm{C}\) with a velocity of $2.5 \mathrm{~m} / \mathrm{s}$. Determine the total drag force and the rate of heat transfer over the entire plate per unit width.
Problem 22
In an experiment, the local heat transfer over a flat plate was correlated in the form of the local Nusselt number as expressed by the following correlation $$ \mathrm{Nu}_{x}=0.035 \mathrm{Re}_{x}^{0.8} \mathrm{Pr}^{1 / 3} $$ Determine the ratio of the average convection heat transfer coefficient \((h)\) over the entire plate length to the local convection heat transfer coefficient \(\left(h_{x}\right)\) at \(x=L\).
Problem 23
Hot water vapor flows in parallel over the upper surface of a 1-m-long plate. The velocity of the water vapor is \(10 \mathrm{~m} / \mathrm{s}\) at a temperature of \(450^{\circ} \mathrm{C}\). A coppersilicon (ASTM B98) bolt is embedded in the plate at midlength. The maximum use temperature for the ASTM B98 copper-silicon bolt is \(149^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-2M). To devise a cooling mechanism to keep the bolt from getting above the maximum use temperature, it becomes necessary to determine the local heat flux at the location where the bolt is embedded. If the plate surface is kept at the maximum use temperature of the bolt, what is the local heat flux from the hot water vapor at the location of the bolt?
Problem 24
Water at \(43.3^{\circ} \mathrm{C}\) flows over a large plate at a velocity of \(30.0 \mathrm{~cm} / \mathrm{s}\). The plate is \(1.0-\mathrm{m}\) long (in the flow direction), and its surface is maintained at a uniform temperature of \(10.0^{\circ} \mathrm{C}\). Calculate the steady rate of heat transfer per unit width of the plate.
Problem 25
The forming section of a plastics plant puts out a continuous sheet of plastic that is \(1.2-\mathrm{m}\) wide and \(2-\mathrm{mm}\) thick at a rate of $15 \mathrm{~m} / \mathrm{min}$. The temperature of the plastic sheet is \(90^{\circ} \mathrm{C}\) when it is exposed to the surrounding air, and the sheet is subjected to airflow at \(30^{\circ} \mathrm{C}\) at a velocity of $3 \mathrm{~m} / \mathrm{s}$ on both sides along its surfaces normal to the direction of motion of the sheet. The width of the air cooling section is such that a fixed point on the plastic sheet passes through that section in $2 \mathrm{~s}$. Determine the rate of heat transfer from the plastic sheet to the air.
Problem 26
Hot carbon dioxide exhaust gas at \(1 \mathrm{~atm}\) is being cooled by flat plates. The gas at \(220^{\circ} \mathrm{C}\) flows in parallel over the upper and lower surfaces of a \(1.5\)-m-long flat plate at a velocity of $3 \mathrm{~m} / \mathrm{s}$. If the flat plate surface temperature is maintained at \(80^{\circ} \mathrm{C}\), determine \((a)\) the local convection heat transfer coefficient at \(1 \mathrm{~m}\) from the leading edge, \((b)\) the average convection heat transfer coefficient over the entire plate, and (c) the total heat flux transfer to the plate.
Problem 28
A transformer that is \(10-\mathrm{cm}\) long, \(6.2 \mathrm{-cm}\) wide, and \(5-\mathrm{cm}\) high is to be cooled by attaching a $10-\mathrm{cm} \times 6.2-\mathrm{cm}\(-wide polished aluminum heat sink (emissivity \)=0.03$ ) to its top surface. The heat sink has seven fins, which are \(5-\mathrm{mm}\) high, 2 -mm thick, and 10 -cm long. A fan blows air at \(25^{\circ} \mathrm{C}\) parallel to the passages between the fins. The heat sink is to dissipate $12 \mathrm{~W}$ of heat, and the base temperature of the heat sink is not to exceed \(60^{\circ} \mathrm{C}\). Assuming the fins and the base plate to be nearly isothermal and the radiation heat transfer to be negligible, determine the minimum free-stream velocity the fan needs to supply to avoid overheating. Assume the flow is laminar over the entire finned surface of the transformer.
