Problem 30
Hot engine oil at \(150^{\circ} \mathrm{C}\) is flowing in parallel over a flat plate at a velocity of \(2 \mathrm{~m} / \mathrm{s}\). Surface temperature of the \(0.5-\mathrm{m}\)-long flat plate is constant at \(50^{\circ} \mathrm{C}\). Determine (a) the local convection heat transfer coefficient at $0.2 \mathrm{~m}$ from the leading edge and the average convection heat transfer coefficient, and \((b)\) repeat part \((a)\) using the Churchill and Ozoe (1973) relation.
Problem 32
Hydrogen gas at \(1 \mathrm{~atm}\) is flowing in parallel over the upper and lower surfaces of a 3 -m-long flat plate at a velocity of $2.5 \mathrm{~m} / \mathrm{s}\(. The gas temperature is \)120^{\circ} \mathrm{C}$, and the surface temperature of the plate is maintained at \(30^{\circ} \mathrm{C}\). Using appropriate software, investigate the local convection heat transfer coefficient and the local total convection heat flux along the plate. By varying the location along the plate for \(0.2 \leq x \leq 3 \mathrm{~m}\), plot the local convection heat transfer coefficient and the local total convection heat flux as functions of \(x\). Assume flow is laminar, but make sure to verify this assumption.
Problem 33
Carbon dioxide and hydrogen as ideal gases at \(1 \mathrm{~atm}\) and \(-20^{\circ} \mathrm{C}\) flow in parallel over a flat plate. The flow velocity of each gas is \(1 \mathrm{~m} / \mathrm{s}\), and the surface temperature of the \(3-\mathrm{m}\)-long plate is maintained at $20^{\circ} \mathrm{C}$. Using appropriate software, evaluate the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient along the plate for each gas. By varying the location along the plate for $0.2 \leq x \leq 3 \mathrm{~m}$, plot the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient for each gas as functions of \(x\). Discuss which gas has a higher local Nusselt number and which gas has a higher convection heat transfer coefficient along the plate. Assume flow is laminar, but make sure to verify this assumption.
Problem 37
Consider a refrigeration truck traveling at \(70 \mathrm{mph}\) at a location where the air temperature is \(80^{\circ} \mathrm{F}\). The refrigerated compartment of the truck can be considered to be a 9 -ft-wide, 7 -ft-high, and 20 -ft-long rectangular box. The refrigeration system of the truck can provide 3 tons of refrigeration (i.e., it can remove heat at a rate of $600 \mathrm{Btu} / \mathrm{min}$ ). The outer surface of the truck is coated with a low-emissivity material, and thus radiation heat transfer is very small. Determine the average temperature of the outer surface of the refrigeration compartment of the truck if the refrigeration system is observed to be operating at half the capacity. Assume the airflow over the entire outer surface to be turbulent and the heat transfer coefficient at the front and rear surfaces to be equal to that on side surfaces. For air properties evaluations, assume a film temperature of \(80^{\circ} \mathrm{F}\). Is this a good assumption?
Problem 38
Consider a hot automotive engine, which can be approximated as a \(0.5-\mathrm{m}\)-high, \(0.40\)-m-wide, and \(0.8\)-m-long rectangular block. The bottom surface of the block is at a temperature of \(100^{\circ} \mathrm{C}\) and has an emissivity of \(0.95\). The ambient air is at $20^{\circ} \mathrm{C}\(, and the road surface is at \)25^{\circ} \mathrm{C}$. Determine the rate of heat transfer from the bottom surface of the engine block by convection and radiation as the car travels at a velocity of $80 \mathrm{~km} / \mathrm{h}$. Assume the flow to be turbulent over the entire surface because of the constant agitation of the engine block.
Problem 40
Heat dissipated from a machine in operation hot spots that can cause thermal burns on human skposed hot spots that can cause thermal burns on human skin are considered to be hazards in the workplace. Consider a $1.5-\mathrm{m} \times 1.5-\mathrm{m}\( flat machine surface that is made of \)5-\mathrm{mm}-$ thick aluminum \((k=237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). During operation, the machine's inner aluminum surface temperature can be as high as \(90^{\circ} \mathrm{C}\), while the outer surface is cooled with $30^{\circ} \mathrm{C}\( air flowing in parallel over it at \)10 \mathrm{~m} / \mathrm{s}$. To protect machine operators from thermal burns, the machine surface can be covered with insulation. The aiuminum/insulation interface has a thermal contact conductance of \(3000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). What is the thickness of insulation (with a thermal conductivity of $0.06 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$ ) needed to keep the local outer surface temperature at \(45^{\circ} \mathrm{C}\) or lower? Using appropriate software, plot the required coefficient along the outer surface in parallel with the airflow. coefficient along the outer surface in parallel with the airflow.
Problem 42
In cryogenic equipment, cold air flows in parallel over the surface of a \(2-\mathrm{m} \times 2-\mathrm{m}\) ASTM A240 \(410 \mathrm{~S}\) stainless steel plate. The air velocity is \(5 \mathrm{~m} / \mathrm{s}\) at a temperature of \(-70^{\circ} \mathrm{C}\). The minimum temperature suitable for the ASTM A240 \(410 \mathrm{~S}\) plate is \(-30^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-1M). The plate is heated to keep its surface temperature from going below \(-30^{\circ} \mathrm{C}\). Determine the average heat transfer rate required to keep the plate surface from getting below the minimum suitable temperature.
Problem 45
The local atmospheric pressure in Denver, Colorado (elevation $1610 \mathrm{~m}\( ), is \)83.4 \mathrm{kPa}$. Air at this pressure and at \(30^{\circ} \mathrm{C}\) flows with a velocity of \(6 \mathrm{~m} / \mathrm{s}\) over a \(2.5-\mathrm{m} \times 8-\mathrm{m}\) flat plate whose temperature is \(120^{\circ} \mathrm{C}\). Determine the rate of heat transfer from the plate if the air flows parallel to the \((a) 8-\mathrm{m}-\) long side and \((b)\) the \(2.5\)-m side.
Problem 48
Warm air is blown over the inner surface of an automobile windshield to defrost ice accumulated on the outer surface of the windshield. Consider an automobile windshield $\left(k_{w}=0.8 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot \mathrm{R}\right)$ with an overall height of 20 in and thickness of \(0.2\) in. The outside air \((1 \mathrm{~atm})\) ambient temperature is \(8^{\circ} \mathrm{F}\), and the average airflow velocity over the outer windshield surface is \(50 \mathrm{mph}\), while the ambient temperature inside the automobile is \(77^{\circ} \mathrm{F}\). Determine the value of the convection heat transfer coefficient for the warm air blowing over the inner surface of the windshield that is needed to cause the accumulated ice to begin melting. Assume the windshield surface can be treated as a flat-plate surface.
Problem 49
The top surface of the passenger car of a train moving at a velocity of $95 \mathrm{~km} / \mathrm{h}\( is \)2.8-\mathrm{m}\( wide and \)8-\mathrm{m}$ long. The top surface is absorbing solar radiation at a rate of $380 \mathrm{~W} / \mathrm{m}^{2}\(, and the temperature of the ambient air is \)30^{\circ} \mathrm{C}$. Assuming the roof of the car to be perfectly insulated and the radiation heat exchange with the surroundings to be small relative to convection, determine the equilibrium temperature of the top surface of the car. Answer: \(37.5^{\circ} \mathrm{C}\)
