Chapter 7

Two metal plates are connected by a long ASTM A479 904L stainless steel bar. Air, at \(340^{\circ} \mathrm{C}\), flows at \(25 \mathrm{~m} / \mathrm{s}\) between the plates and across the bar. The bar has a square cross section with a width of \(10 \mathrm{~mm}\), and the length of the bar exposed to the hot air is \(10 \mathrm{~cm}\). The maximum use temperature for the ASTM A479 904L is \(260^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-1M). The temperature of the bar is maintained by a cooling mechanism capable of removing heat at a rate of \(50 \mathrm{~W}\). Determine whether the heat removed from the bar is sufficient to keep the bar at \(260^{\circ} \mathrm{C}\) or lower.

In flow across tube banks, how does the heat transfer coefficient vary with the row number in the flow direction? How does it vary in the transverse direction for a given row number?

In flow across tube banks, why is the Reynolds number based on the maximum velocity instead of the uniform approach velocity?

A tube bank consists of 300 tubes at a distance of \(6 \mathrm{~cm}\) between the centerlines of any two adjacent tubes. Air approaches the tube bank in the normal direction at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) with a mean velocity of \(6 \mathrm{~m} / \mathrm{s}\). There are 20 rows in the flow direction with 15 tubes in each row with an average surface temperature of \(140^{\circ} \mathrm{C}\). For an outer tube diameter of \(2 \mathrm{~cm}\), determine the average heat transfer coefficient. Evaluate the air properties at an assumed mean temperature of \(70^{\circ} \mathrm{C}\) and $1 \mathrm{~atm}$.

Exhaust gases at \(1 \mathrm{~atm}\) and \(300^{\circ} \mathrm{C}\) are used to preheat water in an industrial facility by passing them over a bank of tubes through which water is flowing at a rate of \(6 \mathrm{~kg} / \mathrm{s}\). The mean tube wall temperature is \(80^{\circ} \mathrm{C}\). Exhaust gases approach the tube bank in the normal direction at \(4.5 \mathrm{~m} / \mathrm{s}\). The outer diameter of the tubes is \(2.1 \mathrm{~cm}\), and the tubes are arranged inline with longitudinal and transverse pitches of $S_{L}=S_{T}=8 \mathrm{~cm}$. There are 16 rows in the flow direction with eight tubes in each row. Using the properties of air for exhaust gases, determine (a) the rate of heat transfer per unit length of tubes, \((b)\) pressure drop across the tube bank, and \((c)\) the temperature rise of water flowing through the tubes per unit length of tubes. Evaluate the air properties at an assumed mean temperature of \(250^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). Is this a good assumption?

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of \(0.8-\mathrm{cm}\)-outer-diameter and \(0.8-\mathrm{m}\)-long tubes inside which the refrigerant is evaporating at \(-20^{\circ} \mathrm{C}\). Air approaches the tube bank in the normal direction at \(0^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) with a mean velocity of \(5 \mathrm{~m} / \mathrm{s}\). The tubes are arranged in-line with longitudinal and transverse pitches of \(S_{L}=S_{T}=1.5 \mathrm{~cm}\). There are 25 rows in the flow direction with 15 tubes in each row. Determine \((a)\) the refrigeration capacity of this system and \((b)\) pressure drop across the tube bank. Evaluate the air properties at an assumed mean temperature of \(-5^{\circ} \mathrm{C}\) and $1 \mathrm{~atm}$. Is this a good assumption?

Combustion air in a manufacturing facility is to be preheated before entering a furnace by hot water at \(90^{\circ} \mathrm{C}\) flowing through the tubes of a tube bank located in a duct. Air enters the duct at \(15^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) with a mean velocity of \(4.5 \mathrm{~m} / \mathrm{s}\), and it flows over the tubes in the normal direction. The outer diameter of the tubes is \(2.2 \mathrm{~cm}\), and the tubes are arranged in-line with longitudinal and transverse pitches of \(S_{L}=S_{T}=5 \mathrm{~cm}\). There are eight rows in the flow direction with eight tubes in each row. Determine the rate of heat transfer per unit length of the tubes and the pressure drop across the tube bank. Evaluate the air properties at an assumed mean temperature of \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). Is this a good assumption?

Air at \(15^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) flows over a \(0.3-\mathrm{m}\)-wide plate at \(65^{\circ} \mathrm{C}\) at a velocity of $3.0 \mathrm{~m} / \mathrm{s}$. Compute the following quantities at \(x=x_{\mathrm{cr}}\) : (a) Hydrodynamic boundary layer thickness, \(\mathrm{m}\) (b) Local friction coefficient (c) Average friction coefficient (d) Total drag force due to friction, \(\mathrm{N}\) (e) Local convection heat transfer coefficient, W/m² \(\mathrm{K}\) (f) Average convection heat transfer coefficient, W/m². \(\mathrm{K}\) (g) Rate of convective heat transfer, W

Air \(\left(1 \mathrm{~atm}, 5^{\circ} \mathrm{C}\right)\) with a free-stream velocity of \(2 \mathrm{~m} / \mathrm{s}\) flows in parallel with 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}\(. Determine \)(a)\( the average friction coefficient, \)(b)$ the average convection heat transfer coefficient, and (c) the average convection heat transfer coefficient using the modified Reynolds analogy, and compare with the result obtained in \((b)\).

Four power transistors, each dissipating \(10 \mathrm{~W}\), are mounted on a thin vertical aluminum plate $(k=237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\( \)22 \mathrm{~cm} \times 22 \mathrm{~cm}$ in size. The heat generated by the transistors is to be dissipated by both surfaces of the plate to the surrounding air at \(20^{\circ} \mathrm{C}\), which is blown over the plate by a fan at a velocity of \(5 \mathrm{~m} / \mathrm{s}\). The entire plate can be assumed to be nearly isothermal, and the exposed surface area of the transistor can be taken to be equal to its base area. Determine the temperature of the aluminum plate. Evaluate the air properties at a film temperature of \(40^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).