A preheater involves the use of condensing steam at $100^{\circ} \mathrm{C}$ on the inside of a bank of tubes to heat air that enters at 1 atm and $25^{\circ} \mathrm{C}$. The air moves at 5 m/s in cross flow over the tubes. Each tube is 1 m long and has an outside diameter of 10 mm. The bank consists of 196 tubes in a square, aligned array for which $S_{T}=S_{L}=15 \mathrm{mm}$. What is the total rate of heat transfer to the air? What is the pressure drop associated with the airflow?

The boundary layer associated with parallel flow over an isothermal plate may be tripped at any x-location by using a fine wire that is stretched across the width of the plate. Determine the value of the critical Reynolds number $R e_{x, c, \mathrm{op}}$ that is associated with the optimal location of the trip wire from the leading edge that will result in maximum heat transfer from the warm plate to the cool fluid.

Simplify.

$$\frac { \frac { 1 } { 2 } + \frac { 1 } { 3 } } { 1 - \frac { 1 } { 6 } }$$

Experimental results for heat transfer over a flat plate with an extremely rough surface were found to be correlated by an expression of the form $N u_{x}=0.04 R e_{x}^{0.9} P r^{1 / 3}$ where $N u_{x}$ is the local value of the Nusselt number at a position x measured from the leading edge of the plate. Obtain an expression for the ratio of the average heat transfer coefficient $\bar{h}_{x}$ to the local coefficient $h_{x}$.

A thermocouple is inserted into a hot air duct to measure the air temperature. The thermocouple $\left(T_{1}\right)$ is soldered to the tip of a steel thermocouple well of length L=0.15 m and inner and outer diameters of $D_{i}=5 \mathrm{mm}$ and $D_{o}=10 \mathrm{mm}$. A second thermocouple $\left(T_{2}\right)$ is used to measure the duct wall temperature. Consider conditions for which the air velocity in the duct is V=3 m/s and the two thermocouples register temperatures of $T_{1}=450 \mathrm{K}$ and $T_{2}=375 \mathrm{K}$. Neglecting radiation, determine the air temperature $T_{\infty}$. Assume that, for steel, $k=35 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$, and, for air $\rho=0.774 \mathrm{kg} / \mathrm{m}^{3}$ $\mu=251 \times 10^{-7} \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}, \quad k=0.0373 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$, and Pr=0.686.

Water $(c_p = 4180 J/kg \cdot K)$ enters the 2.5-cm-internal-diameter tube of a double-pipe counter-flow heat exchanger at $17^\circ C$ at a rate of 1.8 kg/s. Water is heated by steam condensing at $120^\circ C (h_{fg} = 2203 kJ/kg)$ in the shell. If the overall heat transfer coefficient of the heat exchanger is $700 W/m^2 \cdot K,$ determine the length of the tube required in order to heat the water to $80^\circ C$ using (a) the LMTD method and (b) the $\varepsilon — NTU$ method.

A process involves 1.0 kg of steam condensing to water at $100^{\circ} \mathrm{C}.$ (a) The change in entropy of the steam (water) is (1) positive, (2) zero, (3) negative. Why? (b) What is the change in entropy of the steam (water)?

A process involves $0.50 \mathrm{~kg}$ of steam condensing to water at $100^{\circ} \mathrm{C}$.
(a) The change in entropy of the steam (water) is (1) positive, (2) zero, (3) negative. Why?
(b) What is the change in entropy of the steam (water)?

An incompressible fluid flows horizontally in the x–y plane with a velocity given by

$$u=30(y / h)^{1 / 2} \mathrm{m} / \mathrm{s}, \mathrm{v}=0$$

where y and h are in meters and h is a constant. Determine the average velocity for the portion of the flow between y = 0 and y = h.

The altitude in feet y of an albatross who is slowly landing can be given by y = 300 - 50x, where x represents the time in minutes. Graph the equation using the slope and y-intercept.

Consider a sphere with a diameter of 20 mm and a surface temperature of $60^{\circ} \mathrm{C}$ that is immersed in a fluid at a temperature of $30^{\circ} \mathrm{C}$ and a velocity of 2.5 m/s. Calculate the drag force and the heat rate when the fluid is (a) water and (b) air at atmospheric pressure. Explain why the results for the two fluids are so different.

A circular pipe of 25-mm outside diameter is placed in an airstream at $25^{\circ} \mathrm{C}$ and 1-atm pressure. The air moves in cross flow over the pipe at 15 m/s, while the outer surface of the pipe is maintained at $100^{\circ} \mathrm{C}$. What is the drag force exerted on the pipe per unit length? What is the rate of heat transfer from the pipe per unit length?

Create an interesting scenario leading to the following linear programming problem: Minimize c=10x+10y subject to

$$\begin{array}{l}{20 x+40 y \geq 1,000} \\ {30 x+20 y \geq 1,200} \\ {x \geq 0, y \geq 0.}\end{array}$$

When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution. When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population mean?