A -395 kg/s of water is to be cooled from $90^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$ in a shell and tube heat exchanger having four shell passes and eight tube passes. The cooling fluid is also water with a flow rate of $5 \mathrm{~kg} / \mathrm{s}$ that enters at a temperature of $50^{\circ} \mathrm{C}$. The overall heat-transfer coefficient is $800 \mathrm{~W} / \mathrm{m}^2,{ }^{\circ} \mathrm{C}$. Determine the total area of the heat exchanger assuming all four shells are the same size.

Consider a very long rectangular fin attached to a flat surface such that the temperature at the end of the fin is essentially that of the surrounding air, i.e. $20^{\circ} \mathrm{C}$. Its width is $5.0 \mathrm{~cm}$; thickness is $1.0 \mathrm{~mm}$; thermal conductivity is $200 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$; and base temperature is $40^{\circ} \mathrm{C}$. The heat transfer coefficient is $20 \mathrm{~W} / \mathrm{m}^{2}$. $K$. Estimate the fin temperature at a distance of $5.0 \mathrm{~cm}$ from the base and the rate of heat loss from the entire fin.

Nitrogen $(N_2)$ initially at $40^{\circ} \mathrm{F} \text { and } 14.7 \mathrm{lbf} / \mathrm{in}^{2}$ fills a closed, rigid, $6.5-ft^3$ tank fitted with a paddle wheel. During a process, the paddle wheel provides 5 Btu of energy transfer by work to the gas. The gas temperature reaches $80^\circ F$ at the end of the process. Assuming ideal gas behavior, determine the mass of nitrogen, in lb, and the heat transfer, in Btu. Kinetic and potential energy effects can be ignored.

You have just washed your hair and you now blowdry it in a room with 23$^{0} \mathrm{C}$, $\phi$ = 60%, (1). The Dryer, 500 W, heats the air to 49$^{0} \mathrm{C}$, (2), blows it through your hair, where the air becomes saturated(3), and then flows on to hit a window, where it cools to 15$^{\circ} \mathrm{C}$ (4). Find the relative humidity at state 2, the heat transfer per kilogram of dry air in the dryer, the air flow rate, and the amount of water condensed on the window, if any.

Octane gas $\mathrm{C}_8 \mathrm{H}_{18}$ at $25^{\circ} \mathrm{C}$ enters a jet engine and burns completely with $300 \%$ of theoretical air entering at $25^{\circ} \mathrm{C}$, $1 \mathrm{~atm}$ with a volumetric flow rate of $42 \mathrm{~m}^3 / \mathrm{s}$. Products of combustion exit at $990 \mathrm{~K}, 1 \mathrm{~atm}$. If the fuel and air enter with negligible velocities, determine the velocity of the exiting combustion products, in $\mathrm{m} / \mathrm{s}$. Neglect heat transfer between the engine and its surroundings.

A transistor with a height of $0.4 \mathrm{~cm}$ and a diameter of $0.6 \mathrm{~cm}$ is mounted on a circuit board. The transistor is cooled by air flowing over it with an average heat transfer coefficient of $30 \mathrm{~W} / \mathrm{m}^{2} \cdot{ }^{\circ} \mathrm{C}$. If the air temperature is $55^{\circ} \mathrm{C}$ and the transistor case temperature is not to exceed $70^{\circ} \mathrm{C}$, Find the amount of power this transistor can dissipate safely. Disregard any heat transfer from the transistor base.

In a heat exchanger, as shown in the accompanying figure, air flows over brass tubes of $1.8-\mathrm{cm} 1 \mathrm{D}$ and $2.1-\mathrm{cm}$ OD containing steam. The convection heat transfer coefficients on the air and steam sides of the tubes are $70 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$ and $210 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, respectively. Calculate the overall heat transfer coefficient for the heat exchanger (a) based on the inner tube area and (b) based on the outer tube area.

Ammonia enters a valve as saturated liquid at 9 bar and undergoes a throttling process to a pressure of $2\ \text{bar}$. Determine the rate of entropy production per unit mass of ammonia flowing, in $\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}$. If the valve were replaced by a power-recovery turbine operating at steady state, determine the maximum theoretical power that could be developed per unit mass of ammonia flowing, in $\mathrm{kJ} / \mathrm{kg}$, and comment. In each case, ignore heat transfer with the surroundings and changes in kinetic and potential energy.

Obtain a relation for the fin efficiency for a fin of constant cross-sectional area $A_{c}$, perimeter $p$, length $L$, and thermal conductivity $k$ exposed to convection to a medium at $T_{\infty}$ with a heat transfer coefficient $h$. Assume the fins are sufficiently long so that the temperature of the fin at the tip is nearly $T_{\infty}$. Take the temperature of the fin at the base to be $T_{b}$ and neglect heat transfer from the fin tips. Simplify the relation for $(a)$ a circular fin of diameter $D$ and $(b)$ rectangular fins of thickness $t$.

In an air conditioner, 12.65 MJ of heat transfer occurs from a cold environment in 1.00 h. (a) What mass of ice melting would involve the same heat transfer? (b) How many hours of operation would be equivalent to melting 900 kg of ice? (c) If ice costs 20 cents per kg, do you think the air conditioner could be operated more cheaply than by simply using ice? Describe in detail how you evaluate the relative costs.

A steam turbine operating at steady state develops 9750 hp. The turbine receives 100,000 pounds of steam per hour at $400 \text { lbf/in. }^{2}$ and $600^{\circ} \mathrm{F}.$ At a point in the turbine where the pressure is $60 \mathrm{lbf} / \mathrm{in} .^{2}$ and the temperature is $300^{\circ} \mathrm{F},$ steam is bled off at the rate of 25,000 lb/h. The remaining steam continues to expand through the turbine, exiting at $2 \mathrm{lbf} / \mathrm{in}^{2}$ and 90% quality. a. Determine the rate of heat transfer between the turbine and its surroundings, in Btu/h. b. Devise and evaluate an exergetic efficiency for the turbine. Kinetic and potential energy effects can be ignored. Let $T_{0}=77^{\circ} \mathrm{F}, p_{0}=1 \mathrm{atm}.$

Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at 10 MPa, $480^\circ C,$ and the condenser pressure is 6 kPa. Isentropic efficiencies of the turbine and pump are 84% and 73%, respectively. Determine for the cycle a. the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam flowing. b. the thermal efficiency. c. the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam flowing.

Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at $10\ \mathrm{MPa}, 480^{\circ} \mathrm{C}$, and the condenser pressure is $6\ \mathrm{kPa}$. Determine for the cycle (a) the heat transfer to the working fluid passing through the steam generator, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing. (b) the thermal efficiency. (c) the heat transfer from the working fluid passing through the condenser to the cooling water, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing.

Consider the velocity and temperature profiles for airflow in a tube with diameter of 8cm can be expressed as

$$\begin{array}{l}{u(r)=0.2\left[\left(1-(r / R)^{2}\right]\right.} \\ {T(r)=250+200(r / R)^{3}}\end{array}$$

with units in m/s and K, respectively. If the convection heat transfer coefficient is $100 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K},$ determine the mass flow rate and surface heat flux using the given velocity and temperature profiles. Evaluate the air properties at $20^\circ C$ and 1 atm.