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

A hollow spherical iron container with outer diameter 20 cm and thickness 0.2 cm is filled with iced water at $0^\circ C.$ If the outer surface temperature is $5^\circ C,$ determine the approximate rate of heat loss from the sphere, in kW, and therate at which ice melts in the container. The heat of fusion of water is 333.7 kJ/kg.

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

A 300-ft-long section of a steam pipe whose outer diameter is 4 in passes through an open space at $50^\circ F$ The average temperature of the outer surface of the pipe is measured to be $280^\circ F,$ and the average heat transfer coefficient on that surface is determined to be $6 Btu / h \cdot ft^2 ^\circ F$ Determine (a) the rate of heat loss from the steam pipe and (b) the annual cost of this energy loss if steam is generated in a natural gas furnace having an efficiency of 86 percent, and the price of natural gas is $1.10 / therm (1 therm = 100.000 Btu) .

A 300-ft-long section of a steam pipe whose outer diameter is 4 in passes through an open space at $50^{\circ} \mathrm{F}.$ The average temperature of the outer surface of the pipe is measured to be $280^{\circ} \mathrm{F},$ and the average heat transfer coefficient on that surface is determined to be $6 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot^{\circ} \mathrm{F}.$ Determine (a) the rate of heat loss from the steam pipe and (b) the annual cost of this energy loss if steam is generated in a natural gas furnace having an efficiency of 86 percent, and the price of natural gas is $1.10/therm (1 therm = 100,000 Btu).

An aluminum pan whose thermal conductivity is $237 W/m \cdot K$ has a flat bottom with diameter 15 cm and thickness 0.4cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 1400 W. If the inner surface of the bottom of the pan is at $105^\circ C,$ determine the temperature of the outer surface of the bottom of the pan.

Four power transistors, each dissipating 12 W, are mounted on a thin vertical aluminum plate $(k = 237 W/m \cdot K)$ 22 cm × 22 cm in size. The heat generated by the transistors is to be dissipated by both surfaces of the plate to the surrounding air at $20^\circ C,$ which is blown over the plate by a fan at a velocity of 250 m/min. 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 $40^\circ C$ and 1 atm.

A concrete wall, which has a surface area of $20 \mathrm{m}^{2}$ and is 0.30 m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at $25^{\circ} \mathrm{C}$, and the thermal conductivity of the concrete is $1 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. (a) Determine the heat loss through the wall for outer surface temperatures ranging from $-15^{\circ} \mathrm{C}$ to $38^{\circ} \mathrm{C}$, which correspond to winter and summer extremes, respectively. Display your results graphically. (b) On your graph, also plot the heat loss as a function of the outer surface temperature for wall materials having thermal conductivities of 0.75 and $1.25 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. Explain the family of curves you have obtained.

A classroom that normally contains 40 people is to be air-conditioned with window air-conditioning units of 5-kW cooling capacity. A person at rest may be assumed to dissipate heat at a rate of about 360 kJ/h. There are 10 lightbulbs in the room, each with a rating of 100 W. The rate of heat transfer to the classroom through the walls and the windows is estimated to be 15,000 kJ/h. If the room air is to be maintained at a constant temperature of $21^\circ C,$ determine the number of window air-conditioning units required.

Silicon wafer is susceptible to warping when the wafer is subjected to temperature difference across its thickness. Thus, steps needed to be taken to prevent the temperature gradient across the wafer thickness from getting large. As an engineer in a semiconductor company, your task is to determine the maximum allowable heat flux on the bottom surface of the wafer, while maintaining the upper surface temperature at $27^\circ C.$ To prevent the wafer from warping, the temperature difference across its thickness of $500 \mu \mathrm{m}$ cannot exceed $1^\circ C.$

One way of measuring the thermal conductivity of a material is to sandwich an electric thermofoil heater between two identical rectangular samples of the material and to heavily insulate the four outer edges, as shown in the figure. Thermocouples attached to the inner and outer surfaces of the samples record the temperatures. During an experiment, two $0.5 \mathrm{~cm}$ thick samples $10 \mathrm{~cm}$ $\times 10 \mathrm{~cm}$ in size are used. When steady operation is reached, the heater is observed to draw $25 \mathrm{~W}$ of electric power, and the temperature of each sample is observed to drop from $82^{\circ} \mathrm{C}$ at the inner surface to $74^{\circ} \mathrm{C}$ at the outer surface. Find the thermal conductivity of the material at the average temperature.

Four power transistors, each dissipating 12 W, are mounted on a thin vertical aluminum plate 22cm × 22cm in size. The heat generated by the transistors is to be dissipated by both surfaces of the plate to the surrounding air at $25^\circ C,$ which is blown over the plate by a fan. 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. If the average convection heat transfer coefficient is $25 W/m^2 \cdot K,$ determine the temperature of the aluminum plate. Disregard any radiation effects.

The inner and outer surfaces of a 4-m × 7-m brick wall of thickness 30 cm and thermal conductivity $0.69 W/m \cdot K$ are maintained at temperatures of $26^\circ C$ and $8^\circ C,$ respectively. Determine the rate of heat transfer through the wall, in W.

A classroom that normally contains 50 people is to be air-conditioned using window air-conditioning units of 5-kW cooling capacity. A person at rest may be assumed to dissipate heat at a rate of $360 \mathrm{~kJ} / \mathrm{h}$. There are 10 lightbulbs in the room, each with a rating of $100 \mathrm{~W}$. The rate of heat transfer to the classroom through the walls and the windows is estimated to be $12,000 \mathrm{~kJ} / \mathrm{h}$. If the room air is to be maintained at a constant temperature of $21^{\circ} \mathrm{C}$, determine the number of window airconditioning units required.