Air at $20^\circ C$ with a convection heat transfer coefficient of $20 W/m^2 \cdot K$ blows over a pond. The surface temperature of the pond is at $40^\circ C.$ Determine the heat flux between the surface of the pond and the air.

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.

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.

A solid plate, with a thickness of 15 cm and a thermal conductivity of $80 W/m \cdot K,$ is being cooled at the upper surface by air. The air temperature is $10^\circ C,$ while the temperatures at the upper and lower surfaces of the plate are 50 and $60^\circ C,$ respectively. Determine the convection heat transfer coefficient of air at the upper surface and discuss whether the value is reasonable or not for force convection of air.

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.

Air at 20-C blows over a hot plate 50 by 75 cm maintained at 250-C. The convection heat-transfer coefficient is 25 W/m2 - •C. Calculate the heat transfer.

Air at 20 degree C with a convection heat transfer coefficient of $20 W / m^2 \cdot K$ blows over a pond. The surface temperature of the pond is at 40 degree C. Determine the heat flux between the surface of the pond and the air.

An AISI 316 stainless steel spherical container is used for storing chemicals undergoing exothermic reaction that provides a uniform heat flux of $60 kW/m^2$ to the container’s inner surface. The container has an inner diameter of 1 m and a wall thickness of 5 cm. For safety reason to prevent thermal burn on individuals working around the container, it is necessary to keep the container’s outer surface temperature below $50^\circ C.$ If the ambient temperature is $23^\circ C,$ determine the necessary convection heat transfer coefficient to keep the container’s outer surface temperature below $50^\circ C.$ Is the necessary convection heat transfer coefficient feasible with free convection of air? If not, discuss other option to prevent the container’s outer surface temperature from causing thermal burn.

A series of ASME SA-193 carbon steel bolts are bolted onto the upper surface of a metal plate. The metal plate has a thickness of $3 \mathrm{~cm}$, and its thermal conductivity is $15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. The bottom surface of the plate is subjected to a uniform heat flux of $5 \mathrm{~kW} / \mathrm{m}^2$. The upper surface of the plate is exposed to ambient air with a temperature of $30^{\circ} \mathrm{C}$ and a convection heat transfer coefficient of $10 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$. The ASME Boiler and Pressure Vessel Code (ASME BPVC.IV-2015, HF-300) limits the maximum allowable use temperature to $260^{\circ} \mathrm{C}$ for the SA-193 bolts. Formulate the variation of temperature in the metal plate, and find the temperatures at $x=0,1.5$, and $3.0 \mathrm{~cm}$. Would the SA-193 bolts comply with the ASME code?

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 $1^\circ C.$

The inner and outer surfaces of a 0.5-cm-thick 2-m x 2-m window glass in winter are 15$^\circ{}$C and 6$^\circ{}$C, respectively. If the thermal conductivity of the glass is 0.78 W/m$^\circ{}$C, determine the amount of heat loss, in kJ, that occurs through the glass over a period of 10 h. What would your answer be if the glass were 1 cm thick?

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.

An engine block with a surface area measured to be $0.95 m^2$ generates a power output of 50kW with a net engine efficiency of 35%. The engine block operates inside a compartment at $157^\circ C$ and the average convection heat transfer coefficient is $50W/m^2 \cdot K.$ If convection is the only heat transfer mechanism occurring, determine the engine block surface temperature.