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Heat and Mass Transfer

During air cooling of potatoes, the heat transfer coefficient for combined convection, radiation, and evaporation is determined experimentally to be as shown: Air Velocity, m/s: 0.66, 1.00, 1.36, 1.73; Heat transfer Coefficient, W/m^2K: 14.0, 19.1, 20.2, 24.4 . Consider an 8-cm-diameter potato initially at 20C with a thermal conductivity of 0.49 W/mK. Potatoes are cooled by refrigerated air at 5 C at a velocity of 1 m/s. Determine the initial rate of heat transfer from a potato, and the initial value of the temperature gradient in the potato at the surface.

A metallic airfoil of elliptical cross section has a mass of 50 kg, surface area of 12 m^2, and a specific heat of 0.50 kJ/kgK. The airfoil is subjected to air flow at 1 atm, 25 C, and 5 m/s along its 3-m-long side. The average temperature of the airfoil is observed to drop from 160 C to 150 C within 2 min of cooling. Assuming the surface temperature of the airfoil to be equal to its average temperature and using momentum-heat transfer analogy, determine the average friction coefficient of the airfoil surface.

A 15 cm x 20 cm circuit board is being cooled by forced convection of air at 1 atm. The heat from the circuit board is estimated to be 1000 W/m^2. If the air stream velocity is 3 m/s and the shear stress of the circuit board surface is 0.075 N/m^2, determine the temperature difference between the circuit board surface temperature and the airstream temperature. Evaluate the fluid properties at 40 C.

Mercury at 25 C flows over a 3-m-long and 2-m-wide flat plate maintained at 75 C with a velocity of 0.8 m/s. Determine the rate of heat transfer from the entire plate.

Consider a hot automotive engine, which can be approximated as a 0.5-m-high, 0.40-m-wide, and 0.8-m-long rectangular block. The bottom surface of the block is at a temperature of 100 C and has an emissivity of 0.95. The ambient air is at 20 C, and the road surface is at 25 C. Determine the rate of heat transfer from the bottom surface of the engine block by convection and radiation as the car travels at a velocity of 80 km/h. Assume the flow to be turbulent over the entire surface because of the constant agitation of the engine block.

An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 10 percent of the electrical energy it consumes into light while converting the remaining 90 percent into heat. Consider a 10-cm-diameter 100-W lightbulb cooled by a fan that blows air at 30 C to the bulb at a velocity of 2 m/s. The surrounding surfaces are also at 30 C, and the emissivity of the glass is 0.9. Assuming 10 percent of the energy passes through the glass bulb as light with negligible absorption and the rest of the energy is absorbed and dissipated by the bulb itself, determine the equilibrium temperature of the glass bulb.

Cooling water available at 10 C is used to condense steam at 30 C in the condenser of a power plant at a rate of 0.15 kg/s by circulating the cooling water through a bank of 5-m-long 1.2-cm-internal-diameter thin copper tubes. Water enters the tubes at a mean velocity of 4 m/s and leaves at a temperature of 24 C. The tubes are nearly isothermal at 30 C. Determine the average heat transfer coefficient between the water, the tubes, and the number of tubes needed to achieve the indicated heat transfer rate in the condenser.

Water is flowing in fully developed conditions through a 3-cm diameter smooth tube with a mass flow rate of 0.02 kg/s at 15 C. Determine (a) the maximum velocity of the flow in the tube and (b) the pressure gradient for the flow.

A metallic airfoil of elliptical cross section has a mass of 50 kg, surface area of 12 m^2, and a specific heat of 0.50 kJ/kgK. The airfoil is subjected to air flow at 1 atm, 25 C, and 5 m/s along its 3-m-long side. The average temperature of the airfoil is observed to drop from 160 C to 150 C within 2 min of cooling. Assuming the surface temperature of the airfoil to be equal to its average temperature and using momentum-heat transfer analogy, determine the average friction coefficient of the airfoil surface.

A 15 cm x 20 cm circuit board is being cooled by forced convection of air at 1 atm. The heat from the circuit board is estimated to be 1000 W/m^2. If the air stream velocity is 3 m/s and the shear stress of the circuit board surface is 0.075 N/m^2, determine the temperature difference between the circuit board surface temperature and the airstream temperature. Evaluate the fluid properties at 40 C.

Mercury at 25 C flows over a 3-m-long and 2-m-wide flat plate maintained at 75 C with a velocity of 0.8 m/s. Determine the rate of heat transfer from the entire plate.

Consider a hot automotive engine, which can be approximated as a 0.5-m-high, 0.40-m-wide, and 0.8-m-long rectangular block. The bottom surface of the block is at a temperature of 100 C and has an emissivity of 0.95. The ambient air is at 20 C, and the road surface is at 25 C. Determine the rate of heat transfer from the bottom surface of the engine block by convection and radiation as the car travels at a velocity of 80 km/h. Assume the flow to be turbulent over the entire surface because of the constant agitation of the engine block.

An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 10 percent of the electrical energy it consumes into light while converting the remaining 90 percent into heat. Consider a 10-cm-diameter 100-W lightbulb cooled by a fan that blows air at 30 C to the bulb at a velocity of 2 m/s. The surrounding surfaces are also at 30 C, and the emissivity of the glass is 0.9. Assuming 10 percent of the energy passes through the glass bulb as light with negligible absorption and the rest of the energy is absorbed and dissipated by the bulb itself, determine the equilibrium temperature of the glass bulb.

Cooling water available at 10 C is used to condense steam at 30 C in the condenser of a power plant at a rate of 0.15 kg/s by circulating the cooling water through a bank of 5-m-long 1.2-cm-internal-diameter thin copper tubes. Water enters the tubes at a mean velocity of 4 m/s and leaves at a temperature of 24 C. The tubes are nearly isothermal at 30 C. Determine the average heat transfer coefficient between the water, the tubes, and the number of tubes needed to achieve the indicated heat transfer rate in the condenser.

Water is flowing in fully developed conditions through a 3-cm diameter smooth tube with a mass flow rate of 0.02 kg/s at 15 C. Determine (a) the maximum velocity of the flow in the tube and (b) the pressure gradient for the flow.

A fan is installed in a 3.5 m^3 sealed box containing air at 101 kPa and 20 C. The exterior of the box is perfectly insulated. The fan does 250 W of work in stirring the air and operates for 1 h. Find the final temperature and pressure of the air. Ignore the temperature change of any fan parts.

Air (1atm) entered into a 5-mm diameter circular tube at an average velocity of 5 m/s. The tube wall is maintained at a constant surface temperature. Determine the convection heat transfer coefficient for (a) a 10-cm long tube and (b) a 50-cm long tube. Evaluate the air properties at 50 C.

Liquid water flows at a mass flow rate of 0.7 kg/s through a concentric annulus tube with the inlet and outlet mean temperatures of 20C and 80C, respectively. The concentric annulus tube has inner and outer diameters of 10 mm and 100 mm, respectively. The inner tube wall is maintained with a constant surface temperature of 120 C, while the outer tube surface is insulated. Determine the length of the concentric annulus tube.

An electronic device may be modeled as three plane layers, as shown in the figure. The entire package is cooled on both sides by air at 20C. Heat is generated in a very thin layer between two contacting surfaces at a rate of 500 /m^2 , as shown. The heat transfer coefficient on both sides is 8.7 /m^2 K . Assume the layers are very large in extent in the direction not shown. Using data in the figure below, calculate the temperature T_2 .

An elevator is required to carry eight people to the top of a 12-story building in less than 1 min. A counter weight is used to balance the mass of the empty elevator cage. Assume that an average person weighs 155 lbf and that each story has a height of 12 ft. What is the minimum size of motor (in hp) that can be used in this application?

A copper busbar of length 40 cm carries electricity and produces 4.8 W in joule heating. The cross-section is square, as shown in the figure, and is covered with insulation of thermal conductivity 0.036 W/mK. All four sides are cooled by air at 20 C with an average heat transfer coefficient of 18 W/m^2 K. Assuming the copper is isothermal, estimate the maximum temperature of the insulation.

A high torque motor has an approximately cylindrical housing 9.5 in. long and 6 in. in diameter. The motor delivers 1/8 hp in steady operation and has an efficiency of 0.72. All the heat generated by motor losses is removed by natural convection and radiation from the outer surface of the housing. The convective coefficient is 1.68 tu/h ft^2 F , and the housing emissivity is 0.91. If the surroundings are at 58 F, what is the housing’s outer surface temperature?

A CPU chip with a footprint of 3 cm by 2 cm is mounted on a circuit board. The chip generates 0.31 W/cm^2 and rejects heat to the environment at 28 C by convection and radiation. The outer casing of the chip has an emissivity of .88, and the heat transfer coefficient is 48 W/m^2 K. Neglecting the thickness of the chip and any conduction into the circuit board, calculate the chip surface temperature.

Air (1atm) entered into a 5-mm diameter circular tube at an average velocity of 5 m/s. The tube wall is maintained at a constant surface temperature. Determine the convection heat transfer coefficient for (a) a 10-cm long tube and (b) a 50-cm long tube. Evaluate the air properties at 50 C.

Liquid water flows at a mass flow rate of 0.7 kg/s through a concentric annulus tube with the inlet and outlet mean temperatures of 20C and 80C, respectively. The concentric annulus tube has inner and outer diameters of 10 mm and 100 mm, respectively. The inner tube wall is maintained with a constant surface temperature of 120 C, while the outer tube surface is insulated. Determine the length of the concentric annulus tube.

An electronic device may be modeled as three plane layers, as shown in the figure. The entire package is cooled on both sides by air at 20C. Heat is generated in a very thin layer between two contacting surfaces at a rate of 500 /m^2 , as shown. The heat transfer coefficient on both sides is 8.7 /m^2 K . Assume the layers are very large in extent in the direction not shown. Using data in the figure below, calculate the temperature T_2 .

An elevator is required to carry eight people to the top of a 12-story building in less than 1 min. A counter weight is used to balance the mass of the empty elevator cage. Assume that an average person weighs 155 lbf and that each story has a height of 12 ft. What is the minimum size of motor (in hp) that can be used in this application?

A copper busbar of length 40 cm carries electricity and produces 4.8 W in joule heating. The cross-section is square, as shown in the figure, and is covered with insulation of thermal conductivity 0.036 W/mK. All four sides are cooled by air at 20 C with an average heat transfer coefficient of 18 W/m^2 K. Assuming the copper is isothermal, estimate the maximum temperature of the insulation.

A high torque motor has an approximately cylindrical housing 9.5 in. long and 6 in. in diameter. The motor delivers 1/8 hp in steady operation and has an efficiency of 0.72. All the heat generated by motor losses is removed by natural convection and radiation from the outer surface of the housing. The convective coefficient is 1.68 tu/h ft^2 F , and the housing emissivity is 0.91. If the surroundings are at 58 F, what is the housing’s outer surface temperature?

A CPU chip with a footprint of 3 cm by 2 cm is mounted on a circuit board. The chip generates 0.31 W/cm^2 and rejects heat to the environment at 28 C by convection and radiation. The outer casing of the chip has an emissivity of .88, and the heat transfer coefficient is 48 W/m^2 K. Neglecting the thickness of the chip and any conduction into the circuit board, calculate the chip surface temperature.

A well-insulated room with a volume of 60 m^3 contains air initially at 100 kPa and 25 C. A 100-W light bulb is turned on for three hours. Assuming the room is airtight, estimate the final temperature.

The windshield of an automobile is heated on the inside by a flow of warm air. Cold air at -15 F flows over the exterior of the windshield. The heat transfer coefficient on the inside is 16 Btu/hft^2 F, and the heat transfer coefficient on the outside is 49 Btu/hft^2 F . The glass of the windshield has a thickness of 0.25 in. What temperature should the inside air be so that the exterior surface temperature of the windshield is 3 F?

The sun can be approximated as a spherical black body with a surface temperature of 5762 K. The irradiation from the sun as measured by a satellite in earth’s orbit is 1353 W/m^2. The distance from the earth to the sun is approximately 1.5 x 10^11 m. Assuming that the sun radiates evenly in all directions, estimate the diameter of the sun.

A tungsten filament in a 60 W light bulb has a diameter of 0.04 mm and an electrical resistivity of 90 micro ohm cm. The filament loses heat to the environment, which is at 20 C, by thermal radiation. The emissivity of the filament is 0.32 and the voltage across it is 115 V. Find the length of the filament and the filament surface temperature. (Electrical resistance equals electrical resistivity times filament length divided by filament cross-sectional area.)

A living room floor 3 m by 4.5 m is constructed of a layer of oak planks 1.2 cm thick laid over plywood 2.0 cm thick. In winter, the basement air is at 15 C, while the living room air is at 20 C. The heat transfer coefficients on the living room floor and the basement ceiling are 3.6 and 6.8 W/m^2 K, respectiviely. If the home is heated electrically and the cost of electricity is $0.08 per kWh, estimate the cost per month of the energy lost through the floor. If the room is carpeted with wall-to-wall carpeting 1.6 cm thick (k=0.06 W/mK), what would the energy cost be?

A metal plate 16 cm by 8 cm is placed outside on a clear night. The plate, which has an emissivity of 0.7, exchanges heat by radiation with the night sky which is at -40 C. Air at -10 C flows over the top of the plate, cooling it with a heat transfer coefficient of 42 W/m^2 K. The plate is insulated on its underside and heated by an electric resistance heater. How much electric power must be supplied to maintain the plate at 55 C?

An arctic explorer builds a temporary shelter from wind-pack snow. The shelter is roughly hemispherical, with an inside radius of 1.5m. After completing the shelter, the explorer crawls inside and closes off the entrance with a block of snow. Assume the shelter is now airtight and loses negligible heat by conduction through the walls. If the air temperature when the explorer completes the shelter is -10 C, how long will it take before the air temperature inside reaches 10 C? Assume the explorer does not freeze to death or suffocate, but sits patiently waiting for the temperature to rise. The explorer generates body heat at a rate of 300 kJ/h.

The door of a kitchen oven contains a window made of a single pane of ¼-in. thick Pyrex glass. The interior oven temperature is 550 F and the room air is at 68 F. The combined convective/radiative heat transfer coefficient on the oven interior is 1.7 Btu/hft^2 F , and on the oven exterior it is 0.88 Btu/hft^2 F. A toddler comes by and touches the window. Calculate the temperature of the surface that the child’s hand contacts.

The wall of a furnace is a large surface of fire clay brick, which is 6.5 cm thick. The outer surface of the brick is measured to be at 35 C. The inner surface receives a heat flux of 2.3 W/cm^2. Estimate the temperature of the inner surface of the brick.

The windshield of an automobile is heated on the inside by a flow of warm air. Cold air at -15 F flows over the exterior of the windshield. The heat transfer coefficient on the inside is 16 Btu/hft^2 F, and the heat transfer coefficient on the outside is 49 Btu/hft^2 F . The glass of the windshield has a thickness of 0.25 in. What temperature should the inside air be so that the exterior surface temperature of the windshield is 3 F?

The sun can be approximated as a spherical black body with a surface temperature of 5762 K. The irradiation from the sun as measured by a satellite in earth’s orbit is 1353 W/m^2. The distance from the earth to the sun is approximately 1.5 x 10^11 m. Assuming that the sun radiates evenly in all directions, estimate the diameter of the sun.

A tungsten filament in a 60 W light bulb has a diameter of 0.04 mm and an electrical resistivity of 90 micro ohm cm. The filament loses heat to the environment, which is at 20 C, by thermal radiation. The emissivity of the filament is 0.32 and the voltage across it is 115 V. Find the length of the filament and the filament surface temperature. (Electrical resistance equals electrical resistivity times filament length divided by filament cross-sectional area.)

A living room floor 3 m by 4.5 m is constructed of a layer of oak planks 1.2 cm thick laid over plywood 2.0 cm thick. In winter, the basement air is at 15 C, while the living room air is at 20 C. The heat transfer coefficients on the living room floor and the basement ceiling are 3.6 and 6.8 W/m^2 K, respectiviely. If the home is heated electrically and the cost of electricity is $0.08 per kWh, estimate the cost per month of the energy lost through the floor. If the room is carpeted with wall-to-wall carpeting 1.6 cm thick (k=0.06 W/mK), what would the energy cost be?

A metal plate 16 cm by 8 cm is placed outside on a clear night. The plate, which has an emissivity of 0.7, exchanges heat by radiation with the night sky which is at -40 C. Air at -10 C flows over the top of the plate, cooling it with a heat transfer coefficient of 42 W/m^2 K. The plate is insulated on its underside and heated by an electric resistance heater. How much electric power must be supplied to maintain the plate at 55 C?

An arctic explorer builds a temporary shelter from wind-pack snow. The shelter is roughly hemispherical, with an inside radius of 1.5m. After completing the shelter, the explorer crawls inside and closes off the entrance with a block of snow. Assume the shelter is now airtight and loses negligible heat by conduction through the walls. If the air temperature when the explorer completes the shelter is -10 C, how long will it take before the air temperature inside reaches 10 C? Assume the explorer does not freeze to death or suffocate, but sits patiently waiting for the temperature to rise. The explorer generates body heat at a rate of 300 kJ/h.

The door of a kitchen oven contains a window made of a single pane of ¼-in. thick Pyrex glass. The interior oven temperature is 550 F and the room air is at 68 F. The combined convective/radiative heat transfer coefficient on the oven interior is 1.7 Btu/hft^2 F , and on the oven exterior it is 0.88 Btu/hft^2 F. A toddler comes by and touches the window. Calculate the temperature of the surface that the child’s hand contacts.

The wall of a furnace is a large surface of fire clay brick, which is 6.5 cm thick. The outer surface of the brick is measured to be at 35 C. The inner surface receives a heat flux of 2.3 W/cm^2. Estimate the temperature of the inner surface of the brick.

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