Heat Transfer and Energy Flows: Identifying Control Volumes and Processes in Systems, Study notes of Engineering

Download Heat Transfer and Energy Flows: Identifying Control Volumes and Processes in Systems and more Study notes Engineering in PDF only on Docsity! 1-1 For the following systems, define a control volume and state whether the system is open or closed and steady or unsteady. Identify any and all heat transfer, energy flows, mass flows, and energy transformations flows. a. Rocket b. Pot of boiling water with no lid c. Portable space heater with fan d. The jet airplane in Figure 1-1c e. The house in Figure 1-4 Approach: For each system, identify a control volume with a dotted line and then describe the various processes occurring to the system. Solution: a) Define the control volume to surround the rocket. Because the hot exhaust gases cross the boundary, this is an open system. As the propellant burns, a mass flow exits through the rocket’s nozzle and the mass of the rocket decreases (changes with time), so the system is unsteady. The nozzle is very hot compared to its surroundings, so there is heat transfer across the boundary, but it is negligible compared to the energy flow associated with the hot exhaust gases. The stored energy in the rocket propellant is converted to kinetic energy in the rocket’s nozzle. b) Define the control volume as shown in the figure to the right. Heat transfer crosses the boundary from the gas flame to the pot bottom. Because the water is boiling, water vapor crosses (a mass flow rate) the boundary at the top of the pot, so the mass of the system decreases with time, so this is an unsteady system. The vapor leaving the system removes energy from the system. (Note that if the water was not boiling and heat added, then the mass of the water would remain the same, but the temperature of the water would increase with time, so the system would still be unsteady.) c) Define the control volume as shown in the figure. Electricity crosses the boundary in the wire; electricity is considered work. Air is sucked into and pushed out of the heater by the fan; this is the same mass flow rate crossing the boundary in two locations. Because neither air nor energy is stored in the heater, and the air flow is constant, this is a steady system. (Note that once the electricity is inside the heater, some of the electricity is converted to mechanical work to drive the fan, and some electricity is dissipated in the heater to heat the air. Because neither of these conversion processes results in work or heat crossing the boundary we have defined, we do not have heat transfer or a second work process.) Electricity (mechanical work) is converted to thermal energy in the flowing air and kinetic energy in the air. d) Define a control volume to encompass the airplane. The processes are identical to those identified in part (a) for the rocket. e) Define a control volume as shown in the figure to the right. Heat transfer enters the house due to the solar radiation. Assuming the air outside the house is warmer than the air inside the house, there also is heat transfer from the surroundings into the house. Electricity enters the house to drive the air conditioner; electricity is considered mechanical work. A mass flow of refrigerant enters and leaves the house at different conditions where the control volume cuts through the two pipes. Assuming the air temperatures, solar radiation, and flow rate of refrigerant are constant, this is a steady system. 1- 1 1-2 Describe some of the thermal-fluid systems in a typical residence, define a boundary, and describe the energy and/or mass flows associated with them. Approach: Chose several systems, identify a control volume with a dotted line and then describe the various processes occurring to the system. Solution: a) Define a control volume to surround a refrigerator, as shown in the first diagram; the control volume passes along the surface of the heat exchanger at the back of the refrigerator. Assume the cooling unit is operating. Electricity crosses the boundary; electricity is considered work. There is heat transfer from the warmer room to the colder interior of the refrigerator. As the cooling unit is running (for example, to freeze ice cubes), the total energy level in the refrigerator drops, so that the system is unsteady. If the cooling unit is not running, there is no work crossing the boundary, but heat transfer still occurs from the warmer room to the cooler refrigerator interior. The energy level in the refrigerator increases, so the system is unsteady. Note that no mass flows across the boundary, so this is a closed system. Note that the cooling unit has a heat exchanger often on the back of the refrigerator that transfers energy from the hot refrigerant to the cooler room. Depending on where the control volume surface is drawn, the processes occurring will change. Defining the control volume to pass along the surface of the heat exchanger, then this there is a heat transfer process with heat flowing from the surface of the heat exchanger to the room air, but no mass flow, so this is a closed system. If the control volume is drawn farther away from the heat exchange surface to include the air, then there is a mass flow of air at different temperatures into and out of the control volume, but there is no heat transfer; this results in an open system. If the control volume is drawn to cut the tubes conveying the refrigerant, then there is a mass flow of refrigerant at different condition into and out of the control volume, but no heat transfer or mass flow of air, but, again, this is an open system. b) Define a control volume around a gas oven as shown on the figure to the right, and assume the oven has been just turned on. Gas flows (mass flow rate) across the boundary; so this is an open system. Electricity is also flows across the boundary, so there is a work process. Air is needed to burn the gas, so cold air enters and hot exhaust gases exit the control volume, so these are two more mass flows carrying energy that need to be taken into account. The surface of the oven is warmer than the room, so there is a heat transfer process. With time, the oven heats, so this is an unsteady system. If the oven has been on for a long time, and the desired oven temperature has been reached, the oven thermostat maintains the fixed temperature. The gas and air flows remain constant and the temperature is fixed, so this then would be a steady, open system. c) Define a control volume to encompass the lightbulb. No mass crosses the boundary so it is a closed system. Electricity flows to the bulb, so there is a work (power) term. The bulb is hot so there is heat transfer from the bulb to the surrounding air. Likewise, some energy leaves the systems as visible light. When the lightbulb is first turned on, it takes a little while before it reaches a steady temperature, so it would be an unsteady system. After a long time operating, the temperature would stabilize and the system would be steady. 1- 2 1-5 In hydroelectric plants, electric power is generated from the flow of water from a reservoir, such as shown in Figure 1-18. The water flows continuously with a seemingly endless supply. How is the water replenished? Where does the energy in the water come from that is converted to electrical power? Approach: The question can be answered with either an open system analysis or a closed system analysis. For the open system, choose a control volume that includes the dam, the reservoir, and the river water just downstream of the dam. For the closed system, choose a control volume that includes all the water on the planet. Solution: a) Define a control volume that includes the dam, the reservoir, and the river water just downstream of the dam. This is an open system, with mass entering and leaving. Water flows into the reservoir from an upstream river and groundwater sources. Water leaves via the downstream river. If water enters the control volume at a higher flow rate than it leaves, the reservoir water level rises and the system is unsteady. Conversely, if water drains from the reservoir more quickly than it is replenished, the water level falls. If the flow rates are equal, the system is in steady state. This choice of control volume is not useful for determining how the water is replenished. An energy balance on the control volume shows that the potential energy of the water decreases as it flows from the reservoir to the downstream river. This potential energy is converted into work in the hydroturbine and into kinetic energy of the downstream river water. b) Define a control volume that includes all the water on the earth. No water enters or leaves this control volume, so it is a closed system. The water at the base of the dam flows down the river and empties into an ocean. Water evaporates from the ocean surface and is suspended in the air as water vapor and clouds. The water is transported over the land by air currents and eventually falls to the earth as rain, snow or hail. The water runs over the land and soaks into the soil. Some water is stored as snow or ice and later melts into liquid form. Both the runoff and the groundwater eventually reach rivers, sometimes passing through streams, swamps, lakes and ponds. Some of the river water is at a location upstream of the dam and acts to replenish the supply of water. An energy balance on the control volume reveals that heat is added to the earth’s water by the sun and by internal heat generation within the earth’s crust (fission reactions). Work is done by the hydroturbine in the power plant (shown in the figure as being along the Nile river). Thus the turbine work comes from solar or geothermal heat. The river water is replenished because the input heat is driving water circulation on the earth. There are, of course, many more heat and work interactions with the earth’s water than the two shown. 1- 5 1-6 The radiator of a car is a heat exchanger. Energy from the hot water that flows through the heat exchanger is transferred to the cooler air that also flows through the radiator. For the three control volumes defined below, state if the system is steady or unsteady, open or closed, and what heat transfer, energy flows, mass flows, and energy transformations occur. a. Water b. Air c. Complete heat exchanger Approach: For the three systems specified, clearly identify the control volumes with dotted lines and then describe the various processes occurring to the systems. Solution: a) Define a control volume (CV I) to surround the water flowing through the car radiator. Assume the air flow rate and inlet temperature are constant; also assume the water flow rate and inlet temperature are constant. Mass (water) flows across the boundary, so this is an open system. Heat flows from the water across the boundary to the air, so there is a heat transfer process. Everything is constant, so this is a steady system. No mechanical work occurs. b) Define a control volume (CV II) to surround the air flowing through the car radiator. Assume the air flow rate and inlet temperature are constant; also assume the water flow rate and inlet temperature are constant. Mass (air) flows across the boundary, so this is an open system. Heat flows from the water across the boundary to the air, so there is a heat transfer process. Everything is constant, so this is a steady system. No mechanical work occurs. Note that I IIQ Q= − because of the sign convention. c) Define a control volume (CV I + CV II) to encompass the complete heat exchanger, and assume the outside surface of the heat exchanger is well insulated. Assume the air flow rate and inlet temperature are constant; also assume the water flow rate and inlet temperature are constant. Mass (air and water) flows across the boundary, so this is an open system. Everything is constant, so this is a steady system. No mechanical work occurs. Note that there is no heat transfer. Heat transfer occurs only across boundaries. The energy flowing from the water to the air is internal to the control volume and not across a boundary, so by definition, there is no heat transfer. 1- 6 1-7 An acorn is planted in the ground. After many years, the acorn grows into a mighty oak tree. Define a system, and describe the processes involved. Where did the mass in the tree come from? Approach: Define a control volume that includes the tree and the neighboring air and soil. Discuss mass flow and energy transformations. Solution: Define a control volume around the tree including the neighboring air, the root system, and the surrounding soil. The system is open, since mass in the form of air, water, and organic materials crosses the control volume over time. The tree grows, so the system is transient. Sunlight enters the control volume and provides energy for photosynthesis. This energy is stored in the tree as chemical energy in the molecules. The tree is composed of organic molecules with four main constituents: carbon, hydrogen, oxygen, and nitrogen. The tree absorbs carbon dioxide (CO2) from the air, reduces it, and returns oxygen to the atmosphere. The tree also draws water (H2O) and dissolved nutrients (which contain nitrogen) through the roots, trunk and branches. Much of the mass in the tree comes from the carbon in the surrounding air. 1- 7 1-10 A hot cup of coffee is placed on a tabletop to cool. Define a control volume, and state if the system is steady or unsteady, open or closed, and what heat transfer, energy flows, mass flows, and energy transformations occur. Approach: Define a control volume around the coffee in the cup. Choose two time periods – one short so that negligible evaporation occurs, and one long so that significant evaporation occurs. Solution: Define a control volume around the coffee in the cup, as shown. If we take a relatively short time period, such as one hour, we may assume that a negligible amount of coffee evaporates and the system is a closed system. The system is unsteady because the coffee cools during the hour. Heat is transferred from the exposed top of the liquid surface by convection and heat conducts into the sides and bottom of the coffee cup. No work is done on or by the coffee. The internal energy of the coffee decreases as heat is transferred from it. If we choose a relatively long time period, such as a week, then we need an open system analysis. During the week, the coffee will not only cool, but also evaporate. This is an unsteady open system, since mass crosses the control volume as water vapor. Energy leaves by heat transfer as before and also is removed by evaporation. 1- 10 1-11 The water in a canal lock is at the downstream river level and the gates are opened. A boat enters the locks and the downstream gates are closed. A valve is opened, and water from upstream flows into the lock, raising the boat. After the water reaches the upstream river level, the upstream gates are opened, and the boat travels upstream. Finally, the first valve is closed and a second valve is opened, allowing the water in the lock to drain to the downstream river level. Another boat arrives from downstream, and the process is repeated. Neglect the energy required to open and close the gates and valves. Where does the energy come from to raise the boat? Approach: Define a control volume around the canal lock. Alternatively, draw a control volume around the entire earth to show the primary source of the energy used to raise the boat. Solution: Define a control volume around the canal lock. This is an open, transient system, with water and boats entering and leaving. In the context of this control volume, the energy to raise the boat comes from the potential energy stored in the water upstream of the canal. We may also choose a control volume that encloses all the water on the earth. This is a closed, transient system. Heat enters this control volume from the sun and also from nuclear reactions within the crust of the earth. The heat energy evaporates water from the surface of all the bodies of water on the earth. The water is transported throughout the earth by wind and returns to the land as rain, snow, or hail. Water runs into the river upstream of the canal, and acts to raise the boat. Thus the ultimate source of the power to lift the boat is sunlight and geothermal energy. 1- 11 1-12 A closed pan of cold water is placed on a burner of an electric stove, which is already turned on. For the control volumes defined below state if the system is steady or unsteady, open or closed, and what heat transfer, energy flows, mass flows, and energy transformations occur. a. Pan of water b. Burner c. Pan of water plus burner Approach: For the three systems specified, clearly identify the control volumes with dotted lines and then describe the various processes occurring to the systems. Solution: a) Define a control volume (CV I) surrounding the pan of water. Heat crosses the boundary into the control volume from the burner beneath the pan. Because the cold water does not boil initially, no vapor leaves the pan, so the mass is constant, but as the temperature of the water increases, the energy level increases. Thus, this is a closed, unsteady system. No mechanical work occurs. As the temperature of the water/pan combination increases, there is heat transfer from the pan to the surrounding air. The heat transfer is converted to internal energy. b) Define a control volume (CV II) around the burner on the electric stove. Electricity crosses the boundary; electricity is considered mechanical work. Heat transfer crosses the boundary from the heater to the bottom of the pan. The mass is constant. Assume the operating temperature level of the burner is attained quickly, so this is a closed, steady system. The electricity (mechanical energy) is converted to heat. Note that I IIQ Q= − because of the sign convention. c) Define a control volume (CV III) around the pan of water and burner. Electricity crosses the boundary; electricity is considered mechanical work. Because the cold water does not boil initially, no vapor leaves the pan, so the mass is constant but as the temperature of the water increases, the energy level increases. Thus, this is a closed, unsteady system. As the temperature of the water/pan combination increases, there is heat transfer from the pan to the surrounding air. The electricity (mechanical energy) is converted to internal energy. 1-13 Water from a home swimming pool is pumped through a filter and returned to the pool. If the system is all the water in the pool and filter, is this an open or closed system? If the system is just the water in the filter, is this an open or closed system? Approach: If mass crosses the control volume, the system is open, otherwise it is closed. Solution: For the first control volume, which is all the water in the pool, we have a closed system. We are assuming that no mass enters or leaves the pool by evaporation, rainfall, or addition of city water from a hose. For the second control volume, which is the water in the filter, we have an open system. Water enters and leaves the filter, crossing the control volume as it does so. 1- 12