Thermodynamics

244 | ThermodynamicsR-134a. .Qw,in = Q R,outControl volumeboundarySubstituting, we findm # w 162.982 104.832 kJ/kg 16 kg/min2[ 1100.87 303.852 kJ/kg](b) To determine the heat transfer from the refrigerant to the water, we haveto choose a control volume whose boundary lies on the path of heat transfer.We can choose the volume occupied by either fluid as our control volume.For no particular reason, we choose the volume occupied by the water. Allthe assumptions stated earlier apply, except that the heat transfer is nolonger zero. Then assuming heat to be transferred to water, the energy balancefor this single-stream steady-flow system reduces toE # in E # out dE system >dt 0⎫⎪⎪⎪⎬⎪⎪⎪⎭⎫⎪⎪⎬⎪⎪⎭Rate of net energy transferby heat, work, and massm # w 29.1 kg/min¡ 0 (steady)Rate of change in internal, kinetic,potential, etc., energiesFIGURE 5–38In a heat exchanger, the heat transferdepends on the choice of the controlvolume.Surroundings 20°CHot fluid70°C.Q outFIGURE 5–39Heat losses from a hot fluid flowingthrough an uninsulated pipe or duct tothe cooler environment may be verysignificant.Ẇ eControl volumeẆ shFIGURE 5–40Pipe or duct flow may involve morethan one form of work at the sametime.Rearranging and substituting,E # in E # outQ # w, in m # wh 1 m # wh 2Q # w, in m # w 1h 2 h 1 2 129.1 kg/min2[ 1104.83 62.9822 kJ/kg] 1218 kJ/minDiscussion Had we chosen the volume occupied by the refrigerant as thecontrol volume (Fig. 5–38), we would have obtained the same result for Q . R,outsince the heat gained by the water is equal to the heat lost by the refrigerant.5 Pipe and Duct FlowThe transport of liquids or gases in pipes and ducts is of great importance inmany engineering applications. Flow through a pipe or a duct usually satisfiesthe steady-flow conditions and thus can be analyzed as a steady-flowprocess. This, of course, excludes the transient start-up and shut-down periods.The control volume can be selected to coincide with the interior surfacesof the portion of the pipe or the duct that we are interested in analyzing.Under normal operating conditions, the amount of heat gained or lost bythe fluid may be very significant, particularly if the pipe or duct is long(Fig. 5–39). Sometimes heat transfer is desirable and is the sole purpose ofthe flow. Water flow through the pipes in the furnace of a power plant, theflow of refrigerant in a freezer, and the flow in heat exchangers are someexamples of this case. At other times, heat transfer is undesirable, and thepipes or ducts are insulated to prevent any heat loss or gain, particularlywhen the temperature difference between the flowing fluid and the surroundingsis large. Heat transfer in this case is negligible.If the control volume involves a heating section (electric wires), a fan, ora pump (shaft), the work interactions should be considered (Fig. 5–40). Ofthese, fan work is usually small and often neglected in energy analysis.