2–62 The water in a large lake is to be used to generate electricity by the installation of a hydraulic turbine-generator at a location where the depth of the water is 50 m. Water is to be supplied at a rate of 5000 kg/s. If the electric power generated is measured to be 1862 kW and the generator efficiency is95 percent, determine (a) the overall efficiency of the turbine–generator, (b) the mechanical efficiency of the turbine, and(c) the shaft power supplied by the turbine to the generator.

6. (20 points) A heat pump with refrigerant-134a as the working fluid is used to keep a space at 25Cby absorbing heat from geothermal water that enters the evaporator at 60C at a rate of 0.065 kg/sand leaves at 40C. Refrigerant enters the evaporator at 12C with a quality of 15 percent and leaves at the same pressure as saturated vapor. If the compressor consumes 1.6 kW of power, determine (a)the mass flow rate of the refrigerant, (b) the rate of heat supply, (c) the COP, and (d) the minimum power input to the compressor for the same rate of heat supply.

Steam in a heating system flows through tubes whose outer diameter is D1 =3 cm and whose walls are maintained at a temperature of 120°C. Circular aluminum fins (k = 180W/m.°C) of outer diameters D2 = 6 cm and constant thickness t = 2mm are attached to the tubes. The space between the fins is 3 mm. Heat is transferred to the surrounding air at T = 25 °C, with a convection heattransfer coefficient of h = 60 W/m2.°C Determine the number of fins per meter length Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins.2-

Consider atmospheric air at 20°C and a velocity of 30 m/s flowing over both surfaces of a 1-m-long flat plate that is maintained at 130°C. Determine the rate of heat trans-fer per unit width from the plate for values of the critical Reynolds number corresponding to 10°, 5 × 10°, and 10°.

A house has a composite wall of wood, fiberglass insulation, and plaster board, as indicated in the sketch. On a cold winter day, the convection heat transfer coefficients are h, = 60 W/m2-K and h; = 35 W/m2.K. The total wall surface area is 200 m2. The plasterboard thickness is L,= 10 mm, the glass fiber thickness is L= 100 mm, and the plywood siding thickness is L, = 20 mm. The temperature inside is 7; = 20°C and the temperature outside is T, = -15°C. Determine the total heat loss through the wall. Determine the thermal conductivity of the plaster board, in W/m-K. Determine the value of the inside convection resistance, in °C/W. Determine the value of the fiberglass blanket resistance, in °C/W. Determine the value of the total heat transfer resistance, in °C/W. Determine the value of the heat loss, in kW.

• 8-63 A 15-cm x 20-cm printed circuit board whose components are not allowed to come into direct contact with air for reliability reasons is to be cooled by passing cool air through a 20-cm-long channel of rectangular cross section o.2 cm x14 cm drilled into the board. The heat generated by the electronic components is conducted across the thin layer of the board to the channel, where it is removed by air that enters the channel at 15°C.The heat flux at the top surface of the channel can be considered to be uniform, and heat transfer through other surfaces is negligible. If the velocity of the air at the inlet of the channel is not to exceed 4 m/s and the surface temperature of the channel is to remain under 50°C, determine the maximum total power of the electronic components that can safely be mounted on this circuit board. As a first approximation, assume flow is fully developed in the channel. Evaluate properties of air at a bulk mean temperature of 25°C. Is this a good assumption?

Problem 3. (40 points) An incompressible Newtonian liquid is confined between two concentric cylinders of infinite length-a solid inner cylinder of radius RA and a hollow outer cylinder of radius RB. The inner cylinder rotates at angular velocity o and the outer cylinder is stationary.The flow is steady, laminar, and two-dimensional in the r-0 plane. The flow is axi symmetric, meaning that nothing is a function of the coordinate 0. The flow is also circular so that u,=0everywhere from continuity equation, you do not need to derive this. a. Using the 0-momentum equation, generate an exact expression for the velocity component u,as a function of radius r. Ignore gravity. To simplify the solution method for the ODE, use the substitution of terms described in Figure 9-43 and Lesson I.4 b. Derive an expression for the wall shear stress on the inner rotating cylinder. For RA=3 cm, RB=6.0 cm, loi= 2.635 N:s/m?, and w=1500 rpm, plot the velocity profile ue(r)that you found in part a. Also plot a straight line between Ra to RB (the linear velocity profile for Couette flow between two flat plates). Your plot should be done on the computer using a spreadsheet or Matlab. Include a plot title and label the axes with the variable and dimensions. Include a legend identifying each curve. Use only lines, no symbols, to show your analytical solution. Your plot should only show the range from 3 cm to 6 cm. Is the linear velocity profile (planar Couette flow) accurate for this case? 1. For RA=3 cm, Rs=3.01 cm, loi= 2.635 N:s/m?, and w=1500 rpm, calculate the wall shear stress on the inner cylinder in two ways: first using the expression in part b and then by U.wall neglecting the wall curvature and using the planar Couette flow solution, T = !as youh did in HW1P3. (Show the substitution of numbers into each equation before solving.) What is the relative error when the wall curvature is neglected? Is it appropriate to use the planar Couette flow solution for thin lubricating flows as was done for Homework 1? Give your answer for the shear stress values to six digits of accuracy.

• 8-107 A concentric annulus tube has inner and outer diameters of 25 mm and 100 mm,respectively. Liquid water flows at a mass flow rate of o.05 kg/s through the annulus with the inlet and outlet mean temperatures of 20°C and80°C, 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. Assume flow is fully developed.

2-17 Consider a large 3-cm-thick stainless steel plate in which heat is generated uniformly at a rate of 5 x 10 W/m. Assuming the plate is losing heat from both sides, determine the heat flux on the surface of the plate during steady operation. Answer: 75 kW/m²

11.21 A concentric tube heat exchanger for cooling lubricating oil is comprised of a thin-walled inner tube of 25-mmdiameter carrying water and an outer tube of 45-mmdiameter carrying the oil. The exchanger operates in counterflow with an overall heat transfer coefficient of60 W/m2 K and the tabulated average properties.