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Q1: Problem 1: A 100 ft long pipe transporting steam through the PSU campus is made of AISI 316 stainless steel. The pipe is an 8"Schedule 40 pipe (note that 8" is the nominal dimension but you need to look up the actual dimensions of an 8" Schedule 40pipe!). The pipe transports steam through an open space of air at T,=20°C and a heat transfer coefficient of 10 W/m²K. The steady-state inside wall temperature of the steam pipe is at 140°C. Note that you can look up thermal conductivity and other thermophysical properties in Appendix A of the course textbook,or through other reputable sources. (a) Determine the rate of heat loss from the steam pipe if it DOES NOT have insulation. Ans: 25 kW (b) If we want to reduce the heat loss to 10% of its value from part (a), what thickness of calcium silicate pipe insulation should be added to the outside of the pipe? You can assume that the inside surface temperature of the steam pipe remains at 140°C, as well as the outside air conditions. You may need to use an iterative solver (such as Exceľ's Goal Seek, in Data->What If Analysis->Goal Seek; or perhaps Matlab,or even a guess-and-check method).See Answer
Q2: A plane wall (1m x 1m) has 100 infinitely long fins (k = 200 W/m-K) of rectangular profile. The fins are 0.5 mm thick and equally spaced at a distance of 1 cm (100 fins/m). The fins are exposed to cold air (h= 30 W/m²K) and the temperature difference between the wall and the cold air is 100°C. 1. Determine the heat transfer rate of 100 fins. 2. Determine the total heat transfer rate of the entire system including 100 fins and base walls between the fins.See Answer
Q3: Consider a solid cylinder spinning inside a cylindrical cavity The gap between the cylinder and the wall of the cavity is constant in thickness and it is filed with ol with the to lowing constant properties density p800 kgm', kinematic viscosity ve10m'/s, and thermal conductivity k0.13 Wi(mk). The diameter of the cylinder is D-75mm and the thickness of he gap between the cylinder and the cavity wall is L0.25 mm The cylinder spins at 3600 revolutions per minute and the ol flow is assumed to be laminar, steady and two dimensional The system in shown schematically in Figure Q9. See Answer
Q4: Consider the fow of a fluid through a long circular tube. a) In the case of spatially-uniform and constant heat fux from the tube wall to the fluid, on the same graph sketch the evolution of the inner-surface temperature of the tube and of the mean temperature of the fluid as functions of the stream wise coordinate in fully developed conditions.Explain how the slopes of the two temperature curves are related to the wall heat flux per unit area.[3 marks) b) In the case of spatially-uniform and constant inner-surface temperature of the tube, on the same graph sketch the evolution of the inner-surface temperature of the tube and of the mean temperature of the fluid as functions of the stream wise coordinate. Explain the concept of log-mean temperature difference and how this difference is related to the heat transfer cate from the inner surface to the fluid. c) In the case of constant surface temperature, what is the mean temperature of the fluid at a very large downstream distance? Explain Your answer.12 marks)See Answer
Q5: 4) Air modeled as an ideal gas enters a well-insulated diffuser operating at steady state at 270 K with a velocity of 180 m/s and exits with a velocity of 48.4 m/s. For negligible potential energy effects, determine the exit temperature, in K.See Answer
Q6: You are home for Thanksgiving and are roasting a 20-lb m turkey in a forced convection oven for your family. You are interested in deriving a TIME DEPENDENT TEMPERATURE PROFILE OF TURKEY ASSUME THE FOLLOWING . The turkey can be modeled as a sphere There is no viscous dissipation Air is an ideal gas The airflow is laminar, constant, and fully developed Physical properties are constant The hot air in the oven chamber is held steady at 325 Neglect effects from radiation The airflow is only in the radial direction such that the dominant energy terms are radial convectionand radial conduction.See Answer
Q7: 3-(40 points) Water is discharged from a water reservoir through a circular hole of diameter D=0.05 m at the side wall at a vertical distance H from the free surface. If the exit velocity is 3 m/s andfind the heighT of the tank, H. [The pipe has major loss only]. See Answer
Q8: Large, cylindrical bales of hay used to feed livestock in the winter months are D = 2 m in diameter and are stored end-to end in long rows. Microblal energy generation occurs in the hay and can be excessive if the farmer bales the hay in a too-wet condition. Assuming the thermal conductivity of baled hay to be k= 0.04 W/m K,determine the maximum steady-state hay temperature for wet hay in "C (4 = 100 W/m3). Ambient conditions are To - 0°C and h 25 W/m2 K. (Note: Farmers are concerned with baling hay if too wet as the bales will catch on fire due to the heat generation.)See Answer
Q9: 3) Air enters a turbine operating at steady state at 440 K, 20 bar, with a mass flow rate of 6 kg/s, and exits at 290 K, 5 bar. The velocities at the inlet and exit are 18 m/s and 30 m/s,respectively. The air is modeled as an ideal gas, and potential energy effects can be neglected. If the power developed is 815 kW, determine the rate of heat transfer, in kW, for a control volume enclosing the turbine.See Answer
Q10: 2) Water vapor enters a turbine operating at steady state at 500°C, 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of 9.48 m³/s. Find the power developed by the turbine, in kW.See Answer
Q11: The cross-section of a long cylindrical fuel element in a nuclear reactor is shown. Energy generation occurs uniformly in the thorium fuel rod which is of diameter D = 25 mm and is wrapped in a thin aluminum cladding. It is proposed that, under steady-state, conditions the system operates with a generation rate of 4-7x 108 W/m3 and cooling system characteristics of Too = 95°C and h= 7000 w/m2 K. Is this proposal satisfactory? (Hint: Think about material melting) * True * FalseSee Answer
Q12: FILL IN TH BLANKS In the property table based on a mass of 1 ka of each substance See Answer
Q13: 1) A well-insulated turbine operating at steady state develops 28.75 MW of power for a steam flow rate of 50 kg/s. The steam enters at 25 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects,determine the inlet temperature, in °C.See Answer
Q14: Determine the following design parameters for heat exchanger, HX2 Temperature difference diagram b. The required duty . The required heat exchange surface area 1. The heat exchanger with the smallest number of plates, Small, Medium or Large,required to achieve this surface area, based on the specified surface area of a plate for each configuration.See Answer
Q15: Determine the following design parameters for heat exchanger, HX1 a. Temperature difference diagram b. The required duty c. The required heat exchange surface area d. The heat exchanger with the smallest number of plates, Small, Medium or Large,required to achieve this surface area, based on the specified surface area of a plate for each configuration.See Answer
Q16: 5) Determine the following design parameters for the cooling process а.The electrical power required to drive the refrigeration compressor, in order to meet the desired cooling duty.See Answer
Q17: 2) Determine the following design parameters for the heating process a. The required mass flow rate of the brine mixture b. The mass flow rate of steam that would be required to meet the heating duty, in units ofka/hrSee Answer
Q18: 5. For the following materials/situations, determine the maximum thickness (or diameter for cylinders or spheres) for which the lumped capacitance model can be used (i.e., Bi = 0.1) and the temperature of the object can be assumed to be uniform throughout the material as it heats or cools. A. A large flat sheet of tin is cooled from 400 K to 350 K by dropping it in a large vat of water at 298 K with hwater= 138.7 W/m?-K. (you may look up ktin @ 400K) B. A large flat sheet of plate glass is cooled from 400 to 350 K by dropping it in a large vat of water at 298 K with hwater = 138.7 W/m?-K (you may look up kglass @ 300K) C. A solid cylinder made of tin is initially at 400 K and cools in a large vat of water at 298 K with hwater = 138.7 W/m^2-K D. A solid cylinder made of tin is initially at 400 K and cools using air at 298 K with hair = 27.4 W/m²-K E. A solid sphere made of aluminum is heated from 300 K using air at 500 K with hair = 41.7 W/m^2-K F. A hot pancake at 330 K is flipped in the air at 298 K with hair = 27.4 W/m²-K You may treat the pancake as cooked cake batter - and look up k at 300 K (it's in our appendix!). You should treat the pancake as a flat disc (i.e. a slab geometry, not a cylinder). G. A donut hole (spherically-shaped cooked cake batter) comes out of the fryer at 400 K and is cooled by air at 298 K with hair = 27.4 W/m^2-K. H. A donut hole (spherically-shaped cooked cake batter) comes out of the fryer at 400 K and is cooled by air using a fan at 298 K with hair = 88.5 W/m²-K.See Answer
Q19: 6. A 20-m long cylindrical pure iron rod with diameter 3.0 cm initially at 600 K is immersed in large bath of engine oil at 320 K. The oil has a convective heat transfer coefficient of 24.0 W/m²-K; other properties can be found in Table A.5. The properties of iron can be found in Table A.1 You may ignore heat transfer by radiation, and heat transfer from the flat ends of the cylinder. A. Can lumped capacitance by used to solve for T(t)? B. Determine the T(r) temperature profile for the rod after 20 seconds being immersed in the oil, and 5.0 minutes after immersion (sketch this on a T(r) vs. r plot; be as accurate as possible). C. How long will it take for the rod to cool to 400 K? D. If the oil were mixed so that it had turbulent flow and ho = 1480 W/m²-K, show QUALITATIVELY on a plot how the temperature profiles T(r) would look. Discuss any differences with your answer in B.See Answer
Q20: (20)Plot the functions e V and 1-e versus log io t from t = 10 ² to t = 102. Have two curves on the plot for each function, one for t=1 and one for T=.1See Answer

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