Water at 10°C is is flowing at 0.8 m/s across a long cylinder that is made of a material that generates heat by 8.5 kW/m³. The cylinder has a diameter of 0.3 m. Thermal conductivity of the cylinder is 28 W/m.°C. Assuming the film temperature is same as the water temperature, find out the surface temperature of the cylinder. Then comment whether the assumption related to film temperature was reasonable. 622 %
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- Thick fluids such as asphalt and waxes and the pipes in which they flow are often heated in order to reduce the viscosity of the fluids and thus to reduce the pumping costs. Consider the flow of such a fluid through a 100-m-long pipe of outer diameter 30 cm in calm ambient air at 0oC. The pipe is heated electrically, and a thermostat keeps the outer surface temperature of the pipe constant at 25oC. The emissivity of the outer surface of the pipe is 0.8, and the effective sky temperature is −30oC. Determine the power rating of the electric resistance heater, in kW, that needs to be used. Also, determine the cost of electricity associated with heating the pipe during a 10-h period under the above conditions if the price of electricity is $0.09/kWh. Properties The properties of air at 1 atm and the film temperature of (Ts+T∞)/2 = (25+0)/2 = 12.5°C are: k = 0.02458 W/m.oC, ν = 1.448x10-5 m2/s, Pr = 0.7330Air is flowing in parallel over the upper surface of aflat plate with a length of 4 m. The first half of the plate length,from the leading edge, has a constant surface temperatureof 50°C. The second half of the plate length is subjected toa uniform heat flux of 86 W/m2. The air has a free streamvelocity and temperature of 2 m/s and 10°C, respectively.Determine the local convection heat transfer coefficients at1 m and 3 m from the leading edge. Evaluate the air propertiesat a film temperature of 30°C. Is the film temperatureTf = 30°C applicable at x = 3 m?. Castor oil at 36 °C flows over a 6 m long and 1 m wide heated plate at 0.06 m/s. For a surfacetemperature of 96 °C, determine (i) the thermal boundary layer thickness at the end of the plate,(ii) the local heat transfer coefficient at the end of the plate, and (iii) the rate of heat transfer fromthe entire plate
- Consider a 50-cm-diameter and 95-cm-long hot water tank. The tank is placed on the roof ofa house. The water inside the tank is heated to 80℃ by a flat-plate solar collector during theday. The tank is then exposed to windy air at 18℃ with an average velocity of 40 km/h duringthe night. Estimate the temperature of the tank after a 45-min period. Assume the tank surfaceto be at the same temperature as the water inside, and the heat transfer coefficient on the topand bottom surfaces to be the same as that on the side surface. Evaluate the air properties at50℃. (Answer: 69.9 ℃)a 6cm diameter shaft rotates at 3000rpm in a 20cm - long bearing with a uniform clearance of 0.2mm. At steady operating conditions, both the bearing and the shaft in the vicinity of the oil gap are at 50°c, and the viscosity and thermal conductivity of lubricating oil are 0.05N.s/m^2 and 0.17W/m. k. By simplifying and solving the continuity, momentum, and energy equations, determine: a) the maximum temperature of oil. b) the rate of heat transfer to the bearing and the shaft, and the mechanical power wassted by the viscous dissipation in the oil?During a cold winter day, wind at 55 km/h is blowing parallel to a 4m high and 10m long wall of a house. If the air outside is at 5 degrees Celsius and the surface temperature of the wall is 12 degrees Celsius , determine the rate of heat loss from the wall by convection. What would your answer be if the wind velocity has doubled? From Table A-1:thermal conductivity, k = 0.0246 W/m degrees Celsiusviscosity, v = 1.4 x 10^-5 m^2/sPrandtl no. Pr = 0.717
- Consider laminar flow of air across a hot circular cylinder. At what point on the cylinder will the heat transfer be highest? What would your answer be if the flow were turbulent?A 6cm diameter shaft rotates at 3000rpm in a 20cm long bearing with a uniform clearance of 0.2mm. At steady operating conditions, both the bearing and shaft in the vicinity of the oil gap are 50°C. The thermal conductivity and the viscosity of the lubricating oil are k=0.17 W/m-K and µ= 0.05 N-s/m2, respectively. By simplifying and solving the differential continuity, momentum and energy equation, determine the maximum temperature of oil. (Hint: Couette flow)Consider a 50-cm-diameter and 95-cm-long hot water tank. The tank is placed on the roof of a house. The water inside the tank is heated to 80°C by a flat-plate solar collector during the day. The tank is then exposed to windy air at 18°C with an average velocity of 40 km/h during the night. Estimate the temperature of the tank after a 45-min period. Assume the tank surface to be at the same temperature as the water inside, and the heat transfer coefficient on the top and bottom surfaces to be the same as that on the side surface. Evaluate the air properties at 50°C.
- A 8-cm diameter pipe is used to deliver hot water to a residence. A 6-m-long horizontal section of the pipe will pass through a large room of ambient temperature 20℃. The flow of hot water inside the pipe will maintain the outer surface temperature of the pipe at 72℃. If the water is flowing at 0.03 kg/s with an inlet temperature of 86oC, determine the outlet temperature of the water. The properties of air at the film temperature are as follows: k = 0.027 W/m.℃, ν = 17.5*10-6 m2/s, alpha= 25*10-6 m2/s Pr = 0.704, β= 1/Tf = 0.00313 K-1. Take cp,water=4.178 kJ/kgK Select one: a. 67.2 oC b. 104.3 oC c. 89.6 oC d. 82.3oCConsider 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.Reconsider Prob. 9-20. Using the EES (or other) software, evaluate the effect of the plate thickness on the surface temperature exposed to the cold air. By varying the plate thickness from 0.01 to 0.1 m, plot the plate surface temperature on the cold air side as a function of the plate thickness. Prob A 0.2-m-long and 25-mm-thick vertical plate (k = 1.5 W/m∙K) separates the hot water from the cold air at 2°C. The plate surface exposed to the hot water has a temperature of 100°C, and the surface exposed to the cold air has an emissivity of 0.73. Determine the temperature of the plate surface exposed to the cold air (Ts,c).