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A turbine blade 6.3 cm long, with cross-sectional area
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Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
- A single-cylinder air-cooled lawn mower engine operates under steady conditions. The cylinder temperature cannot exceed 300 ⁰C. To cool the engine, annular fins are placed around the cylinder. The fins are 0.3 cm thick and are 2 cm long from base to tip. The fins are made of cast iron (k = 52 W/mK). The outside diameter of the engine cylinder at the base of the fin is 0.3 m. Assume that the engine operates in 30 ⁰C air and that the heat transfer coefficient on the sides and tip of the fin is 12 Wm^-2K^-1. Determine the number of fins needed to cool a 3 kW engine to the given temperature if the engine has an efficiency of 30 % and 50 % of the total heat given off by the engine actually is dissipated through the fins ?arrow_forwardA 0.5-ampere current is flowing through a long electrically conducting cylindrical rod. The diameter of the rod is 6 mm, the electrical resistance of the rod is R = 2000 /m, and k =0.9 W/m K for the rod. The rod is encased in a 2-mm thick Pyrex tube and a 20°C liquid is flowing over the outer surface of the Pyrex tube. The convection heat transfer coefficient for the liquid h= 800 W/m2 . K. The interfacial conductance (contact resistance) at the interface between the rod and the Pyrex tube is h = 1200 W/m² - K. a) Compute the rate of heat generation in the rod and use it compute the volumetric rate of heat generation. b) Find the temperature drop across the interface between the outer surface of the rod and the inner surface of the Pyrex tube. c) Find the temperature at the center of the rod.arrow_forward40°C water with hwater = 800 W/m² K is flowing in a Pyrex tube. The inner and outer diameters of the tube are 25 mm and 35 mm. A thin metallic heater element bonded to the outer surface of the tube is being used to heat the water by transferring 600 W/m of thermal energy to the water flowing in the tube. The Pyrex tube and heater are covered with a 10-mm thick layer of foam insulation. The outer surface of the foam insulation is exposed to air at T = -5°C with hair = 12 W/m².K. The heater = air element must generate more than 600 W/m, because part of the heat being generated is lost to the air surrounding the foam insulation. Assume kp = 1.30 W/m K for Pyrex and k = 0.026 W/m K for the foam insulation. a) Find the temperature of the heater element needed to transfer 600 W/m of thermal energy to the water in the tube. b) Find the total rate at which the heater element must generate thermal energy. Water Pyrex tube, kp = 1.30 W/m.K = 40°C water hwater = 800 W/m².K Heater element Tair=…arrow_forward
- Steam in a heating system flows through tubes whose outer diameter is 5 cm and whose walls are maintained at a temperature of 180 C. Circular aluminum alloy 2024-T6 fins (k =186W/m °C) of outer diameter 6 cm and constant thickness 1 mm are attached to the tube. The space between the fins is 3 mm, and thus there are 250 fins per meter length of the tube. Heat is transferred to the surrounding air at T = 25°C, with a heat transfer coefficient of 40 W/m2 °C. %3D Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins. 23em 3em T-25C 130°C 1 uanarrow_forwardSteam at 350 °C flows through the stainless steel pipe with k=26 W/m.°C. The inner and outer diameters of the stainless steel pipe are 6.0 cm and 7.0 cm, respectively. The pipe is insulated from the outside with a 4.0 cm thick glass wool (k= 0.038 W/m.°C) and then a 3.0 cm thick k=0.25 W/m.K material. The insulated pipe is in the environment at 20 °C. The heat loss from the pipe occurs only by [natural convection+radiation]. Film heat transfer coefficient including the effects of [natural convection+radiation] in the insulated pipe is 30 W/m². is C. Calculate the heat transferred per unit pipe length since the film heat transfer coefficient defined according to the inner area of the pipe is 110 W/m².°C.arrow_forwardExample: 0.5 kg of water per minute is heated from 20° to 40°C when passed through a tube of 2.5 cm diameter steel pipe. The pipe surface temperature is maintained at 110°C by condensing steam on its surface. Find out the length of the pipe required. The properties of water at mean temperature of 70°C are given below: p = 978 kg/m² k= 0.575 W/m. K Cp = 4200 J/kg. K v = 0.415 x 10-6 m²/secarrow_forward
- A circular tube (internal diameter=8 mm, length=20 m) subjected to a uniform heat flux of 30000 W/m2 on its surface. Water (ρ=1000 kg/m3, k=0.6 W/mK, ν=8x10-7 m2/s, cp=4.2 kJ/kg0C, Pr=6) enters the tube at 15 oC with a velocity of 1.1 m/s and leaves at 50 0C. Surface temperature of the tube at the inlet isarrow_forwardThere are 2 different types of fins: circular section and square section. Both fins are 30 cm length and they are made of copper with 380W/mK_conductivity. The circular section fin diameter is D = 3mm and the lateral width of the square section fin is W = 50 mm. The fin base temperature is -10°C. The fins are immersed in an oil bath at 50°C and perpendicular velocity to the axis of the fins. Obtain the maximum heat rate absorbed in each types of fin for an oil velocity of 60 m/s. Justify every calculation and assumption. Answer: 27.42W (circular section); 987.53W (square section parallel oriented); 1018.6W (square section oblique oriented)arrow_forwardQ9: A 2-kW resistance heater wire with thermal conductivity of k = 20 W/m - °C, a diameter of D = 5 mm, and a length of L = 0.7 m is used to boil water. If the outer surface temperature of the resistance wire is Ts = 110°C, determine the temperature at the center of the wire.arrow_forward
- In a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 1.7 cm enters into the boiler that has the thermal conductivity as 0.3 W/mK. The boiler is maintained at 107degreeC and temperature of the water that flows inside the pipe is at 31degreeC. If the energy transfer (Q) is 124925 kJ in 7 hours. Determine the Heat transfer rate, Surface area of the pipe and Diameter & Length of the pipe, if D = 0.012 L.Change in Temperature (in K) Heat Transfer Rate (in W) Surface Area of the Pipe (m2) Pipe Length (in m) Pipe Diameter (in mm)arrow_forwardQ10: In a nuclear reactor, 1-cm-diameter cylindrical uranium rods cooled by water from outside serve as the fuel. Heat is generated uniformly in the rods (k = 29.5 W/m - °C) at a rate of 7 x10' W/m?. If the outer surface temperature of rods is 175°C, determine the temperature at their center.arrow_forwardCopper pipe (k = 400 W/m.K) has an inner diameter of 25 cm and an outer diameter of 27 cm. Saturated steam flows through it at 110 °C. The piping is located in a space at 30 °C and the external convection heat transfer coefficient is estimated at 15 W/m2.K, while the internal convection heat transfer coefficient is 2500 W/m2.K. In order to reduce heat losses, it was decided to install thermal insulation. The available insulation has a thickness of 4.9 cm and a conductivity k = 0.027 W/m.K. Calculate the percentage increase in the "total" thermal resistance resulting from installing the insulation (between the uninsulated and the insulated case).arrow_forward
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