To warm up some milk for a baby, a mother pours milk into a thin-walled cylindrical container whose diameter is 6 cm. The height of the milk in the container is 7 cm. She then places the container into a large pan filled with hot water at 70°C. The milk is stirred constantly so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the container is 120 W/m2 K, determine how long it will take for the milk to warm up from 3°C to 38°C. Assume the entire surface area of the cylindrical container (including the top and bottom) is in thermal contact with the hot water. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Why?
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HEAT+MASS TRANSFER ACCESS CODE
- A person puts a few apples into the freezer at 15°C cool them quickly for guestswho are about to arrive. Initially, the apples are at a uniform temperature of 20°C,and the heat transfer coefficient on the surfaces is 8 W/m2·K. Treating the apples as9-cm-diameter spheres and taking their properties to be 840 kg/m3, Cp 3.81 kJ/kg·K, k = 0.418 W/m·K, and α =10-7 m2/s, determine the center and surface temperatures of the apples in 1 h. Also, determine the amount of heat transfer from each apple. Solve this problem using analytical one-term approximation method (notthe Heisler charts). Answer: Center: 11.2 ℃, Surface: 2.7 ℃, heat transfer: 17.2 kJarrow_forwardConsider a 1.2-m-high and 2-m-wide double-pane window consisting of two 0.0023-m-thick layers of glass (k = 0.78 W/m·K) separated by a 12-mm-wide vacuum space. Take the convection heat transfer coefficients on the inner and outer surfaces of the window to be h1 = 10 W/m2·K and h2 = 25 W/m2·K, and disregard any heat transfer by radiation. Assume that the space between the two glass layers is evacuated.Determine the steady rate of heat transfer (in W) through the glass window. The room is maintained at 24°C while the temperature of the outdoors is –5°C. (Radiation in outer side of the double-pane window should be disregarded but in the inner part, the only mechanism of heat transfer in vacuum is by radiation. Emissivity for glass is around 1, and the temperature of inner surfaces of the double-pane window should be assumed to be 5 and 15 'C.)arrow_forwardConsider hotdog being cooked in boiling water in a pan. Would the heat transfer be modeled as one-dimensional or two-dimensional? Would the heat transfer be steady or transient? Explain.arrow_forward
- What are the mechanisms of heat transfer? How are they distinguished from each other?arrow_forwardConsider steady heat transfer between two parallel plates at a constant temperaturearrow_forwardTo warm up some milk for a baby, a mother pours milk into a thin-walled cylindrical container whose diameter is 6 cm. The height of the milk in the container is 7 cm. She then places the container into a large pan filled with hot water at 70°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the container is 120 W/m2·K, determine how long it will take for the milk to warm up from 3°C to 38°C. Assume the entire surface area of the cylindrical container (including the top and bottom) is in thermal contact with the hot water. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Why?arrow_forward
- An average man has a body surface area of 1.8 m2 and a skin temperature of 330C. The convective heat transfer coefficient for a clothed person walking in still air is expressed as h= 8.6V0.53 where V is the walking velocity in m/s. Assuming the average surface temperature of the clothed person to be 300C, determine the rate of heat lost by convection from an average man walking in still air at 100C at a walking velocity of 1.2 m/s.arrow_forwardConsider a steam pipe of length 15 ft, inner radius 2 in., outer radius 2.4 in., and thermal conductivity 7.2 Btu/hr-ft-°F. Steam is flowing through the pipe at an average temperature of 250°F, and the average convection heat transfer coefficient on the inner surface is given to be 1.25 Btu/hr-ft2-°F. If the average temperature on the outer surfaces of the pipe is 160°F, determine the rate of heat loss from the steam through the pipe. ANSWER:______Btu/hrarrow_forwardA 5 m long section of a steam pipe whose outer diameter is 10 cm passes through an open space at 30°C. The average temperature of the outer surface of the pipe is measured to be 150°C, and the average heat transfer coefficient on that surface is determined to be 180 W/m^2.k. Determine (a) the rate of heat loss through convection from the steam pipe and (b) the annual cost of this energy loss if steam is generated in a natural gas furnace, and the price of natural gas is 0.05 Rs/Kwh, consider a 250 working-day year.arrow_forward
- Why is this equation fundamental in the analysis of heat transfer? Why is this a big deal for engineers?arrow_forwardA cylindrical fuel rod of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel generates heat uniformly at a rate of 150 MW/m3. The convection heat transfer coefficient on the fuel rod is 5000 W/m2∙K, and the average temperature of the cooling water, sufficiently far from the fuel rod, is 70°C. Determine the surface temperature of the fuel rod and discuss whether the value of the given convection heat transfer coefficient on the fuel rod is reasonable.arrow_forwardWhen is the heat transfer through a fluid conduction and when is it convection? For which case is the rate of heat transfer higher? How does the convection heat transfer differ from the thermal conductivity of the fluid?arrow_forward
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