Heat Transfer and Thermal Analysis Problems in Engineering

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Heat Transfer and Thermal Analysis Problems in Engineering2. (25 points)Consider a cylinder with a length of 15 cm and a diameter of 10 cm. The cylinder has a surfacetemperature of 43oC, while the room air temperature is 17oC. Determine whether placing thecylinder horizontally or vertically would achieve a higher heat transfer rate.Cylinder Orientation (Heat Transfer Rate):A vertical cylinder will generally achieve a higherheat transfer rate compared to a horizontal cylinder due to stronger buoyancy effects in verticalorientation.3. (25 points)A silicon chip is cooled by passing water through microchannels etched in the back of the chip, asshown. The channels are covered with a silicon cap. Consider a 12-mm x 12-mm square chip inwhich N = 60 rectangular microchannels, each of width W = 50m and height T = 200m havebeen etched. Water enters the microchannels at a temperature Ti= 290 K, and a total flow rate of0.005 kg/s. The chip and cap are maintained at a uniform temperature of 350 K. Assuming that theflow in the channels is fully developed, all the heat generated by the circuits on the top surface of thechip is transferred to the water, and using circular tube correlations, determine: a) the water outlettemperature, Teand b) the chip power dissipation, We.Circuits generatingpower e WWHSilicon Chip Cooling in Microchannels:For the given chip, you can calculate the outlet watertemperature and power dissipation by using flow and heat transfer correlations (Reynoldsnumber, heat transfer coefficient). These calculations require the use of detailed fluid dynamicsequations.4. (25 points)It was observed on a plant tour that a 45-m-long section of a 2-in nominal (6.03-cm-outer-diameter)steam pipe extended from one end of the plant to the other with no insulation on it. Measurementsrevealed that the average temperature of the exposed surfaces of the steam pipe was 170oC, whilethe temperature of the surrounding air was 20oC. The outer surface of the pipe appeared to beoxidized, and its emissivity can be taken to be 0.7. Taking the temperature of the surroundingsurfaces to be 20oC also, determine the rate of heat loss from the steam pipe.Heat Loss from Steam Pipe:The heat loss from the steam pipe can be determined using both convectiveand radiative heat transfer calculations, considering the pipe's surface temperature, emissivity, andsurrounding air temperature.1. (25 points)A sculptor is making a decorative sphere made of fused silica (polycrystallinesilicon dioxide, k = 2.25 W / m.oC,= 0.834 x 10-6m2/s). The sphere comesout of the furnaceat 1000oC and is cooled by a water mist at 15oC (with h = 45 W/m2.oC). For a sphere of radius0.15 m, determine the time it will take for a position at a distance of one half the radius from thecenter to cool to 120oC.

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