The material to be heated is in a long, cylindrical tube, and is viscous enough that any flow inside the tube can be ignored, i.e. the heating is by conduction alone). Also, consider the glass of the tube to be very thin so its thermal resistance can be ignored. The tube diameter is 1 cm and the properties of the material are the same those of water, given by 0.64 W/m*K, 1000 kg/m3, and 4180 J/kg*K, for thermal conductivity, density, and specific heat, respectively. The water bath temperature is 65 °C, and the initial temperature of the material is 27 °C. Without the agitation of the water bath, the heat transfer coefficient can be considered to be 128 W/m2*K. Considering the tube to be a long cylinder, how long does it take for the coldest point to heat up to a temperature corresponding to 99% of the total possible temperature increase? If the surrounding how water is agitated using a stirrer, leading to a considerably large surface heat transfer coefficient, how long does it take to reach the same temperature as was used in the previous step?
The material to be heated is in a long, cylindrical tube, and is viscous enough that any flow inside the tube can be ignored, i.e. the heating is by conduction alone). Also, consider the glass of the tube to be very thin so its thermal resistance can be ignored. The tube diameter is 1 cm and the properties of the material are the same those of water, given by 0.64 W/m*K, 1000 kg/m3, and 4180 J/kg*K, for thermal conductivity, density, and specific heat, respectively. The water bath temperature is 65 °C, and the initial temperature of the material is 27 °C.
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Without the agitation of the water bath, the heat transfer coefficient can be considered to be 128 W/m2*K. Considering the tube to be a long cylinder, how long does it take for the coldest point to heat up to a temperature corresponding to 99% of the total possible temperature increase?
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If the surrounding how water is agitated using a stirrer, leading to a considerably large surface heat transfer coefficient, how long does it take to reach the same temperature as was used in the previous step?
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