Problem 3 Electrical heating of a pipe. In the manufacture of glass-coated steel

Question

Problem 3 Electrical heating of a pipe. In the manufacture of glass-coated steel pipes, it is common practice first to heat the pipe to the melting range of glass and then to contact the hot pipe surface with glass granules (see figure below). These granules melt and wet the pipe surface to form a tightl,y adhering nonporous coat. In one method of preheating the pipe, an electric current is passed along the pipe, with the result that the pipe is heated. For the purpose of this problem make thc following assumptions The local rate of electrical heat production Se is then uniform throughout the pipe wall are negligible. surroundings air which is at temperature Ta and provides a heat-transfer coefficient h (i) The electrical conductivity of the pipe is constant over the temperature range of interest (ii) The top and bottom of the pipe are capped in such a way that heat losses through them (iii) The inner surface of the pipe is adiabatic and the outer surface of the pipe is exposed to Please find the temperature distribution in the pipe wall T(r) Power supply Ambient air temperature T Pipe wall

Explanation / Answer

There is constant heating of pipe, so it will attain a steady state in some time. As there is no numerical data provided, the explanation will be theoretically based.

the top and bottom of the pipe are sealed and there are no heat losses means, all the heat generated is been occupied by the pipe or the useful work to be done.

the temperature distribution in the pipe wall will be in the following manner:

1) there will be maximum temperature at the endpoints of the pipe

2) the temperature will be comparatively minimum at the middle of the pipe. The temperature will gradually decrease from the end part of the pipe to the middle of the pipe.

this type of temperature distribution is achieved because of the phenomenon of natural convection. the temperature at the source will be maximum, i.e. at the endpoints. As the heat passes through the pipe, air from the surrounding will also flow over the pipe, thus cooling it. As the ambient condition is mentioned, the cool air will cool-off the heated pipe. Since, heating is provided from both the sides, maximum cooling be at the middle of the pipe.

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