District heating lines
Most heating systems involve the transport of sensible heat in a fluid or gas (such as water or air) through pipes or channels. Examples are the solar heating system illustrated in Fig. 4.21, the heat pump in Fig. 4.104 and the geothermal heating plants in Fig. 4.107. Solar heating systems and heat pumps may be used in a decentralised manner, with an individual system providing heat for a single building, but they may also be used on a community scale, with one installation providing heat for a building block, a factory complex, a whole village or a city of a certain size. Many combined heat and power (CHP) systems involve heat transmission through distances of 10-50 km (decentralised and centralised CHP plants). In some regions, pure heating plants are attached to a district heating grid.
Assuming that a hot fluid or gas is produced at the central conversion plant, the transmission may be accomplished by pumping the fluid or gas through a pipeline to the load points. The pipeline may be placed underground and the tubing insulated in order to reduce conduction and convection of heat away from the pipe. If the temperature of the surrounding medium can be regarded as approximately constant, equal to Tref, the variation in fluid (or gas) temperature Tfluid(x) along the transmission line (with the path-length co-ordinate denoted x) can be evaluated by the same expression (4.98) used in the simple description of a heat exchanger in section 4.2.1. Temperature variations across the inside area of the pipe perpendicular to the stream-wise direction are not considered.
The rate of heat loss from the pipe section between the distances x and (x+dx) is then of the form dE/dx = Jm Cpfluid dTfluid(x)/dx = h' (Tref - Tfluid(x)), (5.1)
where h' for a cylindrical insulated pipe of inner and outer radii r1 and r2 is related to the heat transfer coefficient AFipe (conductivity plus convection terms, cf. (3.34)), by h' = 2n Xppe / log(r2/r1).
Upon integration from the beginning of the transmission pipe, x = x1, (5.1) gives, in analogy to (4.98),
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