Radiation/ Convection Network Assessment – System G

Radiation/ Convection Network Assessment – System G
Your thermal system is a small batch water heater, powered by a geothermal heat source. The system consists of a long trough with a pipe filled with water in it. The pipe is suspended in the middle of the trough, see Figure 1. The geothermal source is below the trough (not shown in the figure).
Figure 1 – Geometry of System (Not to scale)
The geometry of the system is specified as L1=20cm and Rpipe=2 cm. The system is to produce hot water, 323 K in batches rather than continuously. The pipe is filled with cold water (293K) warmed up and then emptied and a fresh volume of cold water enters the system and the process repeated.
Including mixed mode heat transfer
In this section, both radiation heat transfer and convection heat transfer will be considered together. The surface properties are summarised in the table below.
Surface Temperature / K  /W m-2K-1 Emissivity
1 500 20 0.8
2 438 15 0.8
3 438 15 0.8
4 293 15 0.8
Extend the resistance network in the grey analysis to include convection between the surfaces and the air in the trough surrounding the pipe.
• Calculate the temperature of the air in the space surrounding the pipe.
• Calculate the net radiation heat flux, convective heat flux and total heat flux to all surfaces.
Assuming the net heat fluxes do not change significantly estimate the time it takes for the water in the pipe to increase from 293K to 323K and thereby calculate a hot water production rate for this system. The thermal resistance of the pipe is negligible and the length of the trough is 200 cm. Use the view factors calculated in the previous section based on a 2D system and the heat transfer from the end plates of the trough can be neglected.

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