# Use the definition of thermal center and show that for the core, having near linear temperature…

Use the definition of thermal center and show that for the
core, having near linear temperature profile, the thermal center is located at
Hcore/2 where Hcore is the core height.

Derive Equation VId.3.13, the thermal center of a U-tube
steam generator, where _SG is measured from the tube
sheet. [Hint: Start with Equation VId.3.12. Then use the definition of the
thermal expansion coefficient to relate density difference to temperature
difference. Find _SG from:

where the numerator is given in Example VId.3.1].

Equation VId.3.12

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Use the definition of thermal center and show that for the
core, having near linear temperature profile, the thermal center is located at
Hcore/2 where Hcore is the core height.

Derive Equation VId.3.13, the thermal center of a U-tube
steam generator, where _SG is measured from the tube
sheet. [Hint: Start with Equation VId.3.12. Then use the definition of the
thermal expansion coefficient to relate density difference to temperature
difference. Find _SG from:

where the numerator is given in Example VId.3.1].

Equation VId.3.12

Equation VId.3.13

Example VId.3.1

Example VId.3.1. Develop the hydrostatic head for flow of
water in the tubes of a U-tube steam generator. Flow enters tubes at pressure P
and temperature TH and leaves at temperature TC.
The tube average length is L.

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