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integrating a scalar field in one direction

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The model that i am working on contains a plate that is locally heated. the temperature field is thus non-uniform over the whole domain. What i want is the average temperature in the Z direction perpendicular on the plate. Thus a temperature plane with the weighted average temperature in Z direction.

How can i accomplish this?
I played around with the derived values but nothing is satisfactory. the volume average gives the average temperature of the plate (scalar).

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