Part $2$: Now for the heat exchanger: $(35$ marks$)$

The condenser of this refrigeration cycle has a heat output requirement achieved using a heat exchanger. Consider a simple water$-$cooled, thin$-$walled, counter$-$flow heat exchanger. The refrigerant gas flows through the inner annulus, and water on the outer annulus. Determine suitable annulus diameters for the counter$-$flow heat exchanger, where the flow is designed to be laminar for water, and laminar for the refrigerant. Hydraulic diameter maybe required.

In terms of a modified cross$-$section, such as the outer region of an annulus, the hydraulic diameter is used for Reynolds numbers, pressure drop, and the actual cross$-$sectional expression is used for the mass flow rate. i$.$e$.$ hydraulic diameter is not used for the mass flow rate.

Design basis:

Assume a condenser heat output of $17$ kW $($which may or may not be the correct previous answer.$)$