$($Exam level problem$).$ PYou are running a small reactor in the lab that generates $1$ kW of heat. You have a

pump that can deliver $15$ g$/$s of a fluid at $20$C to cool the reactor. Lab safety

protocols dictate that the fluid can have a maximum temperature of $85$C$.$ What

is the minimum specific heat capacity required for the fluid?

b$.(15$ points$)$ The fluid must be in a closed loop system, and flows through plastic

tubing with a diameter of $1$ cm and wall thickness of $1$ mm$.$ What length of tubing

is needed such that the fluid returns to $20$C $($the ambient temperature of the

room$)$ by the time it re$-$enters the reactor? You find the following information

about plastic in a heat transfer guide:

Thermal conductivity $($htc$)=0\mathrm{.}33$ W$/($m K$)$

Absorptivity $=$ emissivity $=0\mathrm{.}85$reventing a meltdown

a$.$ You are running a small reactor in the lab that generates $1$ kW of heat. You have a

pump that can deliver $15$ g$/$s of a fluid at $20$C to cool the reactor. Lab safety

protocols dictate that the fluid can have a maximum temperature of $85$C$.$ What

is the minimum specific heat capacity required for the fluid?

b$.(15$ points$)$ The fluid must be in a closed loop system, and flows through plastic

tubing with a diameter of $1$ cm and wall thickness of $1$ mm$.$ What length of tubing

is needed such that the fluid returns to $20$C $($the ambient temperature of the

room$)$ by the time it re$-$enters the reactor? You find the following information

about plastic in a heat transfer guide:

Thermal conductivity $($htc$)=0\mathrm{.}33$ W$/($m K$)$

Absorptivity $=$ emissivity $=0\mathrm{.}85$