Problem $3$: $(20$ pts$)$

Continuation of Problem $5$ from HW$-2$:

A liquid propellant rocket combustor is regeneratively cooled and is characterized by:

Chamber temperature: $Tg=2750K$

Coolant bulk temperature: $Tc=300K$

Wall thickness: tw$=2$ mm

The following heat coefficients: $kw=43\frac{W}{m}-K$;$hg=657\frac{W}{m}2-K$; hc$=26,000\frac{W}{m}2-K$

Calculate:

$($a$)$ The total heat flux

$($b$)$ The wall temperature on the gas side $T_{wg}$

$($c$)$ The wall temperature on the coolant side $T_{wc}$