Glycerin $)=(2000\frac{J}{k}g*C$ at $20C$ and $3k\frac{g}{s}$ is to be heated by ethylene glycol $)=(2500\frac{J}{k}g*C$ at $60C$ in a thin$-$walled double$-$pipe co$-$current heat exchanger. The temperature difference between the two fluids is $15C$ at the outlet of the heat exchanger. If the overall heat transfer coefficient is $300\frac{W}{m^{2\text{@}}}C$ and the heat transfer surface area is $20m^2.$ determine:

$($a$)$ the rate of heat transfer,

$($b$)$ the outlet temperature of the glycerin, and

$($c$)$ the mass flow rate of the ethylene glycol.