A system for heating water from an inlet temperature of
T_(m,i)=20\deg C
to an outlet temperature of
T_(m,o)=60\deg C
. Involves passing the water through a thick walled tube having inner and outer diameter of 20 and 40 mm . The outer surface of the tube is well insulated and electrical heating with the wall provides for a uniform generation rate of
q^(˙)=10^(6)(W)/(m)
for a water mass flow rate of
m^(˙)=0.1k(g)/(s)
. How long must be the tube be to achieve the desired outlet temperature. If the inner surface temperature of the tube is
T_(s)=70\deg C
at the out, what is the local convection heat transfer coefficient at the outlet?(
c_(p)=4179kg.K
)