Discuss the below in detail:
Q: Suppose that a pipe carrying a hot fluid with an external temperature of Ti and outer radius ri is to be insulated with an insulation material of thermal conductivity k and outer radius ro. Show that if the convective heat transfer coefficient on the outside of the insulation is h and the environmental temperature is T?^?, the addition of insulation can actually increase the rate of heat loss if ro < k="" h="" and="" that="" maximum="" heat="" loss="" occurs="" when="" ro="k/" h.="" this="" radius,="" rc,="" is="" often="" called="" the="" critical="">
GIVEN
An insulated pipe
External temperature of the pipe = Ti
Outer radius of the pipe = ri
Outer radius of insulation = ro
Thermal conductivity = k
Ambient temperature = TA?
Convective heat transfer coefficient = h
ASSUMPTIONS
The system has reached steady state
The thermal conductivity does not vary appreciably with temperature
Conduction occurs in the radial directiononly
