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 GIVENAn insulated pipeExternal temperature of the pipe = TiOuter radius of the pipe = riOuter radius of insulation = roThermal conductivity = kAmbient temperature = T??Convective heat transfer coefficient = hASSUMPTIONSThe system has reached steady stateThe thermal conductivity does not vary appreciably with temperatureConduction occurs in the radial directiononly

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T, -To Hot Fluid T. Insulation