Consider the flow of a hot fluid in a copper pipe without insulation and with a strong fluid flow around the outside of the pipe. The pipe itself is a thin-walled tube and because it is made of copper, the thermal resistance of the wall can be neglected. The convection resistances on the inside and the outside, however, are comparable and must both be considered. The bulk temperature, T, of the flowing fluid is different from the free stream temperature so heat transfer will occur. Note that eventually the bulk temperature of the fluid flowing in the pipe will approach the temperature of the free stream outside, Tinfinity.
Start with an energy balance on a small segment of the pipe (dx) and develop an equation for the bulk fluid temperature in the pipe as a function of x, the length of the pipe.
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