Temperature development in pipe flow with uniform surface heat flux condition considering thermal leakage to the ambient

A practical analytical model for the classical pipe flow problem with constant wall heat flux is presented in which leakage of the heat flux to the ambient is taken into account. The results obtained by the model show that the bulk temperature tends to a limiting value (i.e. does not rise linearly as in the classical constant heat flux problem). A value for the generating heat flux is obtained for which the temperature of the fluid and tube surface remains constant, while there is generated heat over the tube. Also, the analytical solution yields a stationary length for the tube beyond which the change in the fluid temperature is insignificant.