Non-uniform heating effects in thermally developing turbulent pipe flows

An analytical and numerical investigation of turbulent pipe flows in the thermal development region subject to an inhomogeneous heat flux distribution around the circumference has been conducted. We show analytically that the mean heat transfer (global Nusselt number Nu) does not depend on how the heat flux is distributed around the circumference. Hence, existing correlations for Nu remain applicable for azimuthally inhomogeneous heating. We present well-resolved numerical data for the thermal entrance region of non-uniformly heated pipe flows at different Prandtl (0.025, 0.71) and bulk Reynolds (5300, 19000) numbers. We show that, while the global Nu is unaffected by azimuthally inhomogeneous heating, the pointwise temperature has a much longer development length compared to a case with homogeneous heat flux. The development length is governed primarily by the azimuthal wavenumber k = 1 in the boundary condition.