Abstract
To analyze the influence of the developing flow in a circular duct on the laminar forced convection heat transfer, the non-linear momentum and linear energy equation are solved successively by employing the Galerkin-Kantorowich method of variational calculus. Assuming constant fluid properties, negligible axial diffusion and temperature boundary condition of the third kind, a closed form solution for velocity and a semi analytic solution for temperature are derived. It is concluded that there can be a considerable difference, depending upon Biot number and Prandtl number, between the local Nusselt number considering the radial convection and that neglecting it.
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