Laminar viscous dissipation in rectangular ducts

In this paper, a theoretical study is conducted, calculating the temperature distribution in the cross-section of a rectangular duct, under the conditions of newtonian and incompressible fluid, fully developed laminar flow and steady-state regime. The governing equations are solved resorting to the finite Fourier transform. The temperature distributions are obtained. The results concerning the temperature distribution in a square duct are shown by tables and figures, and a comparison between the present solution and some literature contributions is also presented. The viscous dissipation is responsible for a power generation that, for a particular Brinkman number (Brq = 1/Φ* or Brw=±∞), allows the wall heat flux to vanish. At last, the effects of viscous dissipation and wall heat flux are presented in some graphs, as a function of the duct aspect ratio.