Laminar-flow heat-transfer in non-circular ducts
A numerical method is employed to obtain solutions for laminar flow heat transfer with fully developed velocity profiles and invariant fluid physical properties for rectangular ducts of various aspect ratios with the thermal boundary conditions of constant wall temperature and constant heat input per unit length of the duct. Since an analytical solution for the fully developed velocity profile in a rectangular duct is available, the varying temperature profile remains to be solved numerically from the energy equation which is transformed into a finite difference form by means of two finite difference operators in two dimensions. Numerical values of the initial and boundary temperatures are fixed by choosing a suitable dimensionless temperature depending upon the, thermal boundary condition. As computation involved is very lengthy, a fast digital computer is required. Numerical results obtained from an I.C.T. Atlas computer are presented as the variation of the Nusselt number with the Graetz number. The numerical method is extended to analyse heat transfer with simultaneously aeveloping velocity and temperature profiles. To determine the development of the velocity profile, some simplifications of the Navier-Stokes equation are made. Results are presented for various aspect ratios with the Prandtl number of 0.72. The effect of Prandtl number on heat transfer is also illustrated by numerical results. The numerical method is also used to solve for heat transfer in right-angled isosceles and equilateral triangular ducts with the same hydraulic and thermal boundary conditions as in the previous cases. The predicted results are compared with experimental data. For constant wall temperature, they agree well for Graetz numbers under 70; for constant heat input per unit length, closer agreement is shown over a much wider range of the Graetz numbers. Accuracy of the numerical method is confirmed by the facts that variations of the predicted Nusselt numbers obtained here follow the same trends as those for circular ducts and parallel plates and at the Graetz number of zero, they approach values of the limiting Nusselt numbers obtained by other methods.