Laminar-flow heat-transfer in non-circular ducts.

摘要

A numerical method is employed to obtain solutionsudfor laminar flow heat transfer with fully developed velocityudprofiles and invariant fluid physical properties for rectangularudducts of various aspect ratios with the thermal boundaryudconditions of constant wall temperature and constant heatudinput per unit length of the duct. Since an analytical solutionudfor the fully developed velocity profile in a rectangular duct is available, the varying temperature profileudremains to be solved numerically from the energy equationudwhich is transformed into a finite difference form by meansudof two finite difference operators in two dimensions. Numericaludvalues of the initial and boundary temperatures are fixedudby choosing a suitable dimensionless temperature dependingudupon the, thermal boundary condition. As computation involvedudis very lengthy, a fast digital computer is required. Numericaludresults obtained from an I.C.T. Atlas computer areudpresented as the variation of the Nusselt number with theudGraetz number.udThe numerical method is extended to analyse heatudtransfer with simultaneously aeveloping velocity and temperatureudprofiles. To determine the development of the velocityudprofile, some simplifications of the Navier-Stokes equation are made. Results are presented for various aspect ratiosudwith the Prandtl number of 0.72. The effect of Prandtl numberudon heat transfer is also illustrated by numerical results.udThe numerical method is also used to solve for heatudtransfer in right-angled isosceles and equilateral triangularudducts with the same hydraulic and thermal boundary conditionsudas in the previous cases.udThe predicted results are compared with experimentaluddata. For constant wall temperature, they agree well forudGraetz numbers under 70; for constant heat input per unitudlength, closer agreement is shown over a much wider range ofudthe Graetz numbers. Accuracy of the numerical method isudconfirmed by the facts that variations of the predictedudNusselt numbers obtained here follow the same trends asudthose for circular ducts and parallel plates and at theudGraetz number of zero, they approach values of the limitingudNusselt numbers obtained by other methods.