Convection In Rectangular Ducts Research Articles

Laminar convection in rectangular ducts of fully developed flow

Benchmark calculations for the Graetz problem in rectangular ducts are performed for three wall conditions (T – constant temperature, H2 – constant heat flux, and H1 – constant axial heat input with constant peripheral temperature). Results are reported for a wide range of duct aspect ratio (1/1 through 1/10) and over a wide span of inverse Graetz number (Z>10−6). This builds on earlier works that neglect the initial ~20% of thermal boundary layer growth in reporting heat transfer results and that omit the H2 wall condition. Using a new generalized approach, Nusselt number results for the T and H1 wall condition are correlated to better than ±2.5% for the entire range of inverse Graetz number and duct aspect ratios. Limitations on correlating the H2 wall condition by the same method are discussed.

End Effects on H2-Forced Convection in Rectangular Ducts of Large Aspect Ratios

The H2-forced convection in a rectangular duct of large aspect ratio (>10) is studied. It is found that the short ends have non-negligible effects on the Nusselt number and the temperature distribution. Even at infinite aspect ratios, the Nusselt number depends on the net heat addition from the ends, but not how they are distributed.

Thermally developing Brinkman–Brinkman forced convection in rectangular ducts with isothermal walls

The Extended Weighted Residuals Method (EWRM) is applied to investigate the effects of viscous dissipation on the thermal development of forced convection in a porous-saturated duct of rectangular cross-section with isothermal boundary condition. The Brinkman flow model is employed for determination of the velocity field. The temperature in the flow field was computed by utilizing the Green’s function solution based on the EWRM. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate. In addition to the aspect ratio, the other parameters included in this computation are the Darcy number, viscosity ratio, and the Brinkman number.

The second-law analysis of mixed convection in rectangular ducts

The rate of entropy generation, S˙′G[W/mK], is examined both theoretically and numerically for forced and mixed convection in a rectangular duct heated at the bottom. Under fully-developed flow conditions S˙′G is expressed in terms of relevant non-dimensional hydrodynamic and thermal parameters. Numerically, it is demonstrated that S˙′G is a single, effective parameter to examine both thermal and hydrodynamic fields and their variations.

On pattern selection in mixed convection in rectangular ducts

Mixed convection in a horizontal rectangular duct has the same critical Rayleigh number as natural convection in a rectangular cavity for the onset of convection. The linear stability analysis predicts either an odd or an even number of convective rolls to appear depending on the aspect ratio of the cross section. However, it has been shown both experimentally and numerically that an even number of convective rolls appears under supercritical conditions for fully developed mixed convection. The paper first presents an analytical solution for the buoyancy-induced mainstream velocity, w b , at the onset of buoyancy-induced motion in a forced convective flow. Then, a comparison in the initial growth rate of w b is made between the case of an odd and an even number of rolls; which shows the selection of an even number of rolls over an odd number in mixed convection except for low aspect ratio ducts.

Fully-developed forced convection in rectangular ducts and illustrations of some general inequalities

New exact laminar convective temperature solutions for rectangular ducts with constant heat flux per unit length have been derived in uniform fashion for a variety of Dirichlet and Neumann boundary conditions. Those with null Dirichlet boundary conditions satisfy the hypothesis of a general inequality theorem. Consequences of the theorem are shown for the velocity and thermal fields of rectangular and elliptical ducts, which provide rigorous bounds for intermediate contours.