Laminar, mixed convection heat transfer for flow between horizontal parallel plates with asymmetric heating

The development of laminar flow in a 180° section of a curved square duct (R/d = 6.45) was studied by laser-Doppler anemometry (LDA). The streamwise flow-velocity component Vϕ and the secondary flow component Vr were measured as a function of Dean number and of the azimuthal angle ϕ. The development of the streamwise flow component was found to be connected with a strong momentum transfer towards the outer wall between ϕ = 0° and ϕ = 60°, with a partial back-transfer of the momentum towards the duct centre (ϕ = 45°–108°), and with little further change of the momentum between ϕ = 108° and 180° near the outer wall. The measurements of the Vr component showed at least one vortex pair in the secondary flow. A second vortex pair with opposing sense of circulation was found to develop near the outer wall only for Dean numbers between 150 and 300, in agreement with numerical calculations. This second vortex pair was found in the region between ϕ = 108 and 171°. Between ϕ = 60 and 108° it was not possible to identify the second vortex pair in the developing flow. However, developing laminar-flow numerical calculations by Humphrey (1982) show that it also arises for K = 485 in a 180° square duct with R/d = 3.35 and Re = 890, and it is a function of inlet flow conditions. From the measured stream-function maximum of the second vortex pair it may be deduced that a curved duct with 180° (20 hydraulic diameters) bend angle is not sufficient to reach fully developed flow conditions at d/R = 1/6.45 and K = 226.

The development and structure of primary and secondary flow in a curved square duct

A laminar, three-dimensional, steady-state model has been solved to determine the nature and effect of thermally driven secondary flows in, a horizontal channel with heated top and bottom surfaces and insulated side walls. The secondary flow is characterized by ascending and descending thermals that form longitudinal vortex rolls and enhance the bottom surface heat transfer and channel friction factor by as much as 400 and 30%, respectively. Parametric calculations have been performed to determine the effect on hydrodynamic and thermal conditions of Reynolds number (100 ≤ Re ≤. 1000), Grashof number (2.5 × 105 ≤ Gr∗ ≤ 6.5 × 104), Prandtl number (Pr = 6.5 and 0.7), top-to-bottom surface heat flux ratio (−1.0 ≤ q1/qb ≤ 5.0), aspect ratio (1 ≤ A ≤ 10), and entrance velocity profile. Conditions near the bottom surface are characterized by mixed convection and are unaffected by heating at the top surface. Conversely, conditions at the top surface are dominated by forced convection and are unaffected by heating...

Numerical simulation of laminar mixed convection in the entrance region of horizontal rectangular ducts

This investigation considers the effects of free convection on the laminar flow of water through a circular duct having essentially constant wall heat transfer rate per unit length of the duct and circumferentially uniform wall temperature. The effect of the Reynolds and Rayleigh number variations on heat transfer results has been analysed for both horizontal and inclined pipe. The experiment has covered the range of the inlet Reynolds number from 200 to 2300, and of the Rayleigh number from 6,000 to 70,000. The effect of pipe inclination has been investigated for slope angle values up to 60°, with laminar ascending flow.

Experimental investigation of combined forced and free convection in horizontal and inclined tubes

This work applies an effective and efficient method, called Numerical Simulation-Aided Parametric Analysis (NSAPA), to derive simple and accurate correlation formulae for a natural convective flow system. The classical natural convection in roofs of triangular enclosures is considered to demonstrate the effectiveness of the approach. The buoyancy force generated by the temperature gradient generates a flow pattern. The NSAPA technique derives a set of algebraic equations in characteristic quantities from mass, momentum, and energy conservative equations for natural convection inside a triangular enclosure. The main advantage of the NSAPA technique is that solving the set of algebraic equations is easier than solving the original system of partial differential equations using a numerical method used in computational fluid dynamics. The heat transfer coefficients can be derived using these characteristic quantities. The numerical solution determines the constant factors of the characteristic velocities, the...

Numerical Simulation-Aided Parametric Analysis of Natural Convection in a Roof of Triangular Enclosures

Buoyancy effects on laminar heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall heat flux for large prandtl number fluid

G.J Hwang

Papers

Buoyancy effects on laminar heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall heat flux for large prandtl number fluid