Parallel Plate Ducts

Huang CH, Ozisik MN (1992) Inverse problem of determining unknown wall heat flux in laminar flow through a parallel plate duct. Numer Heat Trans Part A 21 55-70... 

For r = 1, the concentric annular duct is reduced to a parallel plate duct. The applicable results are given in Table 5.28, the simple Nu being used for the Nusselt number at the heated wall. 

TABLE 5.28 Nusselt Numbers and Influence Coefficients for Fully Developed Thrbulent Flow in a Smooth Concentric Annular Duct With r = 1 (Parallel Plates Duct With Uniform Heat Flux at One Wall and the Other Wall Insulated [111] ... 

Parallel plate ducts, also referred to as flat ducts or parallel plates, possess the simplest duct geometry. This is also the limiting geometry for the family of rectangular ducts and concentric annular ducts. For most cases, the friction factor and Nusselt number for parallel plate ducts are the maximum values for the friction factor and the Nusselt number for rectangular ducts and concentric annular ducts. 

Laminar flow and heat transfer in parallel plate ducts are described in this section. The friction factor and Nusselt number are given for practical calculations. 

Fully Developed Flow. For a parallel plate duct with hydraulic diameter Dh = 4b (b being the half-distance between the plates) and the origin at the duct axis, the velocity distribution and friction factor are given by the following expression ... 

Similar to the four fundamental thermal boundary conditions for concentric annuli, the four kinds of fundamental conditions for parallel plate ducts are shown in Fig. 5.20. The fully developed Nusselt numbers for the four boundary conditions follow [1] ... 

FIGURE 5.20 Four fundamental boundary conditions for a parallel plate duct [2]. 

Uniform Heat Flux at Each Wall. When the heat fluxes on the two walls of parallel plate ducts are equal, qZi = q U, the temperature distribution of fully developed laminar flow is given by ... 

Uniform Temperature at One Wall and Uniform Heat Flux at the Other. When the two walls of a parallel plate duct are subject to a thermal boundary condition such as uniform temperature at one wall and uniform heat flux at the other, the Nusselt numbers for fully developed laminar flow for qZ = 0 and q"w 0 are determined to be ... 

The Exponential Wall Heat Flux Boundary Condition . When both walls of parallel plate duct are subjected to the exponential heat flux of qZ = q% exp(rajt ), the fully developed Nusselt number can be obtained as follows [2] ... 

Hydro dynamically Developing Flow. For hydrodynamically developing flow in parallel plate ducts, Shah and London [1] obtained the apparent friction factor/app and Chen [11] has obtained Lhyf K oo) as the function of x+ and Re, respectively, as shown in the following equations ... 

Thermally Developing Flow,. The results for thermally developing flow in parallel plate ducts are presented for the following practical thermal boundary conditions of interest. 

Equal and Uniform Temperatures on Both Walls. The local and mean Nusselt numbers for parallel plate ducts with equal and uniform temperatures on both walls can be computed from Nusselt s [131] solution, which is displayed in Fig. 5.21. The tabulated values for Fig. 5.21 are available in Shah and London [1]. 

FIGURE 5.21 Local and mean Nusselt numbers in the thermal entrance region of a parallel plate duct with the and (8) boundary conditions [1]. 

Uniform and Equal Heat Flux at Both Walls. Thermally developing flow in a parallel plate duct with uniform and equal heat flux at both walls has been investigated by Cess and Shaffer [132] and Sparrow et al. [133] in terms of a series format for the local and mean Nus-selt numbers. The dimensionless thermal entrance length for this problem has been found by Shah and London [1] to be as follows ... 

Equal and Uniform Temperatures at Both Walls. For simultaneously developing flow in a parallel plate duct with fluids of 0.1 < Pr < 1000, the following equations are recommended for the computation of the local and mean Nusselt numbers [2,136,137] ... 

The local Nusselt number is displayed in Fig. 5.23 for Pr = 0.0,0.01,0.7,10, and °° when one wall of the parallel plate duct is insulated and the other wall is subjected to uniform heat flux heating [140]. Included in Fig. 5.23 are the results for Pr = obtained from the concentric annular duct corresponding to r = 1. The local and mean Nusselt numbers for Pr = 0 were obtained by Bhatti [34]. 

Transition Flow. The lower limit of the critical Reynolds number Recrit for a parallel plate duct is reported to be between 2200 and 3400, depending on the entrance configurations and disturbance sources [143]. The following friction factor formula developed by Hrycak and Andrushkiw [144] is recommended for transition flow in the range of 2200 < Re < 4000 ... 

Fully Developed Flow. Beavers et al. [145] obtained the following friction factor for fully developed turbulent flow in a parallel plate duct for 5000 < Re < 1.2 x 106 from very accurate experimental data ... 

Comparisons of precision using Eqs. 5.220 and 5.221 and Blasius s formula (Table 5.8) in which the diameter of circular duct 2a is replaced by hydraulic diameter 4b, b being the halfspace between two plates, have been conducted by Bhatti and Shah [45]. In the range of 5000 < Re < 3 x 104, Eq. 5.220 is recommended otherwise, Eq. 5.221 should be used to obtain the friction factor for fully developed turbulent flow in a parallel plate duct. However, use of the hydraulic diameter to substitute for the circular duct diameter in the Blasius equation is reasonable for the prediction of the fraction factor [45]. 

Bhatti and Shah [45] and Sparrow and Lin [133] have performed a comparison of Nusselt numbers predicted using Eq. 5.222 or other equations for parallel plate ducts and the Nusselt number calculated using the equation for circular ducts replacing 2a with the hydraulic diameter of the parallel plate duct. It was concluded that the Nusselt number for parallel plate ducts can be determined using the circular duct correlations. 

Analogous to circular ducts, the fully developed turbulent Nusselt numbers for uniform wall temperature and uniform wall heat flux boundary conditions in parallel plate ducts are nearly identical for Pr > 0.7 and Re > 105. This is also true for the Nusselt number of turbulent thermally developing flow in a parallel plate duct [147]. 

For liquid metal, when one wall of the parallel plate duct is heated and the other is adiabatic, the following empirical equation is recommended for Pr < 0.03 by Duchatelle and Vautrey [148] ... 

Fully developed fluid flow and heat transfer results for rough parallel plate ducts can be predicted using the results for rough circular ducts with the use of hydraulic diameter [45]. 

Hydrodynamically Developing Flow. Hydrodynamically developing flow in smooth parallel plate ducts with uniform velocity at the duct inlet has been analyzed by Deissler [92] by means of an integral method. The apparent friction factors/app in the hydrodynamic entrance are presented in Fig. 5.24. 

Few investigations have been conducted for simultaneously developing flow in parallel plate ducts. Therefore, no correlations are provided for practical usage. 

Rectangular ducts are also often used in the design of heat transfer devices such as compact heat exchangers. Unlike circular and parallel plate ducts, two-dimensional analysis is required to obtain the friction factors and Nusselt numbers for rectangular ducts. 

Parallel Plate Ducts With Spanwise Periodic Corrugations at One Wall... 

Two types of corrugations (triangular and rectangular) in parallel plate ducts are displayed in the insets of Figs. 5.60 and 5.61, respectively. Sparrow and Charmchi [290] have obtained the solutions for fully developed laminar flow in these ducts. The flow in the duct is considered to be perpendicular to the plane of the paper. Both ducts are assumed to be infinite in the span-... 

Fully developed laminar flow and heat transfer in a parallel plate duct with spanwise-periodic rectangular corrugations at one wall have been investigated by Sparrow and Chukaev [291]. The end effect is also ignored in their analysis. The fully developed / Re is shown in Fig. 5.61, which is based on the results reported by Sparrow and Chukaev [291] and the extension by Shah and Bhatti [2]. The heat transfer characteristics for the three pairs of geometric parameters can be found in Sparrow and Chukaev [291]. 

Colver and Howell (1980) used the electrostatic EPS (Electric Particulate Suspension) to measure diffusion of spherical copper spheres (74-88 and 125-147 pm) along a copper parallel plate duct having a 1 cm separation distance. The particles were dynamically suspended in the duct by inductive charging... 

Solbrig CW, Gidaspow D. Convective diffusion in a parallel plate duct with one catalytic wall—laminar flow—first order reaction. The Canadian Journal of Chemical Engineering 1967 45 35-39. 

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