Parallel Plate Duct Research Articles

Radiation-convective heat transfer and performance analysis of a parallel-plates duct direct absorption solar heat collection system

Solar photo-thermal conversion and solar heat collection are hot topics today. However, which solar collection mode is the best? The question has puzzled scholars for many years. In this study, a direct absorption solar heat collection (DASC) duct system was investigated. Carbon quantum dots (CQDs) were selected as the heat absorption medium. Different absorption modes were clarified. It is found that the ratio of the radiation penetration depth of nanofluids to duct depth (duct penetration ratio, α) plays a key role in the duct heat transfer and system performance. Totally three solar heat collection modes can be classified depending on the value of α: volume absorption (partial volume 0<α<1 or whole volume α = 1), surface absorption (upper α → 0 or bottom α → ∞) and hybrid absorption for α > 1. Of them, the whole volume absorption has the best performance when α = 1, while the hybrid performs the best when the penetration ratio is not unity. Surprisingly, a higher fluid absorption coefficient does not necessarily lead to a higher photo-thermal performance. The extreme high fluid absorption coefficients (upper surface mode) are inferior to extreme low absorption coefficients (bottom surface mode). Of the different modes, the total Nusselt numbers in the whole volume absorption mode are 2–3 times higher than those in the bottom surface absorption mode. For solar heat collection, convective heat collection is better than standstill collection, and a certain flow velocity should be ensured to have a satisfactory efficiency. The findings were experimentally verified.

Влияние дистанцирующих выступов в щелевом канале малой ширины на его теплогидравлические характеристики при ламинарном течении

The paper presents analytical study of the distancing bulges effect on the thermal-hydraulic characteristics of a band slotted heat-transfer matrix of the rotary heat exchanger. The work was carried out based on mathematical simulation of the thermal-hydraulic processes in the band parallel-plate duct of low height (0.4 mm) at the laminar flow regime characteristic for the rotary heat exchangers. Influence of the distancing elements number in the rows, distance between the rows, as well as the total number of elements in the channel on the average value of the Nusselt number and on the magnitude of the pressure drop was analyzed. Influence of alterations in speed and temperature regimes on the thermal-hydraulic characteristics was analyzed. It was found that installation of the distancing bulges in a band parallel-plate duct led to a decrease in the Nusselt number and the increase in hydraulic resistance of the parallel-plate duct compared to a flat slotted duct without bulges despite the laminar flow regime. It was noted that influence of the distancing elements mutual arrangement on the bands was insignificant for the flow thermal-hydraulic characteristics. It was established that an increase in the temperature of the parallel-plate duct walls also was not leading to significant alteration in the heat transfer nature inside the channels under study; and alteration in the laminar flow speed regime also practically did not affect the heat transfer intensity in the ducts under consideration

Fluid Flow and Heat Transfer of a Gas Stream Containing Dust Particles in a Parallel-Plates Duct

Abstract Fluid flow and heat transfer of a gas stream in various ducts have been studied thoroughly before. However, in real applications, a gas stream usually contains dust particles, whose effects have typically been neglected. In this study, the effects of the dust particles on the flow and heat transfer characteristics in a parallel-plates duct were numerically investigated in detail. A lattice Boltzmann method combined with a modified immersed boundary approach was employed to calculate the velocity and temperature distribution in the duct. The effects of the particles on the development of the hydrodynamic and thermal boundary layers in the duct were predicted. The product of friction factor and Reynolds number (fRe) and local Nusselt number (NuL) along the flow direction were obtained for a particle-laden flow and compared with those for a pure gas flow. The results indicated that for particle-laden flows, the “fully-developed” flow was just an approximation. Both the flow and thermal boundary layers were disrupted by the accompanying particles. The particles would form a stable and dense particulate fouling layer at the walls; this could increase the local (fRe) and reduce the NuL in “fully developed” regions. Moreover, ducts with superhydrophobic properties would be less influenced by the particles due to decreased particle deposition because of the anti-dust property of the surface.

Developing a Grey Forecasting Model for the Air Flowing across the Parallel Plate Duct

The focus of this work is on developing a nonlinear grey model for the laminar flow regime of carrier fluid across the flat plate collector. The trust region reflective algorithm was used to solve the nonlinear laminar flow problem and handle the sparse matrix. The stream function, dimensionless velocity, gradients of velocity components, carrier fluid temperature, and the absorber plate temperature were estimated for a flat plate collector operated with and without a circular chimney. Similarly, the same technique was adopted to determine a model for heat transfer across the absorber plate. The numerically obtained solution was also compared with the parameters obtained through the instrumental measurement. The relative tolerance was kept at 10−5 for the white and grey box solutions. The developed model was noticed to have a smaller deviation than the conventional analytical model to predict the experimental values. The slip condition was observed for the proposed scheme. The uncertainty in the temperature measurement through the proposed model varies from ±0.53 to ±1.47 K. The minimum absolute percentage error (MAPE) lies in the domain of 0.52–1.67% for the nonlinear grey model, whereas the linear grey model for measuring absorber plate temperature has a percentage error of 0.0011–0.02%.

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

AbstractInspired by simulating duct thermal processing of novel functional polymers, a novel mathematical model is developed for buoyancy‐driven heat transfer in non‐Newtonian Williamson fluid flow in a vertical parallel plate duct containing a permeable medium, under mutually orthogonal electrical and magnetic fields. The momentum equation features electrical and magnetic body force terms, and the Darcy–Brinkman–Forchheimer mode is used for non‐Darcy effects. The energy balance equation includes thermal buoyancy (natural convection body force) and a modified viscous dissipation term. The conservation equations with associated boundary conditions are reframed into a system of coupled non‐linear ordinary differential equations via appropriate similarity transformations. The emerging dimensionless boundary value problem is then solved with a differential transform method (DTM). Validation of DTM solutions with the bvp4c MATLAB collocation solver is included. The influence of key parameters on velocity, temperature and average Nusselt number, are computed and illustrated graphically. With elevation in Weissenberg (non‐Newtonian) number, velocity and temperature are reduced. Velocity is suppressed with increasing non‐Darcian parameter (Forchheimer effect) whereas it is enhanced with increment in buoyancy convection parameter. With increasing Forchheimer, Darcy number and Hartmann number, the average Nusselt number is boosted whereas it is decreased with higher values of buoyancy convection parameter, Brinkman number and Weissenberg number. A strong reduction in temperature is computed with increment in ratio of Joule electrical heating to heat conduction parameter. DTM is shown to be an exceptionally accurate and versatile approach for simulating non‐Newtonian electromagnetohydrodynamic transport in ducts.

Lattice Boltzmann simulation of laminar forced convection in a parallel-plate duct with evolving porous layers at the walls

The present study conducts lattice Boltzmann simulation of flow in a duct with evolving porous layers (EPL) on the walls. The effects of elapsed time (0 < t < 125 mins), Darcy number (0.0001 < Da < 0.01), Reynolds number (100 < Re < 400), and porosity (0.85 < ε < 0.99) on the problem are studied. The time history of the average Nusselt number ratio is calculated to study thermal performance reduction of the duct. It is seen that the thermal performance is reduced as the EPL grows on the walls. Two stages in the performance reduction over time are identified in the present study, called the initial and evolution stages. At the initial stage, the performance is reduced slightly, and at the evolution stage, that starts at tev, the performance reduction occurs rapidly and approximately at a constant rate. It is shown that at Re = 200 the thermal performance is reduced by 17% and 3.2% for Da = 10−4 and 10−2, respectively, compared to the clear duct. In the present study, correlations for the evolution starting time and average Nusselt number are proposed in terms of Reynolds number, Darcy number, and elapsed time. It is also seen that the porosity has a negligible effect on thermal performance, whereas the effect of Reynolds number is significant.

Lattice Boltzmann Simulation of Laminar Forced Convection in a Parallel-Plate Duct with Evolving Porous Layers at the Walls

Lattice Boltzmann Simulation of Laminar Forced Convection in a Parallel-Plate Duct with Evolving Porous Layers at the Walls

New correlations for heat transfer in parallel-plate ducts at low Peclet number

Calculations of heat transfer in duct flows generally neglect the effect of axial heat conduction within the fluid. However, in some situations, this effect must be taken into account. The decision on whether or not to consider this phenomenon is driven by the value of the Peclet number. A low value, with 100 commonly considered the threshold, indicates that axial conduction, i.e., conduction parallel to the flow, should be accounted for in the calculations. Microfluidic devices, systems using liquid metal coolant or microchannel heat exchangers are some examples of applications where low Peclet flow conditions may be encountered. While exact analytical solutions exist for such cases, they are often impractical to use for common engineering design purposes due to their mathematical complexity. The present work proposes three new correlations for the estimation of the fully developed Nusselt number, thermal entry length and local Nusselt number in the entrance region of a laminar flow within a parallel-plate duct with constant wall temperature. These correlations allow the simple and accurate evaluation of useful engineering quantities, thus avoiding lengthy and complex calculations. They were developed using rational approximation theory and are effective on a wide range of Peclet numbers and axial coordinates. Accuracy of under 1% relative error is achieved with each of the three correlations when results are compared against exact analytical series solution values.

Electro and magnetorheological fluid damper study with controllable field-flow analysis for parallel plate duct

Electro and magnetorheological fluid damper study with controllable field-flow analysis for parallel plate duct

Refinement of the Generalized Graetz Problem Correlation With New Benchmark Calculations

Abstract A recently proposed generalized correlation for the Graetz problem in heat transfer has two fitted constants that can be related back to two fundamental constants of fully developed transport. A new set of benchmark solutions for convection in annular tubes is used to assess the best linear relationship between fitted and fundamental constants used in this correlation for conditions spanning from circular tubes to parallel plate ducts. This work also improves the Lévêque limit of the general correlation by considering peripheral variation in flow friction. The refined Graetz problem correlation for fully developed flow is able to predict exact thermal entry region solutions to within ±1.2% for all annular tube geometries having either constant temperature (T) or constant heat flux (H1) wall condition.

Hybrid Solution for the Analysis of MHD Micropolar Fluid Flow in a Vertical Porous Parallel-Plates Duct

In this paper, we analyze the transient magnetohydrodynamic (MHD) flow of an incompressible micropolar fluid between a porous parallel-plates channel. The fluid is electrically-conducting subjected to radiation described by the Cogley-Vincent-Gilles formulation and with convective thermal boundary conditions at the plates. The solution methodology employed is the hybrid numerical-analytical approach known as the Generalized Integral Transform Technique (GITT). The consistency of the integral transform method in handling such a class of problem is illustrated through convergence analyses, and the influence of physical parameters such as radiation, and micropolar parameters, and Hartman number. The wall shear stress, the coupled stress coefficient, and heat flux at the walls were also calculated, demonstrating that increasing the gyroviscosity decreases the wall stresses magnitudes. Furthermore, the results show that increasing the radiation heat transfer decreases the fluid temperature distribution. Additionally, the velocity is damped, and the angular velocity is increased by the Lorentz force in the presence of a magnetic field.

Correlations for Convection in Hydrodynamically Developing Laminar Duct Flow

Abstract A generalized correlation for combined entry convection in ducts of arbitrary cross section has been developed. The correlation is constructed for the average Nusselt number using knowledge of fully developed transport constants. The general correlation reproduces the first principle solutions for the well-established round and parallel plate duct geometries to within ±5% for both constant temperature and constant heat flux wall conditions when Pr ≥ 0.7. A survey of the literature demonstrates that the new generalized correlation performs as well or better than existing correlations, which are expressed for specific geometries and wall conditions. The new correlation is generally in good agreement with the first principle solutions of less common duct geometries so long as the duct has a convective surface equal to the wetted perimeter. The new correlation is not recommended for ducts having small aspect ratios that pinch the flow when convection is prescribed by the H2 constant heat flux wall condition.

Sound radiation from a semi-infinite lined duct

In this paper we consider the radiation properties of a pair of semi-infinite, parallel-plate ducts in which the inner duct is buried inside the outer duct. A Robin condition is applied to one of the inner walls (to represent an acoustic lining), while Neumann conditions are applied on all other surfaces. This leads to a matrix Wiener–Hopf problem, which requires the factorisation of a 3×3 matrix of a form which, to our knowledge, has not previously been considered in the literature and which is not directly amenable to standard pole-removal techniques. We derive the exact factorisation of this matrix here, and present results for the far-field scattered sound which show the effect of varying the properties of the wall lining.

Numerical Study on Filtration Combustion in Porous Two-Layer Systems: Influence of Fuel Porosity

Filtration combustion in a two-layer sandwich of reactive and inert porous media placed in a parallel-plate duct with heat- and gas-proof outer surfaces, penetrable interface, and open butt ends was studied by 2D numerical modeling. Spatio-temporal profiles of extent of conversion, temperature, pressure, and gas flow vectors were calculated as a function of width and porosity of fuel layer.

Correlations for the Graetz problem in convection – Part 1: For round pipes and parallel plates

A general correlation is proposed for the laminar Graetz problem associated with convection in round pipes and parallel plate ducts. The general correlation for the average Nusselt number can be expressed under conditions of either constant wall temperature or constant wall heat flux. Additionally, closed form expressions for the local Nusselt number can be derived from the general correlation. New correlations are found to be within ±1.5% of exact solutions to the Graetz problem for round pipes and parallel plates, and are contrasted with existing correlations in the literature.

Hybrid integral transforms for flow development in ducts partially filled with porous media.

A hybrid numerical-analytical solution is developed for laminar flow development in a parallel plate duct partially filled with porous media. The integral transform method is employed in combination with a single domain reformulation strategy for representing the heterogeneous media within the channel. A novel eigenfunction expansion basis is proposed, including abrupt spatial variations of physical properties due to the domain transitions. The introduction of the new basis allows for a solution with similar convergence rates as in previous applications with simpler formulations, as demonstrated through a careful convergence analysis of the expansions. The inherent automatic error control characteristic of the integral transforms approach then provides benchmark results for the developing velocity profile. Moreover, a physical analysis further verifies the consistency of both the proposed expansion and the mixed symbolic-numerical code developed. A detailed verification with a finite-element commercial code is also performed.

Laminar Forced Flow and Heat Transfer in Cross-Corrugated Triangular Ducts

The fluid flow and heat transfer characteristics in a cross-corrugated triangular channel are studied under laminar forced flow and uniform wall temperature conditions. Both the local and the periodic mean values of friction factor and wall Nusselt numbers in the hydro and thermally developing entrance region are investigated. It is found that at higher Reynolds numbers, recirculations in the lower wall valleys are a dominant factor for flow and heat transfer, while at lower Reynolds numbers, parallel flows in the upper wall corrugation are the predominant factor. Compared with a parallel flat plates duct, the Nusselt numbers in a cross-corrugated triangular duct can be enhanced, and can be even higher at higher Reynolds numbers. The growth of steady recirculations and the concomitant periodic disruption and thinning of the boundary layer promote enhanced transport of heat as well as momentum. Effects of heat transfer enhancement are more obvious under higher Reynolds numbers. Two correlations are proposed to predict the periodic mean values of Nusselt numbers and friction factors for Reynolds numbers from 10 to 2000.

Wall-retardation effects on particles settling through non-Newtonian fluids in parallel plates

AbstractWalls can exert a retardation effect on particles settling in bounded fluid media. In this work, the parallel plate retardation effect was studied for particles falling in non-Newtonian fluids along the centreline of parallel plate ducts. The eccentric effect was also investigated for those particles which approached the wall. For spheres settling in sodium carboxymethylcellulose (CMC) solutions, the variation in wall factors against the size ratio of the sphere’s diameter to the parallel plate wall spacing shows a non-linear trend; the particle settling velocity is independent at small size ratio, and then decreases quickly with increase in size ratio. A new correlation was presented covering a wider range of size ratios (0.02 &lt; λ &lt; 0.83) in the flow region of 0.0011 &lt;

Thermal dispersion effects on forced convection in a parallel plate porous channel

Thermal dispersion effects on fully developed forced convection inside a porous-saturated parallel plates duct with uniform heat flux at the wall are investigated on the basis of the Brinkman model. Having known the velocity distribution, the energy equation is solved using asymptotic techniques for the limiting case when thermal conductivity, as a result of thermal dispersion, weakly changes with the Peclet number. A numerical solution, valid for the entire range of thermal dispersion conductivity, is also presented. This latter solution is performed to check the accuracy of the former one. It was seen that in the limiting regions the results of both methods are in close agreement with each other and also with those previously reported in the literature. Validity range for the presented closed form solution is also discussed as a function of the Peclet number.

Optimization of Microchannel Geometries to Enhance Convection Cooling of Parallel Plate Duct Flow

Optimization of Microchannel Geometries to Enhance Convection Cooling of Parallel Plate Duct Flow