Laminar Flow In Rectangular Channel Research Articles

Numerical simulation of pressure drop for three-dimensional rectangular microchannels

PurposeThe purpose of this paper is to numerically investigate the flow characteristics and extend the data of friction factor and Reynolds number product of hydrodynamically developing laminar flow in three-dimensional rectangular microchannels with different aspect ratios.Design/methodology/approachUsing a finite-volume approach, the friction factor characteristics of Newtonian fluid in three-dimensional rectangular ducts with aspect ratios from 0.1 to 1 are conducted numerically under no-slip boundary conditions. A simple model that approximately predicts the apparent friction factor and Reynolds number product fappRe is referenced as a semi-theoretical fundamental analysis for numerical simulations.FindingsThe accurate and reliable results of fappRe are obtained, which are compared with classic numerical data and experimental data, and the simple semi-theoretical model used and all comparisons show good agreement. Among them, the maximum relative error with the classic numerical data is less than 3.9 per cent. The data of fappRe are significantly extended to other different aspect ratios and the novel values of fappRe are presented in the tables. The characteristics of fappRe are analyzed as a function of a non-dimensional axial distance and the aspect ratios. A more effective and accurate fourth-order fitting equation for the Hagenbach's factor of rectangular channels is proposed.Originality/valueFrom the reliable data, it is shown that the values of fappRe and the model can be references of pressure drop and friction factor for developing laminar flow in rectangular channels for researchers and engineering applications.

An Investigation of Heat Transfer for a Pulsating Laminar Flow in Rectangular Channels with a Boundary Condition of the Second Kind

A finite difference method is used for modeling heat transfer in a pulsating laminar flow in rectangular channels with different aspect ratios for the wall boundary condition T w = const. With high amplitudes of oscillation of the cross-section averaged flow velocity, a considerable increase in the cross-section averaged and time-averaged Nusselt number as compared with its stationary value is revealed. The range of dimensionless oscillation frequencies where the Nusselt number increases in the vicinity of the inlet to the heated section and also along the entire length of this section as compared with a steady-state flow is found.

Specific character of heat transfer under pulsating laminar flow in rectangular channels with different boundary conditions on the walls

Heat transfer in a laminar pulsating flow in rectangular channels with different ratios of the side lengths γ was simulated numerically by the method of finite differences for two kinds of the boundary conditions on the wall: the first and the second kind. The maximum ratio of the Nusselt number to its steady-state value near the entrance to the heated portion of the channel was calculated at high amplitude of pulsations. An increase in this ratio in the regime of stabilized heat transfer is explained. The reasons for differences in the dependence of the thermal values on the regime parameters (γ, dimensionless oscillation frequency, the Prandtl number) for the two considered boundary conditions are analysed.

Heat exchange at laminar flow in rectangular channels

Numerical modeling of heat exchange at a laminar stationary and pulsatile flow in rectangular channels with different aspect ratios of side lengths γ has been carried out by a finite difference method for two boundary conditions: a constant wall temperature and a constant heat flux density on the wall. For the boundary condition of the first kind, the similarity of distributions of the heat flux density and shear stress on the walls over the channel perimeter has been established. The reasons for a nonmonotonous dependence of the initial thermal interval length on γ are discussed. For the boundary condition of the second kind, the difference of the Nusselt number averaged over the perimeter at γ → 0 from its value for a flow in a flat channel has been explained. An increase in the Nusselt number averaged over the perimeter and the period of oscillations has been revealed for a pulsatile flow in the quasi-stationary regime at large amplitudes of the oscillations of the velocity averaged over the cross section.

Flow and pressure characteristics in rectangular channels with internal cylindrical bodies

This paper develops models for steady-state, fully developed, laminar flow in rectangular channels with internal coaxial solid cylinders. By casting and solving the parallel-flow momentum equation in a dimensionless setting, correlations are derived for the friction factor f and represented as Ref where Re is the Reynolds number. The correlations consider three positions for the internal cylinder. The cylinder may be in the center of the rectangular channel, in the corner of the channel, or resting at the middle of the channel floor. The correlations incorporate channel aspect ratios in the range 0.1≤α≤1.0. The cylinder-diameter aspect ratios β range from being vanishingly small to being large enough to touch the channel walls. Although the results are general, the study is motivated by considering the effects of diagnostic probes within small channels of catalytic monoliths.

Analytical solutions of heat transfer for laminar flow in rectangular channels

Abstract The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.

Flow resistance characteristics of pulsating laminar flow in rectangular channels

Experimental investigations on the resistance characteristics of pulsating laminar flow in different sizes rectangular channels are performed at ambient temperature and pressure. The influence of the pulsating period was checked for 6<T<600s; the relative amplitude of Re ranged from 0.05 to 0.92. Both the experiments and the theory show that, the ratio Cf signified the time average pulsating frictional resistance coefficient to that of steady flow equals one for the same Reynolds number in part of the laminar region which the time average Re, the pulsating frequency and the relative amplitude of Re are as small as possible. And in this laminar region, the aspect ratio of rectangular channel has no significant effect on the ratio Cf. However, as the time average Re and the relative amplitude of Re increase, the flow regime becomes no longer laminar even though the real time pulsating Re is less than the transition Reynolds number. Two reasons leading to the phenomenon: (1) the acceleration decreases the transition Re, (2) and the maximum of pulsating Re exceeds the transition Reynolds number. The results of pulsating flow experiments on four kinds of different sizes rectangular channels are consistent.

Laminar thermally developing flow in rectangular channels and parallel plates: uniform heat flux

Numerical simulations were conducted for thermally developing laminar flow in rectangular channels with aspect ratios ranging from 1 to 100, and for parallel plates. The simulations were for laminar, thermally developing flow with H1 boundary conditions: uniform heat flux along the length of the channel and constant temperature around the perimeter. In the limit as the non-dimensional length, x* = x/(D h RePr), goes to zero, the Nusselt number is dependent on x* to the negative exponent m. As the non-dimensional length goes to infinity the Nusselt number approaches fully developed values that are independent of x*. General correlations for the local and mean heat transfer coefficients are presented that use an asymptotic blending function to transition between these limiting cases. The discrepancy between the correlation and the numerical results is less than 2.5 % for all aspect ratios. The correlations presented are applicable to all aspect ratios and all non-dimensional lengths, and decrease the discrepancy relative to existing correlations.

Approximate residence time distribution of fully develop laminar flow in a straight rectangular channel

For microfluidic applications the residence time distribution (RTD) of laminar flow in rectangular channels is of interest. The exact velocity profile for this type of flow consists of an infinite series and does not allow analytical evaluation of the RTD curve. In this paper we adopt a simpler binomial product profile which was proposed in literature and serves as good approximation. This allows us to determine in an analytical manner approximate expressions for the diffusion-free RTD of fully developed laminar flow in a straight rectangular channel of arbitrary aspect ratio. Since the evaluation of this RTD is computationally elaborate because it involves the Gauss hypergeometric function, we fit it by an empirical model which is suitable for engineering applications. We find that for a Newtonian fluid there is a narrowing of the RTD as the aspect ratio decreases from unity (square channel) to zero (parallel plates). We investigate the range of applicability of the diffusion-free RTD and show that it is a good estimation for liquids in a certain range of Reynolds numbers. The actual limits of this range depend on the Schmidt number and on the aspect ratio and length-to-hydraulic-diameter ratio of the channel.

Pressure Drop of Impingement Air Cooled Plate Fin Heat Sinks

The performance of impingement air cooled plate fin heat sinks differs significantly from that of parallel flow plate fin heat sinks. A simple impingement flow pressure drop model based on developing laminar flow in rectangular channels is proposed. The model is developed from simple momentum balance and utilizes fundamental solutions from fluid dynamics to predict its constitutive components. To test the validity of the model, experimental measurements of pressure drop are performed with heat sinks of various impingement inlet widths, fin spacings, fin heights, and airflow velocities. The accuracy of the pressure drop model was found to be within 20% of the experimental data taken on four heat sinks and other experimental data from the published literature at channel Reynolds numbers less than 1200. The simple model is suitable for impingement air cooled plate fin heat sinks parametric design studies.

Experimental Investigation of Heat Transfer in Impingement Air Cooled Plate Fin Heat Sinks

Impingement cooling of plate fin heat sinks is examined. Experimental measurements of thermal performance were performed with four heat sinks of various impingement inlet widths, fin spacings, fin heights, and airflow velocities. The percent uncertainty in the measured thermal resistance was a maximum of 2.6% in the validation tests. Using a simple thermal resistance model based on developing laminar flow in rectangular channels, the actual mean heat transfer coefficients are obtained in order to develop a simple heat transfer model for the impingement plate fin heat sink system. The experimental results are combined into a dimensionless correlation for channel average Nusselt number Nu∼f(L*,Pr). We use a dimensionless thermal developing flow length, L*=(L∕2)∕(DhRePr), as the independent parameter. Results show that Nu∼1∕L*, similar to developing flow in parallel channels. The heat transfer model covers the practical operating range of most heat sinks, 0.01&lt;L*&lt;0.18. The accuracy of the heat transfer model was found to be within 11% of the experimental data taken on four heat sinks and other experimental data from the published literature at channel Reynolds numbers less than 1200. The proposed heat transfer model may be used to predict the thermal performance of impingement air cooled plate fin heat sinks for design purposes.

Heat Transfer in Plasma-Facing Components of Fusion Reactors: Non-MHD Laminar Flow in Rectangular Channels

Convective heat transfer in non-MHD laminar flow through rectangular channels in the first wall and limiter/divertor plates of fusion reactors has been analyzed numerically. Even for uniform heat flux, the Nusselt number (Nu) is not constant along the face of a rectangular channel, because the velocity is much smaller near a corner. For uniform heat flux, Nu varies by 67% from the center of a side to the corner (6.7 to 2.2). Therefore, the corners of a rectangular channel are possible hot-spot areas of concern for thermal-hydraulic designs. In addition, the surface heat flux on coolant channels in the plasma-facing components varies circumferentially. This nonuniformity of surface heat flux also affects the Nu. At the center of a side, Nu can be reduced from 6.7 to 2.8, i.e. by about 58%. For large nonuniformity of surface heat flux, the Nu at some locations can become infinity or negative; infinity, when the coolant/wall interface temperature becomes equal to the coolant bulk temperature and, negative, when the bulk temperature becomes larger than the interface temperature at these locations. The entry length is also increased due to the nonuniformity of surface heat flux. This increase can be as much as 4 times the entry length for uniform heat flux. For safe thermal-hydraulic designs of the first wall and limiter/divertor plates of fusion reactors, these effects must be taken into consideration.

Laminar flow in rectangular channels. Part I: Entry analysis. Part II: Numerical solution for a square channel?

Abstract Laminar incompressible flow in rectangular channels is considered. In Part I, the entry region is evaluated by a boundary layer/potential core analysis. It is shown that the three-dimensional displacement induced potential flow can be described with a pair of two-dimensional potential functions. Second-order boundary layer solutions, with and without surface mass transfer, are determined; an interesting secondary flow reversal is predicted. In Part II, numerical solutions are obtained for the viscous channel equations, which are derived from the asymptotic theory of Part I. A two stream function, velocity, vorticity system, independent of the Reynolds Number, is solved with a combined iterative ADI/point-relaxation numerical procedure. A single calculation applied for all Reynolds numbers, which appears only in the coordinate scaling. The axial flow behavior of Parts I and II are in good agreement in the asymptotic entry region where both analysis apply. Secondary flow reversal is calculated; however, the grid is too crude for quantitative comparisons. Numerical solutions are obtained until fully developed conditions are achieved. Agreement with experimental data is good.

Theory of gravitational deposition of particles from laminar flows in channels

A simple, analytical calculation method, based on the analysis of limiting trajectories of particles is developed which enables the determination of the precipitation efficiency of channels of different cross-sections. Using this method the problem of gravity deposition of colloid particles from laminar flow in rectangular channel, from laminar flow of fluid with a free surface and from laminar flow in circular and elliptical horizontal channel is solved.

Laminar to Turbulent Flow in a Wide Open Channel

Theoretical equations are presented, involving the velocity and rate of laminar flow in rectangular channels and in channels of infinite width. Data taken at shallow depths on an open channel 1.5 ft wide and 20 ft long are plotted in a graph showing the relation between the friction factor and the Reynolds number. The point of departure of these data from the theoretical laminar flow line is taken to be the critical value of the Reynolds, Iiumber at which the flow changes from laminar to turbulent. A thread of dye was also injected into the flow to determine whether the flow was laminar, turbulent, or transitional. The two methods of determining the critical velocity gave similar results.