Wavy-walled Channel Research Articles

Improvement of heat transfer in microchannels using nanofluids by numerical contribution on a sinusoidal shaped dissipator

This research conducts an extensive numerical investigation into the enhancement of heat transfer in wavy-walled channels using aluminum oxide-water nanofluids. The study examines the impact of key parameters, including geometric aspects (wave spacing ratio: 0-1), operational conditions (Reynolds number: 5,000-20,000), and varying nanofluid concentrations (1-6% by volume). The results indicate that zero wave spacing combined with a nanofluid concentration of 4% provides the most favorable thermal performance, resulting in a heat transfer enhancement of up to 2.5 times when compared to conventional smooth channels. While the wavy channel geometries significantly improve heat transfer, they also impose additional pressure drops, revealing a critical trade-off between enhanced thermal performance and the increased pumping power required. The study highlights the balance necessary between maximizing heat transfer and maintaining operational efficiency, particularly in systems where space is limited. These findings contribute valuable insights to the design of heat exchange systems that demand both high thermal efficiency and compact dimensions, such as those used in electronics cooling or energy-efficient HVAC systems. Additionally, the study explores the influence of the Reynolds number on both thermal and hydrodynamic behavior within the wavy channels, providing a thorough performance evaluation across different operational ranges. The conclusions drawn from this investigation offer practical guidance for optimizing heat exchanger designs, taking into account both thermal resistance and overall system performance under varying conditions.

Entropy production in the flow of Bingham-Papanastasiou fluid having temperature and shear rate-dependent viscosity

This article comprehensively examines entropy production in a peristaltic flow of Bingham-Papanastasiou fluid in an asymmetric wavy wall channel. The viscosity of the fluid is selected to depend on the temperature in addition to the shear rate. Furthermore, viscous dissipation is considered. The equations governing momentum and energy are adjusted to incorporate the existence of a nonlinear correlation between stress and strain rate. The energy dissipation caused by viscosity in the energy equation exhibits variation between Newtonian and non-Newtonian fluids due to their distinct rheological behaviors and response to shear forces. Newton’s law of viscosity states that the viscous dissipation term for Newtonian fluids follows a simple linear relationship between shear stress and shear rate. In contrast, non-Newtonian fluids exhibit more complex rheological behaviors, with the correlation between shear stress and shear rate described by various constitutive equations, depending on the specific type of non-Newtonian behavior. Consequently, the energy equation for non-Newtonian fluid flow problems becomes more intricate and nonlinear compared to the energy equation for Newtonian fluids, resulting in a more challenging analysis. Modeling of the equations is traditionally obtained using all steps involved in analyzing peristaltic flow. Using MATLAB's bvp5c solver, the obtained coupled set of differential equations is numerically solved. The research explores how the Bingham number and stress growth exponent parameters affect different dimensionless variables, including velocity, streamlines, temperature, axial pressure gradient, entropy production, and the Bejan number.

Lock-key microfluidics: simulating nematic colloid advection along wavy-walled channels.

Liquid crystalline media mediate interactions between suspended particles and confining geometries, which not only has potential to guide patterning and bottom-up colloidal assembly, but can also control colloidal migration in microfluidic devices. However, simulating such dynamics is challenging because nemato-elasticity, diffusivity and hydrodynamic interactions must all be accounted for within complex boundaries. We model the advection of colloids dispersed in flowing and fluctuating nematic fluids confined within 2D wavy channels. A lock-key mechanism between homeotropic colloids and troughs is found to be stronger for planar anchoring on the wavy walls compared to homeotropic anchoring on the wavy walls due to the relative location of the colloid-associated defects. Sufficiently large amplitudes result in stick-slip trajectories and even permanent locking of colloids in place. These results demonstrate that wavy walls not only have potential to direct colloids to specific docking sites but also to control site-specific resting duration and intermittent elution.

Thermohydraulic performance of ammonia, isopropanol, water and nanofluids as cooling fluid for lithium-ion 1C and 3C rating batteries

Cooling Lithium-ion batteries of different C ratings receive excellent attention amongst researchers in thermal management. The present study proposes to investigate the thermohydraulic performance of a wavy channel and compare the finding with the conventional straight channel. The full Navier Stokes equations and the energy equation were solved numerically using the finite element technique. Water is the cooling liquid used in the simulation. The flow is laminar and steady state. It is found that the average Nusselt number is higher as the waviness of the channel wall increases. The average Nusselt number for the wavy channel case was increased by up to 31% compared to the straight channel configuration. Also, the performance evaluation criterion increases by 23% compared to straight channel configuration. Thus, allowing the fluid to absorb more heat. However, at the expense of the pressure drop, the performance evaluation criterion is higher for the wavy wall channel mode than the straight channel wall. Amongst all fluids studied in this paper, including water, ammonia, isopropanol, Ammonia binary mixture and TiO2 nanofluid at different concentrations, ammonia is the most suitable liquid for cooling.

Stationary flow driven by non-sinusoidal time-periodic pressure gradients in wavy-walled channels

The classical problem of secondary flow driven by a sinusoidally varying pressure gradient is extended here to address periodic pressure gradients of complex waveform, which are present in many oscillatory physiological flows. A slender two-dimensional wavy-walled channel is selected as a canonical model problem. Following standard steady-streaming analyses, valid for small values of the ratio ε of the stroke length of the pulsatile motion to the channel wavelength, the spatially periodic flow is described in terms of power-law expansions of ε, with the Womersley number assumed to be of order unity. The solution found at leading order involves a time-periodic velocity with a zero time-averaged value at any given point. As in the case of a sinusoidal pressure gradient, effects of inertia enter at the following order to induce a steady flow in the form of recirculating vortices with zero net flow rate. An improved two-term asymptotic description of this secondary flow is sought by carrying the analysis to the following order. It is found that, when the pressure gradient has a waveform with multiple harmonics, the resulting velocity corrections display a nonzero flow rate, not present in the single-frequency case, which enables stationary convective transport along the channel. Direct numerical simulations for values of ε of order unity are used to investigate effects of inertia and delineate the range of validity of the asymptotic limit ε≪1. The comparisons of the time-averaged velocity obtained numerically with the two-term asymptotic description reveals that the latter remains remarkably accurate for values of ε exceeding 0.5. As an illustrative example, the results of the model problem are used to investigate the cerebrospinal-fluid flow driven along the spinal canal by the cardiac and respiratory cycles, characterized by markedly non-sinusoidal waveforms.

Feature Selection, Clustering, and Prototype Placement for Turbulence Datasets

This paper explores automated approaches for the analysis and categorization of turbulent flow data as a means of assessing the quality of a turbulence dataset used for constructing data-driven turbulence closures. Single-point statistics from several high-fidelity turbulent flow simulation datasets are differentiated into groups using a Gaussian mixture model clustering algorithm. Candidate features are proposed, and a feature selection algorithm is applied to the data in a sequential fashion, flow by flow, to identify a good feature set and an optimal number of clusters for each dataset. Clusters are first identified for plane channel flows, producing results that agree with existing theory and empirical observations. Further clusters are then identified in an incremental fashion for flow over a wavy-walled channel, flow over a bump in a channel, and flow past a square cylinder. Some clusters are closely identified with the anisotropy state of the turbulence, whereas others can be connected to physical phenomena, such as boundary-layer separation and free shear layers. Exemplar points from the clusters, or prototypes, are then identified using a prototype placement method. These exemplars effectively summarize the dataset using a greatly reduced collection of data points. The clusters and their prototypes are used to assess the quality of a training dataset constructed by simply pooling the four flows. We enumerate the dataset’s shortcomings and state the limits of generalizability of any data-driven closure trained on it.

Wavy Walls, a Passive Way to Control the Transition to Turbulence. Detailed Simulation and Physical Explanation

Inducing spanwise motions in the vicinity of solid boundaries alters the energy, mass and/or momentum transfer. Under some conditions, these motions are such that drag is reduced and/or transition to turbulence is delayed. There are several possibilities to induce those spanwise motions, be it through active imposition a predefined velocity distribution at the walls or by careful design of the wall shape, which corresponds to passive control.In this contribution, we investigate the effect that wavy walls might have on delaying transition to turbulence. Direct Numerical Simulation of both planar and wavy-walled channel flows at laminar and turbulent regimes are conducted. A pseudo laminar regime that remains stable until a Reynolds number 20% higher that the critical is found for the wavy-walled simulations. Dynamic Mode Decomposition applied to the simulation data reveals that in these configurations, modes with wavelength and frequency compatible with the surface undulation pattern appear. We explain and visualize the appearance of these modes. At higher Reynolds numbers we show that these modes remain present but are not dominant anymore. This work is an initial demonstration that flow control strategies that trigger underlying stable modes can keep or conduct the flow to new configurations more stable than the original one.

Thermo-hydraulic and entropy generation analysis for non-Newtonian fluid flow through sinusoidal wavy wall channel

The present investigation deals with numerical simulation of thermo-hydraulic transport characteristics of non-Newtonian fluid flowing through a wavy channel subjected to isothermal condition. The power-law constitutive model is adopted to illustrate the rheological behavior of fluid. The influence of various parameters like index of power-law (n), Reynolds number (Re), amplitude of sinusoidal profile (A), etc. on flow, thermal field, and entropy generation characteristics are delineated in detail. Furthermore, the outcome of the sinusoidal channel is compared with that of conventional straight channel in order to check the performance of wavy-wall channels. Results divulge that reliance of the thermo-hydraulic characteristics on wall geometry is unequivocally affected due to the amplitude of sinusoidal profile. Augmentation in heat transfer rate for lower values of amplitude of sinusoidal profile over the conventional channel is inconsiderable although difference upraises considerably owing to two factors namely: higher amplitude of sinusoidal profile and Re. The heat transfer rate diminishes with increment in power-law index. Consequently, heat transfer rate is progressively conspicuous for shear thinning fluids compared to shear thickening fluids. For comparison of pressure drop in the wavy and equivalent straight channel taking into account heat transfer and corresponding enhancement of pressure drop, we have defined a performance parameter. The comparison of performance parameter illustrates that shear-thickening fluids are more appropriate for engineering applications. Two nondimensional numbers are defined to elucidate the behavior of entropy generation with various parameters like Reynolds number, amplitude of sinusoidal profile, and power-law index. The entropy generation increases as the amplitude of waviness increases. Furthermore, entropy generation also intensify with increment in index of power-law for a distinct Reynolds number and amplitude of waviness. Results obtained from present study can be used as a tool to select wall geometry for design of compact and economical energy exchange devices dealing with non-Newtonian power-law fluids.

Passive Control of Vortex Shedding and Drag Reduction in Laminar Flow across Circular Cylinder Using Wavy Wall Channel

Numerical simulations of incompressible laminar flow past a circular cylinder using wavy wall confinement are performed in order to study drag reduction and vortex shedding suppression for Reynolds numbers (50 ≤ Re ≤ 280) and blockage ratios (0.5 ≤ D/H ≤ 0.9), where D is the cylinder diameter and H is the channel height. The optimum configuration of wavy wall confinement is identified to have an amplitude of 0.2D and wavelength of 4D which manifests the minimum drag coefficient and complete vortex shedding suppression (zero lift coefficient). The flow over the cylinder with optimized wavy wall confinement produces a stable vortex pair in the wake of the cylinder. The length of vortex pair in the wake increases by increasing the Reynolds number and decreasing the blockage ratio. The drag on the cylinder reduces when the length of vortex pair increases due to early flow separation and reduction in pressure drag. The drag coefficient decreases by 36% in comparison to the plane wall confinement at D/H = 0.5. The drag coefficient decreases for wavy wall configuration by about 67% for D/H = 0.7 and 94% for D/H = 0.9. The lift coefficient remains zero at all Reynolds numbers and blockage ratios which indicates complete suppression of vortex shedding.

Peristaltic Carreau-Yasuda nanofluid flow and mixed heat transfer analysis in an asymmetric vertical and tapered wavy wall channel

In this study, two-phase asymmetric peristaltic Carreau-Yasuda nanofluid flow in a vertical and tapered wavy channel is demonstrated and the mixed heat transfer analysis is considered for it. For the modeling, two-phase method is considered to be able to study the nanoparticles concentration as a separate phase. Also it is assumed that peristaltic waves travel along X-axis at a constant speed, c. Furthermore, constant temperatures and constant nanoparticle concentrations are considered for both, left and right walls. This study aims at an analytical solution of the problem by means of least square method (LSM) using the Maple 15.0 mathematical software. Numerical outcomes will be compared. Finally, the effects of most important parameters (Weissenberg number, Prandtl number, Brownian motion parameter, thermophoresis parameter, local temperature and nanoparticle Grashof numbers) on the velocities, temperature and nanoparticles concentration functions are presented. As an important outcome, on the left side of the channel, increasing the Grashof numbers leads to a reduction in velocity profiles, while on the right side, it is the other way around.

Nanofluid Heat Transfer in Wavy-Wall Channels with Different Geometries: A Finite-Volume Lattice Boltzmann Study

In this work, we perform an extensive numerical investigation of the heat transfer behavior of nanofluid laminar flows, in wavy-wall channels. The adopted computational approach is based on a finite-volume formulation of the lattice Boltzmann method constructed on a fully-unstructured mesh. We show the validity and effectiveness of this numerical approach to deal with realistic problems involving nanofluid flows, and we employ it to analyze the effects of the wavy-wall channel geometry on the rate of heat transfer, thus providing useful information to the design of efficient heat transfer devices. Results show that an increasing of the wavy surface amplitude has a positive effect on the heat transfer rate, while a phase shift between the wavy walls leads to a decreasing of the mean Nusselt number along the channel. The addition of solid nanoparticles within a base liquid significantly contributes to increase the rate of heat transfer, especially when a relatively high value of nanoparticles volume fraction is employed. The present analysis then suggests that the use of nanofluids within an axis-symmetric configuration of the wavy-wall channel, with high wavy surface amplitude, may represent an optimal solution to enhance the thermal performances of heat transfer devices.

Heat transfer enhancement through periodic flow area variations in microchannels

In this study, annular microchannels with a microscale gap of 300 μm were implemented through the concentric superposition of two macro-sized cylinders. Flow area variations along the streamwise direction were created by introducing sinusoidal wave profiles on either the inner or outer wall of the annular gap while keeping the other wall flat. These variations introduced re-entrant effects along the flow direction. Numerical studies using the finite volume method were performed to elucidate the single-phase, steady-state thermal and hydrodynamic performances of the wavy channels, using water as the fluid medium, with an operating Reynolds number range of 800–2200. The predicted results were validated using the available measured data and classical correlations. This study demonstrated the viability of attaining enhanced heat transfer rates of up to 360% of the original straight channel through the inducement of flow area variations with single wavy-walled channels. Despite magnifications of the friction factors, the single wavy-walled channels attained a 120% increment in heat transfer coefficient when evaluated at the same pumping power. Overall, single-walled wavy passages were deemed suitable for heat exchanger designs demanding very high heat removal rates and efficiencies while the conventional serpentine channels were apt for moderately enhancing heat transfer while requiring low pumping power.

Effect of rotation on forced convection in wavy wall channels

In this paper, flow field and heat transfer performance in stationary and rotating wavy channels with different shapes were numerically investigated. Three different geometries were generated through three different values of phase-shift angles of ∅= 0, 90 and 180° between the two opposite wavy walls. A cell-centred finite-volume technique was employed to solve the three-dimensional governing equations based on the SIMPLE algorithm technique. Besides, the Menter k−−ω SST turbulence model was used to simulate the turbulent flow in the current study. The wavelength and wave amplitude of the channel examined were Lw=20 mm and a = 2 mm, respectively. Numerical simulations were carried out over a range of design and operating conditions including the phase-shift angle of ∅= 0–180°, Reynolds number of Re=1,000–10,000, and rotating speed of Ω= 0–1000 rpm. The results showed that the surface-averaged Nusselt number increases as Re increases for all shapes of the wavy channel, however, at the expense of the raised pressure losses. Also, the wavy channel with a phase-shift of ∅= 0 deg showed the highest enhancement in the performance of heat transfer followed by that of ∅=90 and 180 deg, respectively. The rotation had a strong impact on the flow field and heat transfer performance. With the increase of rotating speed, lower wall heat transfer coefficient significantly increased, while the upper wall heat transfer coefficient exhibited a slight increase, indicating that those three different geometries of the wavy channels had a good versatility at various values of rotating speeds. The numerical results were compared with those available in the literature, and the results were in a good agreement.

Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains

We study spatial and spatio-temporal pattern formation emergent from reaction–diffusion–advection systems formed by considering reaction–diffusion systems coupled to prescribed fluid flows. While there have been a number of studies on the planar dynamics of such systems and the resulting instabilities and spatio-temporal patterning in the plane, less has been done on complicated flows in complex domains. We consider a general approach for the study of bounded domains in order to model two- and three-dimensional geometries which are more likely to be of relevance for modelling dynamics within fluid vessels used in experiments. Considering a variety of problem geometries with finite cross-sections, such as two-dimensional channels, three-dimensional ducts and three-dimensional pipes, we demonstrate the role cross-section geometry plays in pattern formation under such systems. We find that the generic instability is that of an oscillatory or wave Turing instability, resulting in patterns which change in time, often being advected with the fluid flow. As in previous works, we observe a change in patterns formed when progressing from zero to weak to strong advection for uniform advection across the domain, with particularly strong advection destroying patterns. One novel finding is that heterogeneous fluid flow can induce qualitatively different patterns across the domain. For instance, Poiseuille flow with maximal advection in the centre of a vessel and zero advection at the boundary of a vessel is shown to exhibit patterns in the centre of the vessel which are different from patterns near the boundary, with differences attributed to the differential local advection within each region of the vessel. Additionally, we observe sheared patterns, which appear due to gradients in the fluid velocity, and cannot be obtained via any kind of uniform flow. Finally we also explore flow in more complex domains, including wavy-walled channels, continuous stirred-tank reactors, U-shaped pipes and a toroidal domain, in order to demonstrate behaviours when the flow is both heterogeneous and bidirectional, as well as to demonstrate that our results still apply for complex finite domains. Our analysis suggests that such non-trivial advection results in moving patterns which are more complex than observed in simpler reaction–diffusion–advection, and may be more characteristic of realistic flow regimes in biological media.

Heat transfer and entropy generation of the nanofluid flow inside sinusoidal wavy channels

Corrugating channel walls is a way to enhance heat transfer in heat exchangers. In the current investigation, the entropy generation minimization approach has been employed to optimize heat transfer and fluid flow within a wavy channel. A numerical method has been built to compute entropy generation rate in a sinusoidal wavy-wall channel with copper-water (Cu-water) nanofluid flow. The governing equations have been discretized using finite volume method for a two-dimensional steady flow. The effects of geometrical and flow parameters, including nanoparticles volume fraction (0.01 < ϕ < 0.05), Richardson number (0.1 < Ri < 10), wave amplitude ratio (0.1 < α < 0.3) and wave length ratio (1 < λ < 3), have been investigated. Results reveal that increasing nanoparticle volume fraction within investigated Richardson number will increase Nusselt number. In addition, the maximum entropy generation rate declines as Richarson number increases. The optimal wave amplitude ratio (corresponding to lowest entropy generation), for wave length ratios of λ = 1 and λ = 2, found to be α = 0.2. Also, for wave length ratio of λ = 3, the minimum entropy generation approximately occurs at α = 0.1.

Analytical investigation of peristaltic nanofluid flow and heat transfer in an asymmetric wavy wall channel (Part I: Straight channel)

In this study, asymmetric peristaltic nanofluid flow in a two dimensional wavy channel is modeled and the heat transfer analysis is performed for it. Both upper and lower channel walls are considered in constant temperature and wavy shape. The governing equations were solved for five type’s nanofluids and least square method (LSM) analytical method using the Maple 15.0 mathematical software is applied as the efficient solution method for solving the governing equation. The effect of some parameters existed in the equations (Brinkman number, thermal and velocity slip parameters, Grashoff number and etc.), are discussed on the velocities and temperature functions. As an important outcome, reverse flow and maximum velocity were observed in channel throat and maximum temperature area occurred near the lower wall due to its higher temperature in boundary condition. Also, Brinkman number, thermal slip parameter and Grashoff number increments enhanced the temperatures values in channel.

Analytical investigation of peristaltic nanofluid flow and heat transfer in an asymmetric wavy wall channel (Part II: Divergent channel)

In this study, asymmetric peristaltic nanofluid flow in a two dimensional and divergent wavy channel is modeled and the heat transfer analysis is performed for it. The modeling is performed as two-phase model and it is assumed the magnetic field effects on the nanoparticles as magnetohydrodynamic (MHD) flow. Both upper and lower channel walls are considered in constant temperature and constant nanoparticle concentration. The governing equations were solved by analytical least square method (LSM) using the Maple 15.0 mathematical software and compared to available numerical results. The effect of some parameters existed in the equations (Geometry parameter, Brownian motion parameter, Dufour (Du) and Soret (Sr) numbers and etc.), are discussed on the velocities, temperature and nanoparticles concentration functions. As an important outcome, increasing in both Dufour (Du) and Soret (Sr) numbers lead to reduction in nanoparticles concentration while Dufour number increments make larger temperature profiles in the channel.

Combined effects of corrugated walls and porous inserts on performance improvement in a heat exchanger channel

In this paper, a numerical study is performed to investigate the combined effects of corrugated walls and porous inserts on heat transfer enhancement and thermal-hydraulic performance in a channel. Accordingly, a sinusoidal wavy wall channel partially filled with a porous material placed at its core is considered. The Darcy-Brinkman-Forchheimehr model is considered to study the flow in porous region and finite volume method (FVM) with SIMPLE algorithm are applied to solve the governing equations. It was found that the amplitude of the wavy wall has a considerable effect on average Nusselt number especially at small Darcy numbers. For example, at Re = 300, δ=0.3, α=0.2 and Da=10−2 the average Nusselt number of wavy channel increases about 12% in comparison with the straight one, while it improves about 38% at Da=10−4. Moreover, there is an optimum value of Darcy number corresponding to maximum performance evaluation criteria (PEC). At δ=0.3 and Re=300, for straight channel and wavy channel with α=0.1 the optimum value of Darcy number occurs at Da=10−3, while for α=0.2 and 0.3 the Da=10−4 leads to the maximum PEC.

A non-primitive boundary element technique for modeling flow through non-deformable porous medium using Brinkman equation

In this study, we develop a non-primitive boundary integral equation (BIE) method for steady two-dimensional flows of an incompressible Newtonian fluids through porous medium. We assume that the porous medium is isotropic and homogeneous, and use Brinkman equation to model the fluid flow. First, we present BIE method for 2D Brinkman equation in terms of the non-primitive variables namely, stream-function and vorticity variables. Subsequently, a test problem namely, the lid-driven porous cavity over a unit square domain is presented to assert the accuracy of our BEM code. Finally, we discuss an application of our proposed method to flows through porous wavy channel, which is a problem of significant interest in the micro-fluidics, biological domains and groundwater flows. We observe that the rate of convergence ( $$R_{c}$$ ) increases with increasing Darcy number. For low Darcy number streamlines follow the curvature of the wavy-walled channel and no circulation occurs irrespective of the wave–amplitude, while for high Darcy number the flow circulation occurs near the crest of the wavy-walled channel, when the wave–amplitude is large enough.

Numerical study of fully developed unsteady flow and heat transfer in asymmetric wavy channels

The present study aims at the numerical investigation of fully developed flow and heat transfer through asymmetric wavy-walled geometry. The flow characteristics and thermal performance of wavy-walled configuration is assessed for three different geometries generated using three phase shift angles (φ) between the two opposite heated walls. The function y=2a·sin2(πx/L) is used to describe the walls of the wavy channel. For the symmetric geometry (φ=180°) considered in the present study, the ratios Hmin/Hmax and L/a are kept fixed to 0.4 and 8.0 respectively while the four asymmetric channels are created through a desired phase-shift of φ=0°, 45°, 90° and 135° between the two opposite sine-wave walls. The finite volume method on collocated grid has been employed to solve the time dependent Navier–Stokes and energy equation. The fully developed flow and heat transfer has been modeled using periodic boundary conditions. The critical Reynolds number of unsteadiness is found to be the highest for the symmetric (φ=180°) wavy-walled channel. The flow in all three geometries has been found to be equally complex but the asymmetric geometry with 0° phase-shift reveals maximum flow asymmetry about the flow centreline. It has also been observed that the most asymmetric geometry having 0° phase-shift encourages best heat transfer over symmetric configuration with 180° phase-shift, but is accompanied by the highest friction penalty.