Reynolds Number Range Research Articles

Numerical analysis of thermal-hydraulic comprehensive performance of composite corrugated tubes with different cross-section shapes

Composite corrugation is a structure transformed from traditional corrugation to improve the thermal-hydraulic comprehensive performance (THCP) of corrugated tubes. However, compared to simple corrugations, the mechanism by which composite corrugations enhance THCP is still unclear. Therefore, in this work, numerical simulations are performed within the Reynolds number (Re) range of 5000–20,000 to evaluate the mechanism of composite corrugation strengthening THCP. The distributions of flow velocity, streamline, turbulent kinetic energy (TKE), pressure, and normalized force are used to reveal the differences in the effects of simple and composite corrugations on THCP. In addition, the influence of composite corrugation cross-sections and distribution forms on THCP has been explored in detail. The results indicate that increasing the impingement of the fluid on the tube wall, disrupting the fluid boundary layer, and expanding the range of secondary flow are the main mechanisms by which composite corrugations further strengthen THCP compared to simple corrugations (CT-SC). The THCP of composite corrugation (CT-CC-A-F) can be increased by 31.5% at Re = 20,000 compared to CT-SC. Composite corrugations with different cross-sections cause differences in THCP due to their varying effects on the distribution of secondary flow and the impingement of the fluid on the tube wall. The difference in the influence of composite corrugation distribution forms on THCP is still caused by the difference in the impingement of the fluid on the tube wall. This work can provide a reference for the design of composite corrugations to achieve better THCP.

Thermohydraulic performance augmentation of triangular duct solar air heater using semi‐conical vortex generators: Numerical and experimental study

AbstractThermohydraulic performance augmentation using turbulence promotors is a commonly adopted technique in solar air heater (SAH) applications. This article presents the thermohydraulic performance augmentation of triangular duct SAH using semi‐conical vortex generators (SCVG) using computational fluid dynamics and experimental methodology for various flow Reynolds numbers ranging from 6000 to 21,000. An in‐depth parametric analysis is undertaken to establish the influence of flow attack angle, relative longitudinal pitch, relative transverse pitch and cone diameter of SCVG on the thermohydraulic performance as indicated by the thermohydraulic performance parameter (THPP). The results reveal that the SCVG generates longitudinal vortices and introduces flow impingement zones which significantly affects the flow and heat transfer characteristics of air heaters. Correlations for Nusselt number and friction factor are established, which predicts the performance outcomes with an average error of 6.74% and 4.46%, respectively. The optimal THPP is determined to be 1.74 using artificial neural network model and Bonobo Optimization algorithm. The SCVG produces THPP values well above unity for the entire flow Reynolds number range of 6000–21,000.

Vortex-induced rotation of a square cylinder under the influence of Reynolds number and density ratio

Numerical simulations are carried out on the vortex-induced rotations of a freely rotatable rigid square cylinder in a two-dimensional uniform cross-flow. A range of Reynolds numbers between 40 and 150 and density ratios between 0.1 and 10 are considered. Results show eight different characteristic regimes, expanding the classification of Ryu & Iaccarino (J. Fluid Mech., vol. 813, 2017, pp. 482–507). New regimes include the transition and wavy rotation regimes; in the ${\rm \pi}$ -limited oscillation regime we observe multipeak subregimes. Moment-generating mechanisms of these regimes and subregimes are further elucidated. A phenomenon related to the influence of density ratio is the tooth-like shape of the ${\rm \pi} /2$ -limit oscillation regime observed in the regime map, which is explained as a result of the imbalance relation between the main frequencies of rotation response and the vortex shedding frequency. In addition, existence of multiple regimes and multistable states are discussed, indicating multiple stable attractive structures in phase space.

A comprehensive numerical study of the effects of surface roughness on a finite-length cylinder with an aspect ratio of 1.5 for Reynolds numbers ranging from 3.9 × 103 to 4.8 × 105

The aerodynamic performance of the flow around a cylinder with two free ends, which is also referred to as a finite-length cylinder, continues to be a subject of rigorous academic inquiry. However, limited research has been conducted on finite-length cylinders with rough surfaces. To evaluate the impact of relative roughness on the aerodynamic performance of a finite-length cylinder, we performed numerical simulations on a cylinder model with an aspect ratio of 1.5 with various relative roughness values. These simulations covered a range of Reynolds numbers from 3.9 × 103 to 4.8 × 105. The results indicated that both the relative roughness and Reynolds number could affect the aerodynamic characteristics of the cylinder by altering the flow pattern around the cylinder. As the Reynolds number increased, the four spiral eddies behind the finite-length cylinder gradually lost their symmetry in the axial direction and eventually transformed into a pair of recirculating eddies. Moreover, when the Reynolds number was constant at 2.0 × 104, an increase in the surface roughness of the cylinder triggered the same phenomenon. Additionally, the mechanism by which the surface roughness affected the aerodynamic coefficient of a finite-length cylinder in the current Reynolds number range was revealed. This influence was mainly attributed to the impact of pressure on the backside of the cylinder.

Influence of the twisting and nano fluids on performance of a triangular double tube heat exchanger

Abstract The hydraulic and thermals performance of flow in a double-tube heat exchanger with an inner twisted triangle tube of length L = 1 m has been studied numerically. Equations for energy, turbulence, and Navier–Stokes were used to model the fluid flow and heat transfer in a double-tube heat exchanger with an inner twisted triangle tube. The Reynolds number range was 5000–30,000 for nanofluid (water-Al2O3) as a working fluid under a turbulent flow regime. The considered configuration was examined by varying the volume concentration of nanofluid while keeping the twist ratio constant (Tr = 5). Different cases of volume concentration of nanofluid are triggered (0.05 %, 1 %, 2.5 %, and 4 %, respectively). The numerical outcomes of a double-twisted tube heat exchanger with an inner triangle-twisted tube are validated with the obtainable numerical data. The governing equations were solved with ANSYS Fluent 18.2. The findings reveal that the larger volume concentration of nanofluid (4 %) gives a greater Nusselt number and vice versa due to the increased thermal conductivity of the nanofluid in the double twist tube heat exchanger compared with a plain tube. However, the nanofluid Nusselt number grows with the rise of both the Reynolds number and volume concentration (Ø), and the best value of the Nusselt number is 210 when Reynolds number = 30,000 and Ø = 4 %. The effectiveness of the heat exchanger grows with an increase in the concentration of the nanofluid and a reduction in the torsion ratio compared to the normal tube. The effectiveness of the double-tube heat exchanger with an inner twist triangle tube increases to the highest value of 0.38 at Reynolds 30,000 and Ø = 4 %.

Nanofluid cooling of a hot rotating circular cylinder employing cross-flow channel cooling on the upper part and multi-jet impingement cooling on the lower part

This study explores the convective cooling features of a hot rotating cylinder by using the combined utilization of cross-flow on the upper part and multi-jet impingement on the bottom part. The analysis is performed for a range of jet Reynolds number (Re) values (between 100 and 500), cross-flow Re values (between 100 and 1000), rotational Re values (between −1000 and 1000), cylinder size (between 0.25wj and 3wj in radius), and center placement in the y direction (between −1.5wj and 1.5wj). When the cylinder is not rotating, the average Nu increment becomes 102% at the highest jet Re, while it becomes 140.82% at the highest cross-flow Re. When rations become active, the impacts of cross-flow and jet impingement cooling become slight. As compared to a motionless cylinder, at the highest speed of the rotating cylinder, the average Nu rises by about 357% to 391%. For clockwise rotation of the cylinder, a lager cylinder results an increase in the average Nu by about 86.3%. At the lowest and highest cross-flow impinging jet Re value combinations, cooling performance improvement becomes a factor of 8.1 and 2, respectively. When the size of the cylinder changes, entropy generation becomes significant, while the vertical location of the cylinder has a slight impact on entropy generation.

Experimental and numerical study on the pressure drop and flow pattern of liquid foam in a foam generator

In the present study, a comprehensive analysis of the pressure drop, flow pattern, and foam structural properties of vertical upward two-phase flow in a Kenics static foam generator of a compressed air foam system was carried out. A liquid with an extremely low surface tension (16.5 mN/m) was used for making the foam. The effects of the number of elements (number of individual elements combined into the mixer), aspect ratio (the ratio of length to diameter of each element), and transition angle (transition angle between elements) of the Kenics mixers on the pressure loss during foam generation were studied in detail over a wide range of Reynolds numbers through experiments and numerical simulation. A new pressure drop correlation was successfully obtained by scaling analysis and the modified Lockhart–Martinelli correlation was proposed to describe the pressure drop during foam generation. Furthermore, the experimental results validated the proposed correlation and exhibited good reliability and predictive accuracy. Finally, four flow patterns for foam generation in vertical pipes that were different from the classical gas–liquid two-phase flow patterns were proposed, and the relationships among the pressure drop, flow pattern, and foam structural properties were explored. This research expands the study of foam generation in vertical tubes containing a built-in spiral structure with low flow resistance. It provides new insights and guidance for developing continuous foam manufacturing.

Drag reduction assisted emulsification in a micro-channel

An experimental study of the turbulent dynamics of emulsification in a cross-slot microfluidic device is presented. The continuous phase contains a minute amount of an inelastic polymer (xanthan). The Reynolds numbers are sufficiently large (up to 16000) so the drag reduction phenomenon is observed during the emulsification process. The statistics of droplet sizes in the resulting emulsions are measured ex-situ by means of digital microscopy in a wide range of Reynolds numbers and polymer concentrations in the continuous phase. Integral measurements of the statistics of the pressure drops in the micro-channel allow one to systematically map the drag reduction states. Corresponding to each state, the space–time dynamics of the emulsification process are assessed by means of in-situ high speed imaging of the interface between the two fluids which further allows one to extract the characteristic time and space scales associated to the dynamics of the interface. Various dynamic regimes of the microscopic emulsification process are mapped in terms of the Reynolds number and shear thinning rheology of the continuous phase.

A modified drag coefficient model for calculating the terminal settling velocity and horizontal diffusion distance of irregular plume particles in deep-sea mining.

Deep-sea mining inevitably produces plumes, which will pose a serious threat to the marine environment with the continuous movement and diffusion of plumes along with ocean currents. The terminal settling velocity (wt) of irregular particles is one of the crucial factors for determining the plumes' diffusion range. It is generally calculated by drag coefficient (CD), while most existing CD models only consider single shape characteristic parameter or have a smaller range of Reynolds number (Re). In this study, a new shape factor (γ) of irregular particles is proposed by considering the thickness (one-dimension), the projected area (two-dimension), and the surface area (three-dimension) of irregular particles as well as their coupling effect to establish a modified CD model for calculating the wt. A modified Gaussian plume model is proposed to predict the horizontal diffusion distance of the plume particles by considering the settling velocity and diffusion effect of irregular particles. Research results show that the wt increases nearly linearly, with a gradually decreased slope and slightly then greatly with the increasing of γ, dp (diameter) and ρp (density), respectively. The modified CD model is verified to be more valid with a wider application range (Re < 3×105) than five existing CD models by the test results. The larger the ρp or dp, the larger the wt and thus the smaller the Sh. This study could provide a theoretical basis for calculating the plume diffusion range to further study the impact of deep-sea mining on the ocean environment.

A multi-region analysis of unsteady Oseen's equation for accelerating flow past a circular cylinder

It is difficult to find a valid high-order (of Reynolds number) analytical approximation to the uniform viscous flow past an infinite circular cylinder by applying perturbation techniques. In this study, we show that by accelerating flow past a circular cylinder with taking unsteady Stokes' solution as an initial approximation, higher-order approximation solutions to unsteady Oseen's equation can be obtained by an iteration scheme of perturbation, which exactly satisfy the boundary conditions. As a matter of fact, the nonlinear (convective) term linearized by Oseen's approximation is overweighted especially near the body surface. To eliminate the overweight, a multi-region analysis is proposed in this study to improve analytical unsteady Oseen's solution so as to extend the valid range of Reynolds numbers. In other words, the flow region is hypothetically divided into several annular regions, and the linearized convective term in each region is modified by multiplying with a Carrier's coefficient c (0 &amp;lt; c ≤ 1). The results show that, when the accelerating parameter in the range of 0.5 ≤ a ≤ 4, the maximum effective Reynolds number Reeff of the fourth-order five-region solution is both much larger than that of Stokes' and Oseen's ones. For example, when a = 0.5, Reeff = 22.26 is roughly eight times that of Stokes' solution (Reeff = 2.67), and nine times that of Oseen's solution (Reeff = 2.41). Moreover, when the instantaneous Reynolds number Re(t) is smaller than the Reeff, the flow separation angle and the wake length are both consistent with the numerical results obtained by accurately solving the full Navier-Stokes equations. In addition, the flow properties, including the drag coefficients, streamline patterns, and the pressure coefficients, as well as the vorticity distributions also agree well with the numerical results. This study represents a significant extension of our previous study for unsteady Stokes' equation [Xu et al., Phys. Fluids 35, 033608 (2023)] to unsteady Oseen's equation and its generalization.

Alternate method for resolving particle collisions in PRS of freely evolving particle suspensions using IBM

Particle Resolved simulations using the Immersed Boundary Method (IBM) are performed for freely evolving sphere suspensions in the Reynolds number range of [10, 300], solid volume fraction (φ) of [0.1, 0.4] with solid to fluid density ratio of 2, 10 and 100. Collisions between particles are initiated at an inter-particle buffer distance and solved between subsequent fluid time steps using a soft sphere model. Guidelines for permissible buffer distances are developed as a function of solid fraction. Viscous damping effects in the unresolved thin lubrication layer between particles near collision is modeled using a wet coefficient of restitution. Finally, a new correlation for particle fluctuating velocities is proposed and the predicted drag force is compared to previously proposed drag correlations.

Numerical investigation of the thermal-hydraulic performance of a novel parabolic trough wavy tubular receiver by using FMWNCT/oil-nanofluid coupled with fins

This study employs a computational fluid dynamics (CFD) approach to assess the performance of a novel wavy profile tube receiver. It integrates rectangular fins and an Oil-based nanofluid, specifically utilizing Thermodyne GG-03 synthetic oil combined with Functionalized Multi-Wall Carbon Tubes (FMWNCT). The synthesis involves rigorous experimental procedures to characterize the thermophysical properties of the oil and nanofluid. Empirical correlations, validated against Bitam et al.'s model [1], guide the numerical analysis. The investigation, utilizing a steady-state κ - ω SST turbulence model with a non-uniform Gaussian thermal flux distribution, explores thermohydraulic performance in fully developed turbulent flow (Reynolds number range: 2 × 104 – 5 × 104). Comparative analysis with Bitam et al.'s work, employing Syltherm 800 oil as a reference, reveals a 25.76% average Nusselt number enhancement with Thermodyne GG-03. Additional improvements are observed: 124.69% with FMWNCT/oil-nanofluid, 137.04% with fins, and 236.54% with combined FMWNCT/oil-nanofluid and fins. These enhancements lead to increased heat transfer coefficients and rates. The friction coefficient rises by less than 60%, mainly attributed to the Nusselt number improvement. At RE = 20000, the Maximum Performance Evaluation Criteria (PEC) is 5.5, signifying significant improvement. Notably, a 300% PEC enhancement is observed compared to Roger and Mayhew's curved tube model [1]. In conclusion, these findings offer valuable insights for efficiently designing wavy tubular receivers in PTR collectors.

Rigorous benchmarking of an iterative IBM solver by comparison to body-fitted mesh results

This study addresses the validation challenges of Immersed Boundary Method (IBM) solvers by proposing a consistent benchmarking approach. A temporally second-order Arbitrary Lagrangian–Eulerian (ALE) solver implemented in OpenFOAM is verified against lid-driven cavity flow and flow past static and oscillating cylinders. It then serves as the underlying fluid flow solver for a fully implicit diffusive direct forcing IBM solver that achieves temporal second-order accuracy, verified by the static and oscillating cylinder cases. Leveraging the shared numerical framework, the IBM solver is rigorously validated against ALE using identical settings, parameters, and nearly identical grids across twenty test cases, including stationary cylinder flow (Re = 40, 100, 185), oscillating cylinder in quiescent flow (Re = 100, KC = 5), and transversely oscillating cylinders with varying amplitudes and frequencies (16 cases in total). The IBM solver demonstrates robustness (CFL up to 8) and accuracy over a wide Reynolds number range, with relative drag coefficient errors below 7% for all considered cases. Incorporating body force correction, which reduces slip errors at negligible added computational cost, drastically improves accuracy. Proper Rhie–Chow momentum interpolation, including body forces, is critical in the adopted collocated finite volume method. For unsteady problems, the computational cost is greatly reduced without compromising accuracy by using CFL≈1.5−2 with only two outer iterations. The proposed benchmarking framework can be easily used for validation of other IBM approaches and thus potentially help to advance the state of IBM.

Suggestion of Correlations to Obtain Shell and Tube Side Nusselt Numbers in Coiled Heat Exchangers

In coiled tube heat exchangers increase in curvature ratio and effective contact of shell fluid with coil surface led to better thermal characteristics. This work addresses study of thermal performance, shell and tube heat transfer coefficients (ho and hi). Also, mathematical correlations are predicted to obtain shell and tube Nusselt numbers (Nuo and Nui). In the designing of compact coiled heat exchangers consisting of straight helical coil (SHC), conical coil (CC) and spiral coil knowledge of Nuo and Nui is necessary whereas mathematical correlation to calculate Nuo considering variations in shell geometry is not found. Five heat exchangers consisting of three cone coils (angle, ϴ = 30°, 50° and 70°), spiral coil (ϴ = 0°) and SHC (ϴ = 90°) are tested. Using Wilson plot method ho and hi are obtained for wide range of tube side Reynolds numbers (Rei = 3700 - 21000). It is observed that, highest ho is obtained for ϴ = 30°CC with better thermal performance. Lowest ho is obtained for ϴ = 90°SHC. Ratio of height of shell, Hs and diameter of shell, Dso is considered in prediction of single correlation as: Nuo = 16.55.Reo0.55.Pro0.4 *(Hs/Dso)0.096. Comparison with experimental findings shows variation of 0-14%. Similarly two correlations are proposed as: Nui = 0.0512.Rei0.80.Pri0.4.CRave0.18 and Nui = 0.0365.Dei0.815.Pri0.4.CRave-0.3. A fair agreement is found with existing researchers.

Vortex shedding behind porous flat plates normal to the flow

This work examines the influence of body porosity on the wake past nominally two-dimensional rectangular plates of fixed width $D$ in the moderate range of Reynolds numbers $Re = UD/\nu$ (with $U$ the incoming velocity and $\nu$ the kinematic viscosity) between 15 000 and 70 000. With porosity $\beta$ defined as the ratio of open to total area of the plate, it is well established that as porosity increases, the wake shifts from the periodic von Kármán shedding behaviour to a regime where this vortex shedding is absent. This change impacts the fluid forces acting on the plate, especially the drag, which is significantly lower for a wake without vortex shedding. We analyse experimentally the transition between these two regimes using hot-wire anemometry, particle-image velocimetry and force measurements. Coherence and phase measurements are used to determine the existence of regular, periodic vortex shedding based on the velocity fluctuations in the two main shear layers on either side of the wake. Results show that, independent of $Re$ , the wake exhibits the classical Kármán vortex shedding pattern for $\beta &lt;0.2$ but this is absent for $\beta &gt;0.3$ . In the intermediate range, $0.2&lt;\beta &lt;0.3$ , there is a transitional regime that has not previously been identified; it is characterised by intermittent shedding. The flow alternates randomly between a vortex shedding and a non-shedding pattern and the total proportion of time during which vortex shedding is observed (the intermittency) decreases with increasing porosity.

Experimental studies on the effect of Al2O3 + water nanofluid concentrations on dimensionless heat transfer parameters in a cleanroom air handling unit

Nanofluid, a colloidal suspension of nonmetallic or metallic nanoparticles into conventional base fluid and used for heat transfer characteristics enhancement for many industrial applications. Cleanrooms are essential at various industries for controlling airborne contamination and environmental parameters. In this article, heat transfer properties of nanofluid (Al2O3 + water) at various nanoparticle concentrations (1%, 2%, and 3%) on a prototype cleanroom air handling chiller unit was investigated experimentally in laminar flow zone. Thermal conductivity ratio, Nusselt number, Peclet number, and pressure drop were obtained for above nanoparticle concentrations. Experimental investigations indicate the heat transfer properties improvement in a prototype cleanroom air handling chiller unit by using nanoparticle at base fluid. Experimental investigation on varying Al2O3 + water nanofluid concentrations in a cleanroom air handling chiller unit heat exchanger revealed a notable increase in heat transfer by reducing nanoparticle size from 50 to 10 nm and increasing concentration from 1% to 3% volume, resulting in a 17.70% rise in thermal conductivity ratio and a significant 9.23% increase in Nusselt number at higher Peclet numbers. However, this improvement in heat transfer was accompanied by a substantial 72.5% increase in pressure drops, particularly with increased Reynolds number and particle concentration. Manipulating nanoparticle characteristics resulted in substantial improvements in Nusselt number across a wide range of Reynolds numbers, with smaller particle sizes and higher volume concentrations yielding more significant heat transfer improvements. The novelty of this research lies in its investigation of the influence of variable Al2O3 + water nanofluid concentrations, encompassing different nanoparticle sizes, and volume concentrations, on dimensionless heat transfer parameters within a cleanroom air handling unit, offering valuable insights into optimizing heat transfer efficiency in a controlled and critical environment, addressing a significant research gap in the field.

Multi-objective optimization of expansion-contraction micromixer using response surface methodology: A comprehensive study

This study provides a comprehensive analysis of the optimization of micromixers, highlighting their critical role in improving the effectiveness of chemical reactions and fluid mixing processes at a small scale. Employing OpenFOAM, we optimized the geometry of a micromixer comprised of multiple expansion-contraction segments across a Reynolds number range from 0.1 to 100. We established three design variables, P1, P2, and P3, to modify the geometry of each contraction-expansion segment to maximize the overall performance of the micromixer. Our experimental design utilized the optimal space-filling method, followed by the application of the genetic aggregation method to the generated sample to yield response surfaces. Two distinct optimization strategies were implemented following the verification of the response surfaces’ accuracy. The first focused on maximizing the mixing index, while the second aimed to increase the mixing index and reduce the pressure difference simultaneously. A subsequent sensitivity analysis revealed significant relationships between the design variables and objective parameters. Key findings include achieving maximum MI increases of 26.26 % and 23.06 % at Re values of 10 and 100, respectively, and the role of recirculation zones and chaotic convection in enhancing mixing, especially at Re = 100. Furthermore, a comparative analysis with other micromixer optimization studies demonstrated the superiority of the present study, particularly in reducing pressure difference, thereby enhancing overall mixer performance.

A flow-reconstruction based approach for the computation of hydrodynamic stresses on immersed body surface

This study focuses on obtaining reliable hydrodynamic stresses on the surface of rigid bodies in the simulation of fluid-solid interactions using the diffuse-interface immersed boundary method (IBM). In order to obtain the pressure and velocity gradient information on the immersed boundary, we employ a model to reconstruct the near-boundary fluid flow along the surface normal direction. Different from most existing flow reconstruction models in diffuse-interface IBMs based on the boundary layer approximation, we propose a new reconstruction model relying only on the non-slip velocity and local flow information. With this improvement, the present reconstruction model is theoretically applicable to fluid flows with intermediate Reynolds numbers (with the existence of a laminar boundary layer) and low Reynolds numbers (in the absence of a boundary layer). To examine the validity of the present reconstruction model, we conduct a series of simulations, including the uniform flow past a fixed body and the settling of a rigid body in a quiescent fluid. It is demonstrated that the present reconstruction model has a better performance than existing models in predicting hydrodynamic stresses on the immersed boundary within a wide range of Reynolds numbers from O(1) to O(100). The capability and robustness of the proposed model demonstrate its potential to address fluid-solid interaction problems with a-priori unknown or time-varying Reynolds numbers, such as fully resolved simulations of particle laden flows.

Micro-PIV study on the influence of viscosity on the dynamics of droplet impact onto a thin film

This work presents a systematic experimental study of droplet impact onto a wet substrate. Four different silicone oils are used, covering a range of Reynolds number between 116<Re<1106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$116< \ ext{Re} <1106$$\\end{document} at two different initial wall film heights. The objective is to characterize the temporal and radial evolution of the velocity field within the crown crater by means of micro-PIV. Our findings show that the velocity field has the structure of an axisymmetric stagnation point flow with decaying strength a(t). The latter exhibits an exponential decay and can be explained in terms of the exponential decay of the pressure force exerted by the impacting droplet onto the wall film. In this context, the commonly accepted functional dependence a(t)∝t-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a(t) \\propto t^{-1}$$\\end{document} represents only the first-order Taylor approximation of the exponential decay and has therefore only a limited temporal validity. The analysis also corroborates the existence of an inertial regime concerning the velocity field for Re>270\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{Re}} > 270$$\\end{document}. This is not observed at lower Re numbers due to the increased pressure losses caused by the extensional (normal) strain during the radial spreading of the lamella. To validate these findings a holistic approach is chosen, which combines numerical results, analytical solutions and experimental data from literature. In particular, by using the continuity equation, it is shown that the experimental decay of the wall film height can be reconstructed from the velocity measurements. Consilience of results from different approaches provides a robust validation of the micro-PIV data obtained in this work.Graphical abstract

Experimental investigation of heat transfer and aerodynamic drag of novel heat sinks with lamellar fins

Heat transfer and aerodynamic drag of novel small-sized heat sinks with lamellar fins, designed for electronic cooling, were experimentally investigated under conditions of forced convection in the range of Reynolds numbers 1 250–10 500. It was found that a gradual reduction in the fin spacing from 6 mm to 3 mm with a 29° angle of taper between the outermost fins leads to an increase in the heat transfer intensity by 15–32% with a significant increase in aerodynamic drag compared to the surface with a constant fin spacing of 6 mm. Incomplete cross-section cutting of fins at the relative depth of 0.6 in addition to the gradual reduction in the fin spacing provides aerodynamic drag decrease by 5–20% and increase of heat transfer intensity by 18–20% in comparison with the similar heat sink without fins cutting. Proposed novel designs of heat sinks enabled us to decrease by 7°С–16°С the maximum overheating of the heat sink's base in the flow speed range from 2.5 m/s to 7.5 m/s at constant heat load. To ensure a constant value of maximum overheating of the heat sink base the inlet flow velocity for the surface with constant fin spacing should be 1.6–2 times higher than that for the heat sink with 29° taper angle between outermost fins and partially fins cutting. In this case, the aerodynamic drag for the latter will be higher only by 1.6–2.7 times, which is quite acceptable.