Ring Of Functions Research Articles

Baffle and geometry effects on nanofluid forced convection over forward- and backward-facing​ steps channel by means of lattice Boltzmann method

In this study, we present a numerical simulation of MWCNT-Fe3O4/water hybrid nanofluid forced convection heat transfer over the forward- and backward-facing steps channel having a baffle fixed on its top wall. A FORTRAN’s homemade code based the lattice Boltzmann method (LBM) is used here. The effects of the Reynolds number (25 ≤Re≤ 100), the volume fraction of nanoparticles (0 ≤ϕ≤ 0.003), the position of baffle (3 ≤X2≤ 7), the length of baffle (0 ≤h≤ 1.5) and the geometry parameter (2 ≤X1≤ 4) on flow pattern and heat transfer characteristics are provided a deep insight. The results indicate that the average Nusselt number is an increasing function of Re and ϕ. The baffle has a significant effect on the flow pattern and heat transfer characteristics. When the length of the baffle increases, the recirculation region behind the backward-facing step shrinks. The average Nusselt number increases by increasing the length of the baffle or moving the baffle towards the backward-facing step.

Evaluation of thermal and fluid dynamic performance parameters in aluminum foam compact heat exchangers

This paper analyses the behavior of heat exchangers with metal foam. A numerical study in a laminar steady state two-dimensional model is provided to evaluate the thermal - fluid dynamic performance of the system. An aluminum foam block embedded with an array of five circular tubes and assigned uniform temperature, constitute the physical domain. The open-celled metal foam is considered as a porous medium in local thermal non equilibrium (LTNE) and the Darcy – Forchheimer – Brinkman model is assumed. The metal foam has a porosity equal to 0.9353 and a pore density equal to 20 pores per inch (PPI). The numerical simulations are carried out considering air as the cooling fluid with several mass flow rate for assigned temperature of the tube surface. The Reynolds number, Re, based on tube diameter, ranges from 56 to 1120, the ratios between the thickness of metal foam and tube diameter, Lmf/d, and between the tube pitch and tube diameter, 2H/d, are in the ranges from 1 to 20 and 1.5–25, respectively. The goal of this investigation is to find the compact heat exchanger size for an assigned metal foam that allows trade-off between the improvement of the heat transfer and the increment of pressure drop, and to study the fluid dynamics and thermal behavior of these configurations. The study focuses on thermal performances of a metal foam heat exchanger using several conventional parameters employed in the analysis of porous medium heat exchangers to find optimal geometrical configurations. Results are given in terms of Colburn factor, friction factor and area goodness factor as a function of Re, Lmf/d and 2H/d. It is shown that the compact heat exchanger, examined in the investigation, presents optimum Reynolds number values; where the ratio between the Colburn and the friction factor, AG, attains a maximum value for metal foam, with different thickness and distance between the tubes of the heat exchanger. Two correlations for AGmax are proposed for 56 ≤ Red ≤ 1120; one in terms of dimensionless thickness and another for the dimensionless pitch.

Adams operations and symmetries of representation categories

Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point of view, they codify some of the symmetric monoidal structure of the representation category. We show that the monoidal structure on the category alone, regardless of the particular symmetry, determines all the odd Adams operations. On the other hand, we give examples to show that monoidal equivalences do not have to preserve the second Adams operations and to show that monoidal equivalences that preserve the second Adams operations do not have to be symmetric. Along the way, we classify all possible symmetries and all monoidal autoequivalences of representation categories of finite groups.

Numerical simulation of solute removal from a cross-flow past a row of parallel hollow-fiber membranes

A multi-parametric simulation of the 2-D steady transverse flow of viscous incompressible fluid and diffusion transport of a dissolved solute past a model fibrous medium – a row of parallel sorbent fibers or hollow-fiber membranes is performed in a wide range of Schmidt (Sc) and Peclet (Pe) numbers for fiber Reynolds numbers up to Re = 100. The Navier-Stokes and convection-diffusion equations are solved numerically and the fiber capture efficiency for solute molecules is calculated as a function of Re, Sc and inter-fiber distance. The field of solute concentration and the fiber capture efficiency are found with zero concentration-fixed and diffusion flux boundary conditions set at the streamlined fiber surface, and the difference between the results of simulations with the two boundary conditions is shown for high Peclet numbers. It is also shown that the fiber capture efficiencies estimated with both boundary conditions tend to a constant maximum value for low Peclet numbers. The results of simulations for the fiber capture efficiency are validated by comparison with existing analytical asymptotic solutions for low and high Peclet numbers, and the agreement is shown.

Overall performance analysis and GRA optimization of solar air heater with truncated half conical vortex generators

The present numerical study using ANSYS FLUENT 18.1 is based on improving the thermohydraulic performance of a solar air heater by embedding truncated half conical vortex generators (THC-VGs) on the absorber plate. Grey relational analysis (GRA) optimization technique is employed to achieve the best configuration for the applicable range of Reynolds number (Re = 3500–16000). The THC-VGs are fixed on the absorber plate at a relative pitch ratio, P/e range of 2.67–6.67 and placed such that the angle of attack, α lies in between 0° and 90°. RNG k-ε turbulent model is employed to solve the complex governing equations of CFD. Results are analysed by computing different performance parameters like, Nusselt number, Nu, thermal enhancement factor, TEF, friction factor, f, friction factor enhancement factor, FEF and thermohydraulic performance parameter, THPP. A maximum percentage enhancement of 187% in Nu is noted for α = 60°, P/e = 2.67 and Re = 16000. Results are supported with proper justifications by using different contours derived from the post processing unit of the CFD code. Proper flow dynamics along with thermal behaviour due to the introduction of THC-VGs are explored. Correlations for Nu and f are developed as a function of Re, P/e and α.

Correlations of the capture efficiency with the Dean number and its constituents in heterogeneous microfluidic immunosensors

In heterogeneous microfluidic immunosensors, enhanced capture efficiencies of the antigens (Ag) in the carrier fluids by the surface-immobilized antibodies (Ab) facilitate lower detection limits and thus early detection of disease. Capture efficiency depends on the interplay of transport, reaction parameters and the geometry of the system. A detailed analysis on the enhanced capture efficiencies due to secondary flows in heterogeneous immunosensors has not received significant attention and is the theme of the present work. We conducted a systematic study to observe the significance of secondary forces on the capture efficiency, manifested as the average surface concentration (Cs,avg), in serpentine channels of different lengths (l) and radius of curvature (Rc) as a function of the Reynolds number (Re). Experimental observations were validated with numerical simulations. Micro-PIV studies at different planes and sections of the serpentine microchannels were conducted and matched with the simulated velocity profiles. Further investigation of the process and the geometrical parameters was conducted using numerical simulation and the behaviour of Cs,avg as a function of Re and Rc was plotted for different cases. A highlight of the present work are correlations of Cs,avg as a function of the Dean number (De), as well as its constituents (Re and α). The scientific studies of the geometrical and process parameters which affect the analyte capture advance the understanding of the phenomena and the proposed engineering correlations would be useful in the design of more efficient flow-based heterogeneous immunosensors.

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-Bénard convection. High resolution two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 106 ≤ Ra ≤ 107 and the Prandtl number (Pr) of 0.025. Our results show that the global heat transport and momentum scaling in terms of Nusselt number (Nu) and Reynolds number (Re) are Nu = 0.21Ra0.25 and Re = 6.11Ra0.50, respectively, indicating that scaling exponents are smaller than those for moderate-Prandtl number fluids (such as water or air) in the same convection cell. In the central region of the cell, probability density functions (PDFs) of temperature profiles show stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs of temperature profiles show a multimodal distribution at relatively lower Ra, while they approach the Gaussian profile at relatively higher Ra. We split the energy dissipation rate into contributions from bulk and boundary layers and found the locally averaged thermal energy dissipation rate from the boundary layer region is an order of magnitude larger than that from the bulk region. Even if the much smaller volume occupied by the boundary layer region is considered, the globally averaged thermal energy dissipation rate from the boundary layer region is still larger than that from the bulk region. We further numerically determined the scaling exponents of globally averaged thermal energy dissipation rates as functions of Ra and Re.

Investigation of effectiveness and pumping power of plate heat exchanger with rough surface

In the present paper, an experimental study of the effectiveness and pumping power of plate heat exchanger (PHE) with rough surface was performed. The experiments were developed for different values of relative roughness, Rr, of 2.6 * 10−4 (smooth surface), 3.4 * 10−4, 7.5 * 10−4 and 9.8 * 10−4 for Reynolds number, Re, varied from 500 to 5000. The average heat transfer rate, Qavg, hence the effectiveness of PHE, ε, and number of transfer units, NTU, as well as pressure drop, Δp, consequently pumping power, P, and specfic heat rate, SHR, were estimated. The results show that Qavg and NTU are enhanced with increasing Rr; while, they are decreased with increasing Re. At Re = 5000, the effectiveness of PHE with relative roughness of 3.4 * 10−4, 7.5 * 10−4 and 9.8 * 10−4 is greater than that of the smooth surface by 11.5%, 16.6% and 18.6%, respectively. Furthermore, Δp and P are increased by increasing Rr and Re. Moreover, at Re = 500, SHR is enhanced with increasing Rr and its improvements compared with the smooth surface are 39.5%, 23.4% and 6.9% for Rr of 3.4 * 10−4, 7.5 * 10−4 and 9.8 * 10−4, respectively. In addition, empirical correlations are proposed to estimate SHR as a function of Rr and Re with a standard deviation of 5.1%.

Application of an artificial neural network to predict the entrance length of three-dimensional magnetohydrodynamics channel flow

In this paper, a feed-forward, back-propagation neural network was employed for modeling the three-dimension magnetohydrodynamics (MHD) developing fluid flow. The aim of the study is to obtain a correlation for calculating the entrance length by applying an artificial neural network (ANN). To collect the data for training ANN, the numerical finite volume method (FVM) was conducted. The data were collected including Reynolds number (Re) ranging from 500 to 1000 and Hartmann number (Ha) ranging from 4 to 14 for a three-dimensional rectangular channel with four different aspect ratios (AR in a three-layer ANN for modeling the flow and computing the entrance length as a function of AR , Re and Ha. The results obtained from the ANN, FVM and the proposed correlations were compared and it was observed that the variation of the entrance length was different for each AR . Thus, two correlations were proposed with the different range of the AR and Ha. The contours and vectors of the velocity along the channel direction and for different cross-sections were illustrated. In addition, the effect of AR and Ha on the entrance length and pressure loss was presented.

What determines the sizes of bars in spiral galaxies?

ABSTRACT I use volume- and mass-limited subsamples and recently published data from the Spitzer Survey of Stellar Structure in Galaxies (S4G) to investigate how the size of bars depends on galaxy properties. The known correlation between bar semimajor axis a and galaxy stellar mass (or luminosity) is actually bimodal: for $\log \, (M_{\star }/\mathrm{M}_{\odot })\lesssim 10.1$, bar size is almost independent of stellar mass ($a \propto M_{\star }^{0.1}$), while it is a strong function for higher masses ($a \propto M_{\star }^{0.6}$). Bar size is a slightly stronger function of galaxy half-light radius Re and (especially) exponential disc scale length h (a ∝ h0.8). Correlations between stellar mass and galaxy size can explain the bar-size–M⋆ correlation – but only for galaxies with $\log \, (M_{\star }/\mathrm{M}_{\odot })\lesssim 10.1$; at higher masses, there is an extra dependence of bar size on M⋆ itself. Despite theoretical arguments that the presence of gas can affect bar growth, there is no evidence for any residual dependence of bar size on (present-day) gas mass fraction. The traditional dependence of bar size on Hubble type (longer bars in early-type discs) can be explained as a side effect of stellar mass–Hubble-type correlations. Finally, I show that galaxy size (Re or h) can be modelled as a function of stellar mass and both bar presence and bar size: barred galaxies tend to be more extended than unbarred galaxies of the same mass, with larger bars correlated with larger sizes.

Influence of three-dimensional transverse micro-ridges on the Poiseuille number in a gaseous slip flow

Micro-ridges are regular micro-engineering structures protruding outward from the microchannel wall surface. The role of these micro-ridges in changing the friction factor (f) of a microchannel with internal rarefied gas flows is not explored in the literature. In this work, we present three-dimensional numerical simulations in a microchannel containing ridges arranged transverse to the flow direction. The length of the ridges is varied with respect to the pitch of the ridges; this ratio being christened as ridge fraction (δ). The effect of δ, ridge height ratio (h/H), Reynolds number (Re), Knudsen number (Kn) and Tangential momentum accommodation coefficient (αv) on the flow friction in terms of Poiseuille number (fRe) is investigated. In the continuum and slip regimes, it is found that fRe decreases with an increase in δ and h and a significant reduction in flow friction was shown with respect to a straight microchannel. There exists a critical height after which decrease in fRe does not occur. Further, fRe was observed to be a strong function of Re at high δ, which is attributed to the intensity of acceleration–deceleration experienced by the gas during the flow. Also, fRe is established to be directly proportional to αv. The various flow characteristics are scrutinised where vortices are found trapped inside the ridge affecting the dynamics of flow in the ridges, whose size increases on increasing the gas rarefaction. This comprehensive investigation of behaviour of slip flow in complex microchannels will be useful in designing micro-devices with reduced friction.

CFD Investigation of Spacer-Filled Channels for Membrane Distillation.

The membrane distillation (MD) process for water desalination is affected by temperature polarization, which reduces the driving force and the efficiency of the process. To counteract this phenomenon, spacer-filled channels are used, which enhance mixing and heat transfer but also cause higher pressure drops. Therefore, in the design of MD modules, the choice of the spacer is crucial for process efficiency. In the present work, different overlapped spacers are investigated by computational fluid dynamics (CFD) and results are compared with experiments carried out with thermochromic liquid crystals (TLC). Results are reported for different flow attack angles and for Reynolds numbers (Re) ranging from ~200 to ~800. A good qualitative agreement between simulations and experiments can be observed for the areal distribution of the normalized heat transfer coefficient. Trends of the average heat transfer coefficient are reported as functions of Re for the geometries investigated, thus providing the basis for CFD-based correlations to be used in higher-scale process models.

Parametric study on thermal enhancement and flow characteristics in a heat exchanger tube installed with protruded baffle bundles

Influence of protruded baffle turbulators (P-BTs) on turbulent convective heat transfer rate and thermal performance behavior in round tubes was experimentally studied. The following geometrical parameters of P-BTs were considered (i) spacing ratio (SR = s/Dob = 1.0–3.0), (ii) diameter ratio (DR = d/Dob = 0.2–0.4), (iii) baffle orientation angle (θ = 0° (without rotation), 60°, 120° and 180°), and (iv) Reynolds number (Re = 6000 to 20,000). Air was used as working fluid at Prandtl number of Pr = 0.71. The plain tube data was examined for comparison with tube installed with protruded baffle turbulators (P-BTs). The experimental results obvious that increasing baffle orientation angle (θ), increasing diameter ratio (DR) and decreasing spacing ratio (SR) lead to the significant increases in heat transfer (Nu) and pressure loss (f). It can be also reveal that thermal performance (η) at a given Re considerably increases with the increasing spacing ratio (SR) and the reduction of diameter ratio (DR) and baffle orientation angle. The P-BTs with larger baffle orientation angle, induce stronger vortex ring and longitudinal vortex behind the baffles, give higher the thermal performance. Furthermore, all of empirical correlations (Nu, f and η) were derived as a function of Re and the protruded baffle turbulator (P-BT) geometry parameters including spacing ratio (SR), and protrusion-diameter ratio (DR).

Velocity Distribution in Rough Pipe: the Model Based on the Analytical Description of Resistance Curves in Nikuradse’s Experiments

Calculation and optimization of such complex systems as ventilating networks, water supply systems, etc. taking into account roughness of a surface and possible processes of heat and mass transfer demands use simple hydrodynamic models, which are at the same time sufficiently exact for engineering calculations. The goal of this paper is to develop such model. Prandtl’s model of a two-layer flow in the smooth pipe with the linear law of velocity distribution for a near-wall laminar layer and the logarithmic law for a turbulent core is used as a basis, which spreads to a case of rough pipes. The velocity profile equation and also the equations for the coordinate Yb of the laminar and turbulent border and its velocity Ub are derived. This paper is based on the use of the analytical description of Nikuradse’s experimental curves λ(Re,δ) (λ is the resistance coefficient, δ is the relative roughness) which earlier was found by the author. The dependence λ(Re*,δ) (Re* is the dynamic Reynolds number) is included into all above-mentioned equations. Results of numerical calculations of Yb and Ub as functions of Re* for the values of δ which are the same as in Nikuradse’s experiments are given. The calculation of velocity profiles for some values of Re* and δ is also fulfilled. Comparisons with the experimental velocity profiles obtained by Nikuradse demonstrate a good agreement.

Semi-empirical pressure loss model for viscous flow through high aspect ratio rectangular orifices

A predictive model is developed for the pressure loss coefficient for a viscous flow through a rectangular orifice on a pipe-installed thick plate. The model is developed based on the 1-dimensional Navier-Stokes equation and an asymptotic increase in velocity modeled to have a direct relation with the flow convergence in the near-inlet region. Here, the flow velocity increases asymptotically from the steady mean upstream value to the orifice velocity. This phenomenon is represented by a convergence parameter, ϕ, used in the velocity transition model to quantify the length of the convergence zone. The static pressure drop is measured experimentally for varying orifice aspect ratio, AR, at creeping Reynolds numbers (0.01 ≤ Re ≤ 0.1). A significantly wider range of AR is covered (1 ≤ AR ≤ 250), compared to related works in the literature. Results show that the relative dominance of the convergence phenomenon is affected by AR. The maximum length of convergence is for the square orifice (AR = 1), as the flow experiences comparable convergence from all directions, whereas for higher AR, convergence becomes less dominant in one of the two midplanes of investigation. The loss coefficient thus decreases as AR increases. At constant Re, higher AR generally leads to higher pressure drop but lower values of the loss coefficient. The velocity gradient in the convergence zone is also determined as a function of AR and Re which verifies that lower AR takes a longer distance for the velocity transition due to increased convergence.

The function ring functors of pointfree topology revisited

This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued functions, and for the related functors ${mathfrak R}^*$ and ${mathfrak Z}^*$ corresponding to the bounded functions. Further it is shown that some familiar facts concerning these functors are simple consequences of the present results.

Experimental investigation of heat transfer of impinging jet on a roughened plate by a micro cubic shape

ABSTRACTAn experimental study of average heat transfer from air jet impinging on a rough plate by a micro cubic pin is investigated. The main objective of the present study is to investigate the effect of a roughened degree on both local and average Nusselt number. The micro cubic size is (400 µm × 400 µm) with different depths (100, 200, and 300 µm). Therefore, the roughened degree varies between 1.0 (considered smooth surface), 1.64, 2.28, and 2.92 and the Reynolds number varies between 3150 and 10150 as well as separation distance ranged from 1 to 9. Results revealed that the average Nusselt number for rough plate is improved ranging from 9.9% to 32.17% compared to the smooth surface. This improvement depended on a roughened degree as well as a Reynolds number and separation distance. In addition, the enhancement factor is considered during this study. The enhancement factor is improved by 8.9%, 16%, and 24% for a roughened degree of 1.64, 2.28, and 2.94, respectively. Finally, the empirical correlations are presented to expect the value of average Nusselt number as a function of Re for different values of a roughened degree.

Hydrothermal analysis of MHD nanofluid (TiO2-GO) flow between two radiative stretchable rotating disks using AGM

Nanofluid flow between two stretchable and rotating disks with homogeneous and heterogeneous reactions and Joule heating is investigated in existence of magnetic field. Thermal radiation effect has been considered in energy equation. AGM Method is selected for solving ODEs. The effects of stretching parameters and Reynolds number on the concentration, temperature, axial, radial and tangential velocities are studied. The results showed that with increment of the values of stretching rate of lower disk, the radial and axial velocities enhances near the lower disk. Also the concentration and temperature is increasing behavior with stretching rate of lower disk. The impact of the increase of value of stretching rate of upper disk is opposite of the lower disk on the axial, radial and tangential velocities. The influence of Reynolds number on concentration, temperature and velocities are studied. It is shown that concentration is a decreasing function of Re while temperature is an increasing one. Also it is described that Nusselt number enhances with stretching parameter and Reynolds number at upper disk while it is decreased at lower one.

Hydrodynamic and thermal study of a trapezoidal cylinder placed in shear-thinning and shear-thickening non-Newtonian liquid flows

Hydrodynamic and thermal features of two-dimensional, incompressible shear-thinning and shear-thickening non-Newtonian power-law liquids under forced convection across a trapezoidal cylinder are the focus of this study, carried out at Reynolds number Re = 1–40, power-law index n = 0.4–1.8 and Prandtl number Pr = 50 using ANSYS Fluent. In this steady system, the drag coefficient is found to decrease, whereas the wake size and the average Nusselt number increase with the increase in Re. However, with the increase in n value, the average Nusselt number decreases. Similar to a square cylinder, compared to Newtonian liquids, shear-thinning liquids increases heat transfer and shear-thickening reduces it. The maximum increase in heat transfer for shear-thinning liquids compared to Newtonian liquids for a trapezoidal cylinder is approximately 25%, while the average heat transfer is somewhat lower for shear-thickening liquids than for Newtonian. The average Nusselt number is smaller for the trapezoidal cylinder than for a square cylinder in the parameter domain investigated; the largest difference is around 25%. A simple relationship for the average Nusselt number as a function of Re and n has been determined.

Heat transfer distribution on a cylindrical convex surface due to obliquely impinging row of circular jets

Heat transfer characteristics on a cylindrical convex surface impinged by a row of circular jets are presented in this study. Two different jet-jet spacing values equal to 4d and 8d were studied with the curvature ratio (ratio of diameters of jet and impinging surface, d/D) keeping constant at 0.05. Results for a single jet impinging onto the convex surface are also reported. The impinging angle ‘θ’, dimensionless jet-target distance ‘L/d’, and Reynolds number ‘Re’ were varied in the range 0°−45°, 2–10 and 5000–40,000 respectively. The Nusselt number variations from impinging point till midpoint between adjacent jets for jet-jet spacing of 8d were similar in nature with those for single jet with a maximum difference approximately equal to 5% at the secondary peak region. The Nusselt number distribution for the multiple jets with spacing equal to 4d was different as the interaction of adjacent walljets restricted the spread of inner jets, especially for inclined impingement, with nearly 10% increase in the secondary peak value compared to single jet. The peak Nusselt number occurs at the impinging point for perpendicular impingement and moves to the uphill side with inclination of jet. Secondary peaks are observed for all jet configurations at Re > 10,000 and L/d ≤ 4 for perpendicular impingement, but for large jet inclinations, no secondary peaks were observed on the uphill side. The magnitude of secondary peak in the downhill side reduces with increase in inclination and the position shifts further downstream in the downhill side. A correlation for peak Nusselt number is proposed as a function of Re, L/d and θ.