Nu Values Research Articles

Optical and thermodynamic properties of a rotating dyonic black hole spacetime in {mathcal {N}} = 2, U(1)^2 gauged supergravity

The null geodesics and the distance of closest approach for photon around a rotating dyonic black hole in {mathcal {N}} = 2, U(1)^2 gauged supergravity is studied. The phenomenon of black hole shadows with various black hole parameters has also analyzed. Further, the investigation of various thermodynamic properties for this black hole is performed with various thermodynamic parameters at the horizon. The heat capacity to study the thermodynamic stability of this black hole spacetime is also studied. The influence for different values of the black hole parameters nu , e, nu , g and N_{g} on the phenomenon of black hole shadows and thermodynamic parameters is also investigated visually.

Numerical simulation of adiabatic/cooled/heated spherical particles with Stefan flow in supercritical water

When droplets or particles are in complex fluid-temperature-environment conditions, the spatial variation in temperature-dependent properties affects the overall particle-laden flow behavior. Particularly, in a high-temperature environment, the components on the particle surface are heated and volatilize to form a mass flow, named the Stefan flow, that influences the mass, momentum, and energy transfer between particles and the fluid. For supercritical fluids, small changes in temperature and pressure cause substantial changes in thermophysical properties. Hence, in this work, we study the characteristics of supercritical water flowing past an adiabatic/cooled/heated sphere for Re = 10–200 with and without Stefan flow. The three-dimensional numerical simulations that are conducted consider the exact water thermophysical properties. The flow field, the Nusselt number (Nu), the drag coefficient (Cd), and the velocity and temperature distribution around the particle are analyzed. The results demonstrate that the vortex is strongly influenced by the variation in viscosity near the particle. The Cd and Nu values of the cooled and heated spheres show different deviations in different conditions. The influence of Stefan flow cannot be ignored as it increases the vortex size and decreases both Cd and Nu. Finally, the effect of Stefan flow on both Cd and Nu of the cooled sphere is greater than that of the heated sphere.

Thermo-fluids effects of a grooved circular cylinder in laminar flow regimes

The force coefficients and heat transfer related to a circular cylinder with grooved surfaces are studied at Re ≤ 200. Three types of grooved surfaces are examined: square, triangle, and dimple. The grooves are arranged at θ = 0°, 30°, 45°, 60°, 90° from the forward stagnation point of the cylinder. It is shown that the existence of a groove controls the dynamic behavior of the vortices; as such lift and drag coefficients have been varied considerably, depending on the shape of the groove and θ. The coefficients appear very sensitive to triangle grooved surface, in particular, as θ varies to 45°. The results reveal that triangle grooved surface could produce minimum drag coefficient when θ varies to 450 for all examined Re; this is found much lower than that of the square and dimple grooved surfaces and even smooth cylinder. A significant enhancement of the Nu is attained in the wake of the triangle grooved cylinder surface with the angle of the location of 450. At low Reynolds number (Re = 50), the Nu value of triangle grooved surface with θ = 0°is shown higher than that of other grooved surfaces, whereas this value is found to the lowest at high Reynolds number (Re = 200).

Numerical study and artificial neural network modeling of the tube banks arrangement considering exergetic performance

The present study investigates numerically heat transfer rate (HTR) and generation of entropy (GOE) for turbulent NF flow in an electronic cooler equipped with four sinusoidal pipes. The heat transfer fluid (HTF) is water-based MWCNT nanofluid (NF) in different NVFs (ϕ = 0.2, 0.4, 0.6 and 0.8%). Four different wave amplitudes (α = 2, 4, 6 and 8 mm), three different wavelengths (λ = 40, 60 and 80 mm) are studied in this paper. According to obtained results, the average Nusselt number (Nu) always increases by increase in wave amplitude or decrease in wavelength. Therefore, at α = 8 mm or λ = 40 mm the highest Nu value is achieved. Besides, Reynolds numbers (Re) variation has a significant influence on Nu distribution in tube and the Nu values always intensify by augmentation of Re. The optimum Reynolds number in thermal viewpoint is 11,000 and in second law viewpoint is 5000. Furthermore, therefore higher nanoparticles volume fraction (NVF) always leads to higher HTR in channel. But it also increases dynamic viscosity and pressure drop penalty in channel. The results of the models obtained from the neural network algorithm show that the variation of the Nusselt number with respect to the Reynolds number, wave amplitude and wavelength is mitotically so that heat transfer increases by increasing the amount of these three parameters. An increase in the wave amplitude leads to a 38% increase in the average Nusselt number and a 50% increase in the total Nusselt number. However, the effect of the wavelength is small. An increase in the wavelength results in an enhancement in the average Nusselt number by 6% and the total Nusselt number by 16%.

A numerical study of the entropy generation and heat transfer rate of airflow around a NACA 0015 airfoil subjected to an external magnetic field

In the present study, the thermal Lattice Boltzmann Technique is combined with the Ghost Fluid method to simulate the flow and heat transfer rate around a NACA 0015 airfoil in the presence of an external magnetic field source. It is tried to investigate the mutual effects of the Hartmann and Reynolds numbers as well as the magnetic field angle and the attack angle of the airfoil on the flow and heat transfer characteristics. Besides, the total entropy generation rate of the system was studied through its main components, i.e. entropy generation rate due to friction, heat transfer, and Magneto Hydrodynamics. Therefore, the tests were carried out for various Re and Ha numbers, plus different magnetic field angles and airfoil attack angles, and their influence on the active parameters which are Cd, Cl, and Nu, along with the entropy generation rate of the system, were recorded. The results revealed that with an increment of the Re number the Cd and Cl graphs drop, but the Nu value raises. Also, the total entropy generation rate of the system is at its maximum around γ = 60.

Computational analysis of perforation effect on the thermo-hydraulic performance of micro pin-fin heat sink

This paper investigates the hydrodynamic and thermal characteristics of perforated micro pin-fin (MPF) heat sink with different shapes and numbers of perforations under a low range (100–1000) of Reynolds number (Re) and constant base wall heat flux thermal boundary condition with air as the working fluid. The results show that the perforated MPFs provide higher Nusselt number (Nu) values and lower pressure drop levels (ΔP) than a solid MPF. These perforations have also shown higher fin effectiveness compared to solid square-shaped MPFs. Besides, the perforated MPFs show a superior performance (i.e., ≥45%) than solid MPFs. This study also infers that the circular-shaped perforation offers the best system performance (η) amidst the all different perforation shapes irrespective of the perforation number, followed by the elliptical and square-shaped perforation. For the circular-shaped perforation, performance improves by 30% when going from one to two perforations, and it improves up to 28% while moving from two to three perforations. This study reveals that there is a greater potential to employ circular perforation on a solid square MPF heat sink for better thermal management in electronic devices.

How equation of state selection impacts accuracy near the critical point: Forced convection supercritical CO2 flow over a cylinder

Increasing application of supercritical fluids leads to increased use of numerical simulations to guide designs. However, the impact of Equations of State (EoS) selection on computational cost and accuracy is not well understood. Laminar flow around a heated cylinder is used as a test case. A robust matrix of 99-simulations is used to analyze the flow of carbon dioxide just above the critical point at the isobaric condition of 8 MPa and temperatures between 305 and 390 K. Four EoS were studied: Ideal Gas Law, cubic EoS’s Peng-Robinson and Soave-Redlich-Kwong, and the Span-Wagner EoS. Results were identical for isothermal cases, but for heated or cooled cases, the high-fidelity Span-Wagner EoS simulations presented drastically different wake structures. Compared to the high-fidelity SW EoS, cEoS’s underestimated Nu values by up to 38% and cEoS’s underestimated CD values by 18–42%. The Span-Wagner EoS required only 17% more computation time then the cubic EoS simulations, making the Span-Wagner EoS recommended for engineering design.

Impacts of rotating surface and oriented magnetic field on mixed convection and melting behavior of CNT-water nanouid in a horizontal annulus

Combined rotational surface and inclined magnetic effects on the mixed convection and melting behavior of CNT-water nanofluid in an annulus is analyzed with finite element method. Constant temperatures are used for the inner and outer walls while the inner surface is also rotating. Melting behavior and convection features are analyzed by varying different parameters such as Hartmann number, magnetic field inclination angle, inner wall rotational speed and nanoparticle volume fraction. The average Nu value and melt fraction increase with higher values of nanoparticle solid volume fraction while reverse impact is seen for higher Ha number values. The overall heat transfer rate is reduced for higher rotational velocity of the inner wall but contribution of various hot walls to the average Nu is different. The melt front propagation can be controlled by using the rotation of the inner surface.

Impact of local elasticity and inner rotating circular cylinder on the magneto‐hydrodynamics forced convection and entropy generation of nanofluid in a U‐shaped vented cavity

This study analyzes the effects of a partial elastic wall and rotating circular cylinder on the convective heat transfer of carbon nanotube (CNT)–water nanofluid filled U‐shaped cavity with entropy generation by considering inclined magnetic field effects. Numerical simulation is performed by using ALE with finite element method (FEM). Impacts of various important parameters such as Re number, Ha number, magnetic field orientation, elastic wall size and modulus, angular velocity, and horizontal position of the rotating cylinder on the forced convection are analyzed. When the values of Re number, strength of magnetic field (up to Ha number of 50), and orientation angle are increased, the average Nu value rises while the impact is opposite for higher elastic wall size and horizontal position of the cylinder above 0.4H. When the rotational cylinder effects are considered, enhancement up to 60% is obtained at the highest speed as compared to motionless cylinder case. The average Nu variation is in the range of 9%–10.45% at the highest value when varying the size and modulus of the elastic wall. Flexible wall effects on the average Nu number variation becomes more pronounced when the angular rotational velocity is highest at the clockwise rotation and for the highest Re number. The average Nu number enhancements are 13%–14% at the highest Ha number. The entropy generation rates with varying Ha number, rotational velocity, and location of the cylinder are different for the left and right parts of the domains while impacts of elastic wall properties on the entropy generation rate are slight.

Effects of a rotating tube bundle on the hydrothermal performance for forced convection in a vented cavity with Ag–MgO/water hybrid and CNT–water nanofluids

In this study, effects of rotating tube bundle on the hydrothermal performance for the forced convection in a vented cavity are numerically studied with a mixture of Ag and MgO nanoparticles suspended in water, forming a hybrid nanofluid and CNT–water nanofluid. The finite volume method is used for the numerical simulations. The simulation study is performed for various values of Reynolds number (between 100 and 1000), rotational Reynolds number (between − 100 and 100), size (between 0.01H and 0.12H), vertical (between 0.3H and 0.65H) and horizontal locations (between 0.3H and 0.65H) of the cylinder in the tube bundle and nanoparticle volume fraction (between 0 and 0.02). An experimental correlation was used for the description of the Ag–MgO/water hybrid nanofluid. Results indicated that the rotational effects of the tube bundle contribute to the hydrothermal performance. The average Nusselt number enhancements are 8.95% and 40% when CNT–water is used for solid volume fraction of 0.02 at the highest speed, while these values are 31.5% and 37.7% for hybrid nanofluid. The pressure coefficients are higher for negative value of $${\text {Re}}_{\upomega }$$ and hybrid nanofluid. The size of the tube bundle is effective at the highest size, while the increment amount is 16.8% both for CNT–water and for hybrid nanofluids. The center location of the tube bundle resulted in heat transfer enhancement which is in the range of 11% and 18%. As the solid volume fraction of nanoparticles becomes higher, discrepancies between the average Nu values of CNT–water nanofluid and Ag–MgO/water hybrid nanofluid become higher which is also observed for the pressure coefficient. It is advantageous to use CNT particles since higher heat transfer coefficients with lower values of pressure coefficient are obtained.

Weather impact on airborne coronavirus survival.

The contribution of this paper toward understanding of airborne coronavirus survival is twofold: We develop new theoretical correlations for the unsteady evaporation of coronavirus (CoV) contaminated saliva droplets. Furthermore, we implement the new correlations in a three-dimensional multiphase Eulerian–Lagrangian computational fluid dynamics solver to study the effects of weather conditions on airborne virus transmission. The new theory introduces a thermal history kernel and provides transient Nusselt (Nu) and Sherwood (Sh) numbers as a function of the Reynolds (Re), Prandtl (Pr), and Schmidt numbers (Sc). For the first time, these new correlations take into account the mixture properties due to the concentration of CoV particles in a saliva droplet. We show that the steady-state relationships induce significant errors and must not be applied in unsteady saliva droplet evaporation. The classical theory introduces substantial deviations in Nu and Sh values when increasing the Reynolds number defined at the droplet scale. The effects of relative humidity, temperature, and wind speed on the transport and viability of CoV in a cloud of airborne saliva droplets are also examined. The results reveal that a significant reduction of virus viability occurs when both high temperature and low relative humidity occur. The droplet cloud’s traveled distance and concentration remain significant at any temperature if the relative humidity is high, which is in contradiction with what was previously believed by many epidemiologists. The above could explain the increase in CoV cases in many crowded cities around the middle of July (e.g., Delhi), where both high temperature and high relative humidity values were recorded one month earlier (during June). Moreover, it creates a crucial alert for the possibility of a second wave of the pandemic in the coming autumn and winter seasons when low temperatures and high wind speeds will increase airborne virus survival and transmission.

Transport phenomena in a differentially heated lid-driven cavity: A study using multi-relaxation-time thermal lattice Boltzmann modeling

In this study, investigation of mixed convection phenomena in a lid driven square cavity with heated side walls is carried out. The left and right walls are maintained at different constant temperatures, while the upper and bottom walls are thermally insulated. The left wall temperature is higher than the cavity fluid temperature, and the right wall is maintained at the initial fluid temperature. Transport phenomena inside the cavity within a wide parametric range are investigated. The parameters include the Reynolds number (10 ≤ Re ≤ 1000), the Prandtl number (0.01 ≤ Pr ≤ 50), and the Richardson number (0.01 ≤ Ri ≤ 10). It was observed that the flow is induced in the cavity by a shear force resulting from the motion of the upper lid combined with the buoyancy force due to the temperature difference in the cavity. The effects of Re, Pr, and Ri within the cavity were observed simultaneously. The numerical simulations were carried out using the thermal lattice Boltzmann method with multi-relaxation time collision model. The present investigation generates a benchmark dataset for the average Nusselt number (Nuavg) with varying Re, Pr, and Ri within the laminar flow regime. Results show that heat transfer from the side wall is not affected significantly by change in Pr in low levels of Ri, but as Ri increases, average Nu increases significantly. It is also observed that the average value of Nu increases with Pr and Re at a particular value of Ri. However, at a given Ri, for Re above 500 and Pr over 10, the Nu value remains unaffected by change in Re and Pr, which defines the limiting heat transfer in the laminar regime.

Thermal stack airflows inside the solar chimney with discrete heat sources: Reversal flow regime defined by chimney inclination and thermal Rayleigh number

Present work numerically and theoretically investigates the fluid flow and heat transfer in an inclined solar chimney induced by thermal buoyancy within a range of thermal Rayleigh numbers (Ra) and chimney inclination angles (α). Transport paths of fluid and heat were visualized by streamlines and heatlines, respectively. Backflow could be observed in the solar chimney when Ra increases beyond a certain value, and it directly paralyses the ventilation of the chimney. Numerical results further demonstrate that the larger the inclination angle α is, the smaller the corresponding critical Ra number of the reverse flow occurs at the glass side is. The larger the inclination angle α is, the greater Nusselt (Nu) value of the absorber wall is, while its increment rate decreases gradually with the increase of the inclination angle α, when thermal Ra is maintained. As α varies from 30° to 90°, corresponding critical Ra for reversal flows gradually decreases; furthermore, these critical values obtained by the theoretical solutions were higher than those from simulation. Volume flow rates increase positively with Ra when α is no more than 30°; however, they increase initially and then decline with Ra when α is no less than 45°. In order to enhance ventilation performance, a solar chimney flush attached with discrete heating sources on the glazing wall is proposed. The numerical results indicated that modified inclined solar chimney with discrete heating sources could enhancing its ventilation performance by preventing reverse flow occurring in the channel. Our investigations also showed that the optimal inclination angle for maximum volume flow rate heavily depends on Ra. This research could provide necessary technical support and guidance for solar energy utilization and building energy conservation through air channel in building envelopes.

Non-monotonic transport mechanisms in vertical natural convection with dispersed light droplets

Abstract

Quantitative evaluation of watershed attributes for water resources management in the Rift Valley Lakes Basin, Ethiopia: a case from Tikur Wuha river watershed

Characterization of watershed hydrological process is vital for sustainable water resource management. The principal goal of this study was to investigate the inference of drainage attributes on basic hydrological processes using spatial-based morphometric analysis on Tikur Wuha river watershed. The result obtained indicated that the area was characterized with fifth-order stream. Drainage area with higher stream order has lower infiltration capacity, and the shorter stream lengths were associated with the steepness of the area which affects water flow. Based on Nu value, sub-watersheds were categorized in the active erosion stage (SW7) and matured topography development (SW6). The interpretation from watershed geometry identified circular areas most susceptible to rapid hydrological response (SW11). Hydrological process and underlying materials are mainly correlated with the drainage texture parameter, and the lower the values indicated less rocky terrain and very high infiltration capacity which contributes toward less erosion (SW11). Relief parameters such as Rr value indicate the rate of stream flow and are well used in sediment yield estimation. The findings of this investigation will provide core information for water resource planning and further studies like identification of groundwater potential zones; flood risk assessment; erosion-prone area prioritization; and to select suitable sites for the construction of water harvesting structures.

On p-adic valuations of certain m colored p-ary partition functions

Let kin mathbb {N}_{ge 2} and for given min mathbb {Z}{setminus }{0} consider the sequence (S_{k,m}(n))_{nin mathbb {N}} defined by the power series expansion 1(1-x)m∏i=0∞1(1-xki)m(k-1)=∑n=0∞Sk,m(n)xn.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\frac{1}{(1-x)^{m}}\\prod _{i=0}^{\\infty } \\frac{1}{(1-x^{k^{i}})^{m(k-1)}}=\\sum _{n=0}^{\\infty }S_{k,m}(n)x^{n}. \\end{aligned}$$\\end{document}The number S_{k,m}(n) for min mathbb {N}_{+} has a natural combinatorial interpretation: it counts the number of representations of n as sums of powers of k, where the part equal to 1 takes one among mk colors and each part >1 takes m(k-1) colors. We concentrate on the case when k=p is a prime. Our main result is the computation of the exact value of the p-adic valuation of S_{p,m}(n). In particular, in each case the set of values of nu _{p}(S_{p,m}(n)) is finite and the maximum value is bounded by {text {max}}{nu _{p}(m)+1,nu _{p}(m+1)+1}. Our results can be seen as a generalization of earlier work of Churchhouse and recent work of Gawron, Miska and Ulas, and the present authors.

Numerical investigation of heat transfer enhancement of an inclined heated offset jet

Offset jet is a commonly used flow in different industrial applications, such as in cooling electronic devices or heat exchange systems. Determining the exact behaviour of the thermal characteristics of such flow, as a function of several independent parameters, is quite interesting and useful. The aim of the current study of an inclined heated and turbulent offset jet is to investigate numerically the dynamic and thermal characteristics of the flow. To figure out which parameter is the most significant for the heat transfer process, The effects of the Reynolds number (Re), the offset ratio (OR) and the inclination angle(α) were discussed in details. Note that the OR is varied in two domains: from 20,000 to 40,000, from 5 to 15 and the inclination angle is varied from −20° to +20°.The simulations are carried out using the CFD solver Ansys Fluent. The SST k-ω turbulence model was selected among four different turbulence models and using the velocity-pressure coupling. Velocity and pressure and streamlines, contours are provided to examine the dynamic behaviour of the flow. Furthermore, local Nusselt evolution is presented for different parameter combinations (Re, OR and α) to outline their simultaneous effects on the convective transfer phenomenon. Finally, based on the gathering data, triple-parameter correlations were developed to govern the maximum Nu value and the average Nusselt estimations throughout the different flow's zones. These correlations will broad the current knowledge in different engineering applications to enhance the heat transfer in different heat exchange systems such as electronics cooling systems.

Hydro-thermal performance of CNT nanofluid in double backward facing step with rotating tube bundle under magnetic field

In this study, a novel method for convective heat transfer control of flow past a double backward facing step with combined effects of oriented magnetic field, rotating tube bundle and inclusion of highly conductive CNT nanoparticles in the base fluid is offered. Hydro-thermal performance assessment of double backward facing step is numerically performed with finite volume method in laminar flow regime. Effects of Reynolds number, rotational Reynolds number, circular cylinder arrangement and horizontal local of the tube bundle, distance between the steps and magnetic field strength on the fluid flow, heat transfer, pressure drop and hydro-thermal performance coefficient variation are examined. The rotation of the cylinder, arrangement and location were found to alter hydro-thermal performance while the average Nu is enhanced with higher Reynolds and Hartmann numbers. The presence of the upper vortex location resulted in higher deflection of the main stream toward the hot bottom wall which resulted in higher local heat transfer rates. This is especially the case for clockwise direction rotation at the height speed and local Nu value increment is 244% as compared to non-rotating cylinder case. Best performance coefficient is obtained with MHD flow at Hartmann number of 5 while performance increase is 13% as compared to non-magnetic field configuration. The vertical size and location of the upper vortex changes with the horizontal location of the tube bundle and spacing between the steps. As compared to reference configurations, variations in the hydrothermal performance coefficients are 15% and 20% when varying the horizontal location and distance between the steps. The CNT nanoparticles inclusion in the base fluid resulted in performance coefficient enhancement of 52% at the highest solid volume fraction. As flow separation and subsequent attachments are encountered in a variety of heat transfer engineering applications, the results of the present work will be helpful in the design and optimization of various thermal engineering systems.

Cognitive performance and Heart rate variability: The influence of menstrual cycle in young subjects

Menstrual cycle characterized by various dynamic alterations in sex steroidal hormones not only alters the reproductive organs but also various systemic organs and hence higher functions are one among them. This study is an attempt to determine the influence of various hormones on cognitive function using short term heart rate variability analysis in different phases of menstrual cycle. Thirty participants were subjected for the baseline recording of HRV and psychomotor vigilance test and short term memory test along with HRV recording in three subsequent numbers of times to study variations in three different phases of menstrual cycle . Both time domain and frequency domain parameters were studied during resting state and while performing psychomotor vigilance test and short term memory test. The time domain and frequency domain parameters on comparison with resting state to during psychomotor vigilance test and short term memory test parameters were statistically insignificant in all three phases recorded. Unlikely on comparison of heart rate variability parameters both times domain and frequency domain values of RRI, RMSSD and LF (nu) values were statistically significant across the different phases suggesting upper hand of sympathetic tone. The present study indicated increased sympathetic discharge during follicular phase on comparison to luteal and menstrual phase. The results also indicated a change in cognitive functioning during different phases due to hormonal variations.

Cosmological framework for renormalization group extended gravity at the action level

General relativity (GR) extensions based on renormalization group (RG) flows may lead to scale-dependent couplings with nontrivial effects at large distance scales. Here we develop further the approach in which RG effects at large distance scales are fully encoded in an effective action and we apply it to cosmology. In order to evaluate the cosmological consequences, our main assumption is the use of a RG scale such that the (infrared) RG effects only appear at perturbative order (not at the background level). The emphasis here is on analytical results and qualitative understanding of the implied cosmology. We employ commonly used parametrizations for describing modified gravity in cosmology (as the slip parameter). From them, we describe the dynamics of the first order perturbations and estimate bounds on the single dimensionless parameter (nu ) introduced by this framework. Possible impacts on dark matter and dark energy are discussed. It is also shown here that the nu parameter effects to fsigma _8 are stronger at low redshifts (z<1.5), while different values for nu do not appreciably change fsigma _8 at higher redshifts, thus opening a window to alleviate an issue that is currently faced by Lambda CDM.