Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy＇s framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convec- tion, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross- diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabiliza- tion of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.

Effect of Non-Uniform Basic Concentration Gradient on the Onset of Double-Diffusive Convection in Micropolar Fluid

The effect of non-uniform basic concentration gradient on the onset of double diffusive convection in a micropolar fluid layer heated and saluted from below and cooled from above has been studied. The linear stability analysis is performed. The eigen value of the problem is obtained using Galerkian method. The eigen values are obtained for 1) free-free 2) rigid-free 3) rigid-rigid velocity boundary combination with isothermal temperature condition on spin-vanishing permeable boundaries. The influence of various micropolar parameters on the onset of convection has been analyzed. One linear and five non linear concentration profiles are considered and their comparative influence on onset is discussed and results are depicted graphically. It is observed that fluid layer with suspended particles heated and soluted from below is more stable compare to the classical fluid without suspended particles.

Visualization of Double-Diffusive Convection and Unsteady Solidification on a Vertical Circular Cylinder

This paper describes experimental results on the solidification process over the vertically positioned circular cylinder, placed in an aqueous solution of sodium nitrate, where the aqueous solution in the vessel is heated from the bottom. After the initiation of solidification by cooling the cylinder below the liquidus temperature, the pure ice formation on the cylinder causes the rejection of solute into the surrounding aqueous solution. The solute enriched vertical fluid layer over the ice then falls on the bottom of the vessel due to its higher density, and accumulates there. This process results in the formation of solute rich and hot horizontal layer (heavy layer), underlying the relatively cold but less concentrated fluid layer (light layer). As this process advances, however, because of the continuing influx of solute rich fluid, the lower heavy layer occupies more space, and the interface of the two layers rises slowly. The pH indicator method has been successfully employed in order to visualize the flows during this process. In this report, we document the evolution of both temperature and flow fields in the aqueous solution quantitatively, as the solidification progresses and the density discontinuity of the two layers rises.

Numerical simulation for 2D double-diffusive convection(DDC) in rectangular enclosures based on a high resolution upwind compact streamfunction model Ⅰ: numerical method and code validation

A high resolution upwind compact streamfunction numerical algorithm for two-dimensional(2D)double-diffusive convection(DDC)is developed.The unsteady Navier-Stokes(N-S)equations in the streamfunction-velocity form and the scalar temperature and concentration equations are used.An optimized third-order upwind compact(UCD3 opt)scheme with a low dispersion error for the first derivatives is utilized to approximate the third derivatives of the streamfunction in the advection terms of the N-S equations and the first derivatives in the advection terms of the scalar temperature and concentration equations.The remaining first derivatives of the streamfunction(velocity),temperature,and concentration variables used in the governing equations are discretized by the fourth-order compact Pade(SCD4)schemes.With the temperature and concentration variables and their approximate values of the first derivatives obtained by the SCD4 schemes,the explicit fourth-order compact schemes are suggested to approximate the second derivatives of temperature and concentration in the diffusion terms of the energy and concentration equations.The discretization of the temporal term is executed with the second-order Crank-Nicolson(C-N)scheme.To assess the spatial behavior capability of the established numerical algorithm and verify the developed computer code,the DDC flow is numerically solved.The obtained results agree well with the benchmark solutions and some accurate results available in the literature,verifying the accuracy,effectiveness,and robustness of the provided algorithm.Finally,a preliminary application of the proposed method to the DDC is carried out.

Isolated deep convections over the Tibetan Plateau in the rainy season during 2001–2020

The Tibetan Plateau(TP)is a prevalent region for convection systems due to its unique thermodynamic forcing.This study investigated isolated deep convections(IDCs),which have a smaller spatial and temporal size than mesoscale convective systems(MCSs),over the TP in the rainy season(June-September)during 2001–2020.The authors used satellite precipitation and brightness temperature observations from the Global Precipitation Measurement mission.Results show that IDCs mainly concentrate over the southern TP.The IDC number per rainy season decreases from around 140 over the southern TP to around 10 over the northern TP,with an average 54.2.The initiation time of IDCs exhibits an obvious diurnal cycle,with the peak at 1400–1500 LST and the valley at 0900–1000 LST.Most IDCs last less than five hours and more than half appear for only one hour.IDCs generally have a cold cloud area of 7422.9 km^(2),containing a precipitation area of approximately 65%.The larger the IDC,the larger the fraction of intense precipitation it contains.IDCs contribute approximately 20%–30%to total precipitation and approximately 30%–40%to extreme precipitation over the TP,with a larger percentage in July and August than in June and September.In terms of spatial distribution,IDCs contribute more to both total precipitation and extreme precipitation over the TP compared to the surrounding plain regions.IDCs over the TP account for a larger fraction than MCSs,indicating the important role of IDCs over the region.

Experimental Study of Thermal Convection and Heat Transfer in Rotating Horizontal Annulus

A genuine technological issue–the thermal convection of liquid in a rotating cavity–is investigated experimentally.The experiments are conducted within a horizontal annulus with isothermal boundaries. The inner boundaryof the annulus has a higher temperature, thus exerting a stabilising influence on the system. It is shown that whenthe layer rotation velocity diminishes, two-dimensional azimuthally periodic convective rolls, rotating togetherwith the cavity, emerge in a threshold manner. The development of convection is accompanied by a significantintensification of heat transfer through the layer. It is shown that the averaged thermal convection excitation inthe form of a system of two-dimensional rolls occurs against the background of oscillations of a non-isothermalfluid in the cavity reference frame caused by the gravity field. The excitation threshold and the structure ofconvective rolls are consistent with the results of the earlier theoretical studies by the authors performed usingthe equations of “vibrational” convection obtained by the averaging method. Furthermore, the experiments haverevealed a new type of averaged flow in the form of a spatially periodic system of toroidal vortices. It is shown thata steady streaming, excited by the inertial oscillations of the fluid, is responsible for the generation of the toroidalvortices. These flows develop in a non-threshold manner and are most clearly manifested in a case of resonantexcitation of one of the inertial modes.

Convection and Stratification of Temperature and Concentration

This study is devoted to an analysis of natural convection and the emergence of delamination in an incompressible fluid encapsulated in a closed region heated from the side.Weak,medium and intensive modes of stationary laminar thermal and thermo-concentration convection are considered.It is shown that nonlinear flow features can radically change the flow structure and characteristics of heat and mass transfer.Moreover,the temperature and concentration segregation in the center of the square region display a non-monotonic dependence on the Grashof number(flow intensity).The formation of a nonstationary periodic structure of thermal convection in boundary layers and in the core of a convective flow in the closed region is also examined.Details of the formation of countercurrents inside the region with the direction opposite to the main convective flow are given.Finally,the influence of vertical and horizontal vibrations on oscillatory convection is analyzed in detail.

Shallow Convection Dataset Simulated by Three Different Large Eddy Models

Shallow convection plays an important role in transporting heat and moisture from the near-surface to higher altitudes,yet its parameterization in numerical models remains a great challenge,partly due to the lack of high-resolution observations.This study describes a large eddy simulation(LES)dataset for four shallow convection cases that differ primarily in inversion strength,which can be used as a surrogate for real data.To reduce the uncertainty in LES modeling,three different large eddy models were used,including SAM(System for Atmospheric Modeling),WRF(Weather Research and Forecasting model),and UCLA-LES.Results show that the different models generally exhibit similar behavior for each shallow convection case,despite some differences in the details of the convective structure.In addition to grid-averaged fields,conditionally sampled variables,such as in-cloud moisture and vertical velocity,are also provided,which are indispensable for calculation of the entrainment/detrainment rate.Considering the essentiality of the entraining/detraining process in the parameterization of cumulus convection,the dataset presented in this study is potentially useful for validation and improvement of the parameterization of shallow convection.

Numerical Simulation of Thermocapillary Convection with Evaporation Induced by Boundary Heating

The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.In particular,the cases of local heating from below and distributed thermal load from the lateral walls are considered.The simulation is carried out within the frame of a two-sided evaporative convection model based on the Boussinesq approximation.A benzine–air system is considered as reference system.The variation in time of the contact angle is described for both heating modes.Under lateral heating,near-wall boundary layers emerge together with strong convection,whereas the local thermal load from the lower wall results in the formation of multicellular motion in the entire volume of the fluids and the appearance of transition regimes followed by a steady-state mode.The results of the present study can aid the design of equipment for thermal coating or drying and the development of methods for the formation of patterns with required structure and morphology.

Natural Convection of a Power-Law Nanofluid in a Square Cavity with a Vertical Fin

The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically.In particular,the impact of nanofluids,composed of water and Al_(2)O_(3),TiO_(2),and Cu nanoparticles,on heat transfer enhancement is examined.The aim of this research is also to analyze the influence of different parameters,including the Rayleigh number(Ra=10^(4)-10^(6)),nanoparticle volume fraction(φ=0%-20%),non-Newtonian power-law indexes(n=0.6-1.4),and fin dimensions(Ar=0.3,0.5,and 0.7).Streamlines and isotherms are used to depict flow and related heat transfer characteristics.Results indicate that thermal performance improves with increasing Rayleigh number,regardless of the nanoparticle type or nanofluid rheological behavior.This suggests that the buoyancy force has a significant impact on heat transfer,particularly near the heat source.The Nusselt number is more sensitive to variations in Cu nanoparticle volume fractions compared to Al₂O₃and TiO₂.Moreover,the average Nusselt numbers for power-law nanofluids with n<1(n>1)are greater(smaller)than for Newtonian fluids due to the decrease(increase)in viscosity with increasing(decreasing)shear rate,at the same values of Rayleigh number Ra owing to the amplification(attenuation)of the convective transfer.Notably,the most substantial enhancement is observed with Cu-water shear-thinning nanofluid,where the Nusselt number increases by 136%when changing from Newtonian to shear thinning behavior and by 154.9%when adding 16%nanoparticle volume fraction.Moreover,an even larger increase of 57%in the average Nusselt number is obtained on increasing the fin length from 0.3 to 0.7.

Libration-Generated Average Convection in a Rotating Flat Layer with Horizontal Axis

The study of average convection in a rotating cavity subjected to modulated rotation is an interesting area for the development of both fundamental and applied science.This phenomenon finds application in the field of mass transfer and fluid flow control,relevant examples being crystal growth under reduced gravity and fluid mixing in microfluidic devices for cell cultures.In this study,the averaged flow generated by the oscillating motion of a fluid in a planar layer rotating about a horizontal axis is experimentally investigated.The boundaries of the layer are maintained at constant temperatures,while the lateral cylindrical wall is thermally insulated.It is demonstrated that libration results in intense oscillatory fluid motion,which in turn produces a time-averaged flow.For the first time,quantitative measures for the instantaneous velocity field are obtained using the Particle Image Velocimetry technique.It is revealed that the flow has the form of counter-rotating vortices.The vortex circulations sense changes during a libration cycle.An increase in the rotation rate and amplitude of the cavity libration results in an increase in the flow intensity.The heat transfer and time-averaged velocity are examined accordingly as a function of the dimensionless oscillation frequency,and resonant excitation of heat transfer and average oscillation velocity are revealed.The threshold curve for the onset of the averaged convection is identified in the plane of control parameters(dimensionless rotational velocity and pulsation Reynolds number).It is found that an increase in the dimensionless rotational velocity has a stabilizing effect on the onset of convection.

Understanding Simulated Causes of Damaging Surface Winds in a Derecho-Producing Mesoscale Convective System near the East China Coast Based on Convection-Permitting Simulations

A mesoscale convective system(MCS) occurred over the East China coastal provinces and the East China Sea on 30April 2021, producing damaging surface winds near the coastal city Nantong with observed speeds reaching 45 m s^(–1). A simulation using the Weather Research and Forecasting model with a 1.5-km grid spacing generally reproduces the development and subsequent organization of this convective system into an MCS, with an eastward protruding bow segment over the sea. In the simulation, an east-west-oriented high wind swath is generated behind the gust front of the MCS. Descending dry rear-to-front inflows behind the bow and trailing gust front are found to feed the downdrafts in the main precipitation regions. The inflows help to establish spreading cold outflows and enhance the downdrafts through evaporative cooling. Meanwhile, front-to-rear inflows from the south are present, associated with severely rearward-tilted updrafts initially forming over the gust front. Such inflows descend behind(north of) the gust front, significantly enhancing downdrafts and near-surface winds within the cold pool. Consistently, calculated trajectories show that these parcels that contribute to the derecho originate primarily from the region ahead(south) of the east-west-oriented gust front, and dry southwesterly flows in the low-to-middle levels contribute to strong downdrafts within the MCS. Moreover, momentum budget analyses reveal that a large westward-directed horizontal pressure gradient force within the simulated cold pool produced rapid flow acceleration towards Nantong. The analyses enrich the understanding of damaging wind characteristics over coastal East China and will prove helpful to operational forecasters.

Unsteady Flow of Hybrid Nanofluid with MagnetohydrodynamicsRadiation-Natural Convection Effects in a U-Shaped Wavy Porous Cavity

In this paper,the unsteady magnetohydrodynamic(MHD)-radiation-natural convection of a hybrid nanofluid within a U-shaped wavy porous cavity is investigated.This problem has relevant applications in optimizing thermal management systems in electronic devices,solar energy collectors,and other industrial applications where efficient heat transfer is very important.The study is based on the application of a numerical approach using the Finite Difference Method(FDM)for the resolution of the governing equations,which incorporates the Rosseland approximation for thermal radiation and the Darcy-Brinkman-Forchheimer model for porous media.It was found that the increase of Hartmann number(Ha)causes a reduction of the average Nusselt number(Nu),with a maximum decrease of 25%observed as Ha increases from 0 to 50.In addition,the influence of the wall’s wave amplitude and the heat source length on the heat transfer rate was quantified,and it was revealed that at high wave amplitude,the average Nu increases by up to 15%.These findings suggest that manipulating magnetic field strength and cavity geometry can significantly enhance thermal performance.The novelty of this is related to the exploration of a U-shaped wavy cavity,which is not covered in previous studies,and to the detailed examination of the combined effects of magnetic fields,radiation,and hybrid nanofluids.

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

In this paper,we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid.The layer is subjected to a gravitational field and a strictly vertical temperature gradient.Typically,problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer,which prevent these systems from supporting conductive(non-convective)states.The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications.In an earlier work,we carried out a linear stability analysis of the conductive state.It was shown that at any layer tilt angles,the most dangerous type of disturbances are longitudinal rolls.Moreover,a non-zero velocity component exists in z-direction.In the present work,threedimensional non-linear convection regimes are studied.The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v_(z)=v_(z)(x,y).It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles,are in a good agreement with those predicted by the linear theory.The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry.Calculations carried out at low supercriticalities show that a direct bifurcation takes place.With increasing supercriticality,no transitions to other convective regimes are detected.The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient,where the ensuing fluid convection can affect the distribution of oil throughout the layer.

On the Features of Thermal Convection in a Compressible Gas

The fully nonlinear equations of gas dynamics are solved in the framework of a numerical approach in order to study the stability of the steady mode of Rayleigh-Bénard convection in compressible,viscous and heat-conducting gases encapsulated in containers with no-slip boundaries and isothermal top and bottom walls.An initial linear temperature profile is assumed.A map of the possible convective modes is presented assuming the height of the region and the value of the temperature gradient as influential parameters.For a relatively small height,isobaric convection is found to take place,which is taken over by an adiabatic mode when the height exceeds the critical value,or by a super-adiabatic mode in case of a relatively high temperature gradient.In the adiabatic mode,convective flow develops due to adiabatic processes given a stable initial stratification.An analytic formula for the critical height of the region is derived taking into account and neglecting the dependence of the gas viscosity on the temperature.Moreover,an analytic formula is obtained for the upper boundary of the region of applicability of the Boussinesq approximation for incompressible gases.These models for compressible gases are relevant to practical situations such as the study of convective flows in spatially extended gas mixtures when dealing with safety issues related to hydrocarbons stored in gas stations.A dangerous situation arises when the tank is almost empty but some hydrocarbon is left at the bottom of the tank.In the presence of convective flows,the vaporized fuel is mixed with the oxidizer(air)forming a gas-vapor medium.However,if the volumetric concentration of fuel vapor(hydrocarbon)is in the interval between the lower and upper concentration limits of ignition,then the gas-vapor mixture becomes explosive and any accidental spark is sufficient to cause an emergency.

Updated Lagrangian Particle Hydrodynamics (ULPH)Modeling of Natural Convection Problems

Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.

2-D Modeling and Calculations of Stratospheric Ozone and Influences of Convection, Diffusion, and Time

An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone DO3 and active atomic oxygen DO on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen DO was found to be more sensitive and important than that of ozone DO3 on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .

Lattice Boltzmann method formulation for simulation of thermal radiation effects on non-Newtonian Al_(2)O_(3) free convection in entropy determination

The simultaneous investigation on the parameters affecting the flow of electrically conductive fluids such as volumetric radiation,heat absorption,heat generation,and magnetic field(MF)is very vital due to its existence in various sectors of industry and engineering.The present research focuses on mathematical modeling to simulate the cooling of a hot component through power-law(PL)nanofluid convection flow.The temperature reduction of the hot component inside a two-dimensional(2D)inclined chamber with two different cold wall shapes is evaluated.The formulation of the problem is derived with the lattice Boltzmann method(LBM)by code writing via the FORTRAN language.The variables such as the radiation parameter(0–1),the Hartmann number(0–75),the heat absorption/generation coefficient(−5–5),the fluid behavioral index(0.8–1.2),the Rayleigh number(103–105),the imposed MF angle(0°–90°),the chamber inclination angle(−90°–90°),and the cavity cold wall shape(smooth and curved)are investigated.The findings indicate that the presence of radiation increases the mean Nusselt number value for the shear-thickening,Newtonian,and shear thinning fluids by about 6.2%,4%,and 2%,respectively.In most cases,the presence of nanoparticles improves the heat transfer(HT)rate,especially in the cases where thermal conduction dominates convection.There is the lowest cooling performance index and MF effect for the cavity placed at an angle of 90°.The application in the design of electronic coolers and solar collectors is one of the practical cases of this numerical research.

Understanding the factors influencing cloud-core vertical accelerations during deep convection formation in the WRF model

本文将扰动气压利用一个线性诊断关系代替,重新推导了WRF模式框架地形追随坐标系下的垂直动量方程,建立了垂直加速与对流触发(DCI)影响因子(如温度,水汽等)的直接联系.研究发现,DCI过程与对流核垂直加速相关,三维副散,扰动位势在垂直方向的二阶非均匀性,扰动位温垂直梯度,比湿及其垂直梯度,水凝物拖曳,均是能够直接影响垂直加速和对流触发的物理因子,这些量与模式基本预报量相关,通过解析基本预报量对对流发展的直接影响,可能有助于理解模式对DCI过程预测失败的原因.