Variable Density Fluid Research Articles

Exploring Natural Convection and Entropy Generation in a Closed Water Tank Utilizing Nanofluid: a Computational Study

Theoretical framework: This study presents a comprehensive investigation into three-dimensional natural convection within a confined cavity filled with an alumina-water nanofluid. Objective: Utilizing numerical simulations, we explore the influence of nanoparticles' volume fraction and Rayleigh number () on entropy generation, heat transfer efficiency, and fluid behavior within the water tank. Method: The study delves into the conservation equations governing mass, momentum, and energy within the context of three-dimensional laminar natural convection. It focuses on steady, incompressible flow, employing the Boussinesq approximation to account for variations in fluid density due to temperature gradients. Results and conclusion: Our findings indicate that increasing Rayleigh numbers lead to heightened entropy generation, with values ranging from to, primarily driven by intensified buoyant flow. However, the presence of nanoparticles significantly mitigates entropy generation, enhancing the overall thermal performance of the system. Moreover, nanofluids demonstrate superior heat transfer capabilities compared to pure fluids, with higher nanoparticle concentrations resulting in increased heat transfer rates, ranging from to alumina. Research implications: As a result of such thorough research, qualitative examinations of velocity fields and entropy generation patterns further highlight the role of nanofluids in improving heat transfer efficiency while reducing irreversible processes within the cavity.

Influence of interstitial fluid pressure, porosity, loading magnitude, and anisotropy in cortical bone adaptation

Adaptive elasticity in cortical bone has traditionally been modeled using Strain Energy Density (SED). Recent studies have highlighted the importance of interstitial fluid in bone adaptation, yet no research has quantified the role of interstitial fluid pressure and its effects, specifically incorporating both SED and interstitial fluid pressure in the adaptation process. This study introduces a novel formulation combining theory of porous media and theory of adaptive elasticity that considers both SED and interstitial fluid’s pressure in cortical bone adaptation. The formulation is solved using ANSYS Fluent and a MATLAB script, and sensitivity analyses were conducted, analyzing various porosities, loading magnitudes, anisotropic properties of cortical bone, and involvement coefficients of interstitial fluid’s pressure. This study reveals that bones with different vascular porosities (PV) tend to achieve similar density distributions under uniform loading over time. This highlights the significant role of interstitial fluid pressure in accelerating the convergence to optimal bone properties, especially in specimens with larger PV porosities. The findings emphasize the importance of fluid pressure in bone remodeling, aligning with previous studies. Furthermore, this study demonstrates that considering transversely isotropic material properties can significantly alter the remodeling configuration compared to isotropic material properties. This highlights the importance of accurately representing the anisotropic nature of cortical bone in models to better predict its adaptive responses. However, aspects such as fluid density variations and bone geometry changes remain unexplored, suggesting directions for future research. Overall, this research enhances the understanding of cortical bone adaptation and its mechanical interactions.

Data-informed characterization of spatio-temporal scales in experiments of microconfined high-pressure transcritical turbulence

The spatio-temporal scales of microconfined high-pressure transcritical turbulence are characterized in relation to the resolution capabilities of present time-resolved two-dimensional μPIV technology. Utilizing CO2 as the working fluid, the physical scales are examined by considering the main dimensionless groups of the problem, which correspond to the Reynolds, Brinkman, and Stokes numbers and the mass fraction of particles in the fluid. In detail, the methodology employed leverages direct numerical simulation data to inform the estimation of hydrodynamic, thermophysical, and particle-related scales, and selects a state-of-the-art μPIV setup to describe the optical performance of the current technology. The results indicate that the temporal scales can be experimentally captured for a wide range of operating conditions. However, the scenario becomes much more complex when trying to capture the spatial scales of microconfined high-pressure transcritical turbulent flow. Particularly, the Kolmogorov and Batchelor spatial scales can be captured for bulk Reynolds numbers below O(103). Otherwise, the spatial scales can only be partially captured and/or remain completely masked due to insufficient resolution, like for example in the case of boundary layer viscous scales and fluid density variations. This limitation is not imposed by the tracer behavior of microparticles, as the Stokes number remains significantly low for all the system configurations studied. Instead, the limitation is mainly a result of the optical capabilities of present μPIV systems. Finally, given the generalizable properties of dimensionless numbers, the results and insight obtained can be extended to other experiments of μPIV-based visualization/quantification of microconfined multiscale flows involving large thermophysical variations.

Dynamics of spinning pipes conveying a variable-density fluid

Dynamics of spinning pipes conveying a variable-density fluid

Real-time dynamic and structural behavior estimation of a steel lazy wave riser through finite-element-based digital twin and hull-motion sensor

A digital twin (DT) method is proposed to estimate the dynamic and structural behaviors of a Steel Lazy Wave Riser (SLWR) under environmental conditions. This method uses a 1D finite element (FE) riser model that can include various loads and boundary conditions measured from sensors. We selected a spread-moored Floating Production Storage and Offloading (FPSO) vessel to validate the proposed method, which hosts multiple Production and Injection SLWRs. Using the time-domain dynamics simulation program, we built a reference model considering the fully coupled FPSO with mooring lines and risers in various wind/wave/current conditions. The synthetic sensor data, which represents the motions and internal fluid density changes, were generated from the simulation of the reference model. Then, two riser DT models, the Top Oscillation Model (TOM) and the Two-Point Oscillation Model (TPOM), were built, considering only a single riser made of the 1D FE model. TOM employed vessel motions as boundary conditions while internal fluid density and ocean current could be inputted as external loads. TPOM incorporated an additional motion sensor attached to the riser. The motion data obtained from the reference model were first inputted into the respective riser DT models. Next, we further evaluated their performance with and without the estimated ocean currents and slugs of internal fluid. The time histories, spectra, and statistical data of displacements and stresses along the riser were systematically compared and analyzed for various test cases and environments. While the hull-motion sensor alone can provide practically acceptable results using the developed methodology, additional consideration of current load and internal fluid's density variation improves the overall riser monitoring performance. The present method can significantly reduce the number of sensors compared to traditional riser monitoring methods.

Similarity solution for the magnetogasdynamic shock wave in a self-gravitating and rotating ideal gas under the influence of radiation heat flux

The Lie invariance method is used to analyze the one-dimensional, unsteady flow of a cylindrical shock wave in a rotating, self-gravitating, radiating ideal gas under the influence of an axial or azimuthal magnetic field, with an emphasis on adiabatic conditions. The analysis assumes a stationary environment just ahead of the shock wave and considers variations in fluid velocity, magnetic field, and density within the perturbed medium just behind the shock front. In the governing equations, the impact of thermal radiation under an optically thin limit is integrated into the energy equation. Utilizing the Lie invariance method, the set of partial differential equations governing the flow in this medium is transformed into a system of nonlinear ordinary differential equations (ODEs) using similarity variables. Two distinct cases of similarity solutions are obtained by selecting different values for the arbitrary constants associated with the generators. Among these cases, one yields similarity solutions assuming a power-law shock path and the other an exponential-law shock path. For both cases, the resulting set of nonlinear ODEs are numerically solved using the 4th-order Runge–Kutta method in MATLAB software. The article thoroughly explores the influence of various parameters, including γ (adiabatic index of the gas), Ma−2 (Alfvén–Mach number), σ (ambient density exponent), l1 (rotational parameter), and G0 (gravitational parameter) on the flow properties. The findings are visually presented to offer a comprehensive insight into the effects of these parameters.

The Influence of Large Variations in Fluid Density and Viscosity on the Resonance Characteristics of Tuning Forks Simulated by Finite Element Method

The use of tuning forks to measure fluid density and viscosity is widely employed in fields such as food, medicine, textiles, automobiles, petrochemicals, and deep drilling. The explicit analytical model based on the Euler–Bernoulli cantilever-beam theory for the relationship between tuning-fork resonance characteristics and the density and viscosity of fluid is only applicable to the situation where the fluid viscous effect is very small. In this paper, the finite element method is used to simulate the influence of large variations in fluid density and viscosity on the resonance characteristic parameters (resonant frequency and quality factor) of the tuning fork. The numerical simulation results are compared with the analytical analysis results and experimental measurement results. Then, the sensitivity of tuning-fork resonance characteristic parameters to fluid density and viscosity is studied. The results show that compared with the analytical results, the numerical simulation results have a higher degree of agreement with the experimental measurement results. The relative difference in resonant frequency is less than 2%, and the relative difference in quality factor is less than 4%. This indicates that the finite element method includes the influence of fluid viscosity on tuning-fork resonance parameters, which is more in line with the actual conditions than the analytical model. Simulating and analyzing the sensitivity of the tuning fork to fluid density and viscosity by the finite element method, it is possible to consider the situation where fluid density and viscosity vary over a large range. Compared with experimental measurements, this method has higher efficiency and can significantly save time and economic costs. This study can overcome the limitation of existing explicit analytical models, which are only applicable when the viscous effects of the fluid are very small. It enables a more accurate simulation of the coupling vibration between tuning forks and fluids, thereby providing theoretical references for further optimizing tuning-fork structural parameters to enhance the accuracy of measuring fluid characteristic parameters.

Time-Lapse Geophysical Measurements for Monitoring Coastal Groundwater Dynamics in an Unconfined Aquifer.

The coastal zone, which is the interface between land and sea, is hydrodynamically very active due to the complex interactions of various hydrological controls and variable-density fluids. These forces vary over time, resulting in a state of dynamic equilibrium in the system. The major hydrological processes in coastal aquifer systems are salt water intrusion and submarine groundwater discharge, which are interdependent. Monitoring these complex processes is crucial for sustainable coastal zone management but poses a significant research challenge. In this study, we demonstrate the effectiveness of non-invasive geophysical techniques, specifically the time-lapse electrical resistivity imaging method, in conjunction with groundwater monitoring, for monitoring coastal groundwater dynamics in an unconfined aquifer at varying time scales and hydrogeological settings present at formerly glaciated sites worldwide. We generated two-dimensional baseline salt water intrusion maps for the test site, located on the coast of Rhode Island, USA. The time-lapse electrical resistivity survey method enables the rapid estimation of fresh groundwater discharge. Our approach offers insight into the mechanisms and seasonably variable salt water-freshwater interactions in unconfined heterogeneous aquifers. Although the results are site-specific, their implications are broad and may stimulate other studies related to sea to land pollution (sea water intrusion) and land to sea pollution (groundwater discharge) in heterogeneous coastal aquifer settings.

Investigating the Role of Stator Slot Indents in Minimizing Flooded Motor Fluid Damping Loss

This research examines how fluid damping loss affects the operation of a two-pole, 5.5 HP (4 kW) induction machine (IM) within the context of different slot opening configurations developed for downhole water pump applications. Since these motors operate with their cavities filled with fluid, the variations in fluid viscosity and density, compared to air, result in the occurrence of damping losses. Furthermore, this loss can be attributed to the motor’s stator and rotor surface geometry, as the liquid within the motor cavity moves unrestrictedly within the motor housing. This study involves the examination of the damping loss in a 24-slot IM under different stator slot indentations. The investigation utilizes computational fluid dynamics (CFD) finite element analysis (FEA) and is subsequently validated through experiments. The aim of this work is to emphasize the significance of fluid damping loss in submerged machines. Results reveal that the damping loss exceeds 8% of the motor output power when the stator surface has indentations, and it diminishes to 3.2% of the output power when a custom wedge structure is employed to eliminate these surface indentations.

Investigation of gravity influence on EOR and CO2 geological storage based on pore-scale simulation

Gravity assistance is a critical factor influencing CO2–oil mixing and miscible flow during EOR and CO2 geological storage. Based on the Navier–Stokes equation, component mass conservation equation, and fluid property–composition relationship, a mathematical model for pore-scale CO2 injection in oil-saturated porous media was developed in this study. The model can reflect the effects of gravity assistance, component diffusion, fluid density variation, and velocity change on EOR and CO2 storage. For non-homogeneous porous media, the gravity influence and large density difference help to minimize the velocity difference between the main flow path and the surrounding area, thus improving the oil recovery and CO2 storage. Large CO2 injection angles and oil–CO2 density differences can increase the oil recovery by 22.6% and 4.2%, respectively, and increase CO2 storage by 37.9% and 4.7%, respectively. Component diffusion facilitates the transportation of the oil components from the low-velocity region to the main flow path, thereby reducing the oil/CO2 concentration difference within the porous media. Component diffusion can increase oil recovery and CO2 storage by 5.7% and 6.9%, respectively. In addition, combined with the component diffusion, a low CO2 injection rate creates a more uniform spatial distribution of the oil/CO2 component, resulting in increases of 9.5% oil recovery and 15.7% CO2 storage, respectively. This study provides theoretical support for improving the geological CO2 storage and EOR processes.

COMPARISON OF FLOW DYNAMICS AND AIR ENTRAINMENT UNDER LABORATORY PLUNGING AND SPILLING BREAKING WAVES

Wave breaking plays a vital role in enhancing transfer of mass, momentum, and energy across the air-sea interface. Even though wave breaking has been intensively studied, a vast part of the air entrainment process is still poorly understood. One major reason is that multiphase approaches considering air-water mixture density variation have rarely been used. To quantify certain flow properties that involve air entrainment and fluid density variation, such as the mean and turbulent kinetic energy as well as potential energy under breaking waves, void fraction measurements are essential. In the present study, through combined velocity and void fraction measurements, flow kinematics, turbulence, void fraction, and the effects of void fraction to energy dissipation were investigated. The data uniquely characterize and compare kinematic and dynamic properties of the multiphase flow, including flow structure in the highly aerated region, under plunging and spilling breaking waves.

Surface Tension of the Planar Interface of a Vapor–Liquid System on a Two-Dimensional Square Lattice

In an earlier work, the authors described a theoretical approach to deriving equations for equilibrium particle distributions by means of heterogeneous cluster variation (CV) that converges to the exact solution as the basis cluster grows. In this work, they present calculations of the surface tension (ST) of the planar interface of a vapor-liquid system on a two-dimensional square lattice by means of heterogeneous CV. The transitional region of the interface is a sequence of monomolecular layers with a variable fluid density fluidа. Calculations are made for six types of clusters with different sizes inside the phases (2 × n, n = 1–4, 3 × 3, and the k1s cluster with the nearest neighbors of any central site), and for eight clusters inside the transitional region (2 × 1, 2 × 2, 2 × 3, 3 × 2, 2 × 4, 4 × 2, 3 × 3, k1s) that differ by each cluster’s orientation relative to the normal to the surface. As the clusters grow, so does the accuracy of describing indirect correlations of laterally interacting particles. The temperature dependence of the ST is calculated. A monotonically growing ST is obtained as the temperature falls, starting from zero at the critical temperature. The calculation results converge to the exact Onsager solution as the clusters grow. Differences between thermodynamic requirements and ST calculations performed with the Ising model are discussed.

Effects of Numerical Schemes of Contact Angle on Simulating Condensation Heat Transfer in a Subcooled Microcavity by Pseudopotential Lattice Boltzmann Model

Various numerical schemes of contact angle are widely used in pseudopotential lattice Boltzmann model to simulate substrate contact angle in condensation. In this study, effects of numerical schemes of contact angle on condensation nucleation and heat transfer simulation are clarified for the first time. The three numerical schemes are pseudopotential-based contact angle scheme, pseudopotential-based contact angle scheme with a ghost fluid layer constructed on the substrate with weighted average density of surrounding fluid nodes, and the geometric formulation scheme. It is found that the subcooling condition destabilizes algorithm of pseudopotential-based contact angle scheme. However, with a ghost fluid layer constructed on the substrate or using geometric formulation scheme, the algorithm becomes stable. The subcooling condition also decreases the simulated contact angle magnitude compared with that under an isothermal condition. The fluid density variation near a microcavity wall simulated by pseudopotential-based contact angle scheme plays the role of the condensation nucleus and triggers “condensation nucleation”. However, with a ghost fluid layer constructed on the substrate or using geometric formulation scheme, the simulated fluid density distribution near the wall is uniform so that no condensation nucleus appears in the microcavity. Thus, “condensation nucleation” cannot occur spontaneously in the microcavity unless a thin liquid film is initialized as a nucleus in the microcavity. The heat flux at the microcavity wall is unphysical during the “condensation nucleation” process, but it becomes reasonable with a liquid film formed in the microcavity. As a whole, it is recommended to use pseudopotential-based contact angle scheme with a ghost fluid layer constructed on the substrate or use the geometric formulation scheme to simulate condensation under subcooling conditions. This study provides guidelines for choosing the desirable numerical schemes of contact angle in condensation simulation by pseudopotential lattice Boltzmann model so that more efficient strategies for condensation heat transfer enhancement can be obtained from numerical simulations.

Numerical Stability and Accuracy of Contact Angle Schemes in Pseudopotential Lattice Boltzmann Model for Simulating Static Wetting and Dynamic Wetting

There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann (LB) model for simulating the wetting phenomenon: The pseudopotential-based scheme (PB scheme), the improved virtual-density scheme (IVD scheme), the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall (MPB-C scheme), the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes (MPB-W scheme) and the geometric formulation scheme (GF scheme). But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past. In this paper, the numerical stability and accuracy of these schemes are clarified for the first time, by applying the five widely used contact angle schemes to simulate a two-dimensional (2D) sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively. (i) It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle, but the simulated contact angles by the PB scheme, IVD scheme, MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength. The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios. (ii) Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes, the magnitude of the spurious velocity in the PB scheme, IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme. (iii) The fluid density variation near the wall in the PB scheme is the most significant, and the variation can be diminished in the IVD scheme, MPB-C scheme and MPB-W scheme. The variation totally disappeared in the GF scheme. (iv) For the simulation of capillary imbibition, the MPB-C scheme, MPB-W scheme and GF scheme simulate the dynamics of the liquid-vapor interface well, with the GF scheme being the most accurate. The accuracy of the IVD scheme is low at a small contact angle (44 degrees) but gets high at a large contact angle (60 degrees). However, the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface. As a whole, it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting, while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.

Numerical Investigation of the Temperature and Flow Fields in a Solar Chimney Power Plant

In this work, a parametric two-dimensional computational fluid dynamics (CFD) analysis of a solar chimney power plant (a prototype located in Manzanares, Spain) is presented to illustrate the effects of the solar radiation mode in the collector on the plant performances. The simulations rely on a mathematical model that includes solar radiation within the collector; energy storage; air flow and heat transfer, and a turbine. It is based on the Navier-Stokes equation for turbulent flow formulated according to the standard k-ε model. Moreover, the Boussinesq approach is used to account for the fluid density variations. Different solar radiation modes in the collector are compared and discussed. The obtained results are also compared with available experimental results. It is shown that the radiation model is essential to avoid overestimation of the energy absorbed by the plant and that results based on a two-dimensional model can resemble closely those produced by three-dimensional models.

Vorticity screening by dense layers

We investigate variable density layers in the presence of vortices, by analogy to line charges in the presence of a dielectric slab. We adapt solutions for dielectric layers from the literature to the variable density fluid case, obtaining exact hypergeometric expressions for flow velocities induced everywhere by a vortex in the vicinity of a finite-thickness slab of different densities. The dimensionless Atwood number, which appears naturally in other variable density phenomena, such as the Rayleigh–Taylor instability, reappears here as the natural ordering parameter for the influence of the slab, which acts primarily to screen the influence of vorticity across the slab to a lower effective circulation. The solution takes the form of scaling correction factors that might be applied to computational models or evaluated directly. Extensions, where vorticity is localized within the dense layer itself and amplified outside of it, are considered, as well as some speculative applications such as inertial confinement fusion capsule designs.

Constructing a ghost fluid layer for implementation of contact angle schemes in multiphase pseudopotential lattice Boltzmann simulations for non-isothermal phase-change heat transfer

The PP scheme (primitive pseudopotential-based scheme), the MP scheme (modified pseudopotential-based scheme) and the IVD scheme (improved virtual-density scheme) are the three most widely used contact angle schemes in pseudopotential lattice Boltzmann (LB) models to simulate wetting characteristics of multiphase flow over solid surfaces under isothermal conditions. In this paper, we apply these schemes to simulate the problem of sessile droplet evaporation on a heated substrate, which is an example of non-isothermal phase-change heat transfer process. It is found that the substrate heating effect destabilizes algorithms of these schemes in certain ranges of contact angles of a heated substrate. The droplet interface shapes simulated by the PP scheme and the MP scheme are inaccurate at obtuse contact angles due to large fluid density variations near the wall. The spurious currents near the droplet triple-phase contact line are very large in the MP scheme, causing the deformation of the Marangoni vortex shape inside the droplet and the erroneous droplet interface temperature distribution near the triple-phase contact line. The addition of a special ghost fluid layer on the wall proposed in this study can improve numerical stability of the PP and the MP schemes for application under non-isothermal conditions as well as under high saturated liquid/vapor density ratios. Although the IVD Scheme (with the nearest fluid layer temperatures above the heated wall chosen for calculating the effective mass of wall nodes) is also stable at low liquid/vapor density ratios, its numerical stability at high density ratios is not as robust as those of the PP and the MP schemes if a special ghost fluid layer is added in these schemes. It is shown that by adding such a special ghost fluid layer on the wall, large near-wall fluid density variations diminish in the PP and MP schemes and accurate droplet interface shapes can be recovered at obtuse contact angles. The spurious current in the MP schemes can be also reduced and accurate Marangoni vortex shapes in the droplet and droplet interface temperature distribution near the triple-phase contact line can be predicted.

Semi‐analytical solution of solute dispersion model in semi‐infinite media

AbstractThe advection–dispersion equation (ADE) is one of the most widely used methods for estimating natural stream pollution at different locations and times. In this paper, variational iteration method (VIM) is utilized to obtain a semi‐analytical solution for 1D ADE in a temporally dependent solute dispersion within uniformsteady flow. Through a computational validation, the effect of different parameters such as uniform flow velocity and dispersion coefficient on the solute concentration values has been investigated. Results show that the change in velocity has a strong effect on fluid density variation. However, when the diffusion coefficient has been increased, the change in flow and velocity behaviors is negligible. To verify the proposed semianalytical solution, the results were compared to analytical solutions and errors were found to be <0.7% in all simulations.

Enhancement of thermal mixing under supercritical condition by increasing shear rate

The dynamical characteristics of the shear-driven mixing layer can be inhibited due to the variations in fluid density. In this work we expect to address this issue by increasing shear rate. Direct numerical simulations of mixing layer between two streams with different temperatures at supercritical pressure are conducted. We confirm that the turbulent characteristics of mixing layer are inhibited with increasing density ratio between the lower and upper streams, resulting in the destruction of large-scale vortex, especially at the high-density side. By increasing the velocity ratio between the two streams, however, the mixing performance is enhanced with regeneration of the hairpin vortex due to increase in mean shear. The enstrophy production thus increases due to enhancement of vortex stretching and the thermal mixing efficiency is enhanced due to the entrainment of vortical structures. Further, the streamwise spectra of the temperature fluctuations follow a slope of −3 in the viscous-diffusive range.

Adaptive Computations to Pressure Profile for Creeping Flow of a Non-Newtonian Fluid With Fluid Nonconstant Density Effects

Abstract The sperm density through the cervical canal plays a dynamic part in promoting the pregnancy progressions of organisms. Therefore, this study aims to probe the combined effects of concentration and temperature-dependent density on the creeping flow of Carreau nanofluid in the cervical canal as the first look in this direction. Chemical reaction and Hall effects are considered. The system of a physical model is simplified/streamlined using appropriate transformation (δ≪1). The system that describes the fluid model is recurrence/rearranged with aid of adaptive shoot techniques (AST) by a computer program using mathematica 13.1.0. Solutions are offered via sketches on the pressure profiles. Besides, graphs of streamlined are achieved in dissimilar values of the nonconstant density of the fluid. To get accurate results and approve the validation of the proposed technique, a comparison with Ibrahim (2022, “Adaptive Simulations to Pressure Distribution for Creeping Motion of Carreau Nanofluid With Variable Fluid Density Effects: Physiological Applications,” Therm. Sci. Eng. Prog., 32, p. 101337) is obtained and seems to be very good. The results indicate that high values of nonconstant density parameters impose a pressure gradient in the cervical canal, which supports the sperm to be more energetic in ovum fertilizing.