Ventilation is paramount in sanitary and stormwater sewer systems to mitigate odor problems and avert pressure surges. Existing numerical models have constraints in practical applications in actual sewer systems due to insufficient airflow modeling or suitability only for steady-state conditions. This research endeavors to formulate a mathematical model capable of accurately simulating various operational conditions of sewer systems under the natural ventilation condition. The dynamic water flow is modeled using a shock-capturing MacCormack scheme. The dynamic airflow model amalgamates energy and momentum equations, circumventing laborious pressure iteration computations. This model utilizes friction coefficients at interfaces to enhance the description of the momentum exchange in the airflow and provide a logical explanation for air pressure. A systematic analysis indicates that this model can be easily adapted to include complex boundary conditions, facilitating its use for modeling airflow in real sewer networks. Furthermore, this research uncovers a direct correlation between the air-to-water flow rate ratio and the filling ratio under natural ventilation conditions, and an empirical formula encapsulating this relationship is derived. This finding offers insights for practical engineering applications.

The laminar boundary layer flow of a Zinc Oxide-Society of Automotive Engineers 50 alias nano-lubricant (ZnO-SAE50) past a permeable shrinking cylinder is investigated. The flow is unsteady, incompressible, and Ohmic dissipative. The present study holds immense significance in different engineering as well as scientific domains. It combines research on nanoparticle effects, unsteady flows, and solid surface interactions. The study claimed that the use ofZnO-SAE50nanofluid in the unsteady flow past a permeable shrinking cylinder led to significant heat transfer enhancement. The acquired results from the study would be fruitful in the fields of thermal engineering and heat transfer. The findings of the study can aid in optimizing cooling systems, heat exchangers, and energy-efficient designs. A governing model has been achieved for the flow and heat transfer by using conservation laws related to mass, momentum, and energy. Governing system of partial differential equations is solved to a nonlinear system of ordinary differential equations by using similarity transformation, which is later on solved with the help of the Shooting method and RK-Fehlberg duos. Plots are shown for both velocity and temperature profiles, to display the impacts of involved dimensionless parameters. Additionally, graphs for Nusselt Number have also been represented which shows the local rate of heat transfer. It is examined that the Ohmic dissipation as well as the volumetric ratio of the nanoparticles greatly influence the overall thermal performance of the system.

Blood flow in stenosed arteries is a common cause of cardiovascular diseases, leading to serious health problems. The present study aims to investigate the unsteady Womersley blood flow in a stenosed, porous saturated artery under the influence of acceleration and magnetic fields. The study utilizes a Carreau constitutive equation to model blood rheology and employs the finite difference technique to compute the governing equations under the assumption of unsteady, unidirectional, and laminar flow. The importance of this study lies in its potential to provide a better understanding of the complex behavior of hemodynamic flow in the presence of external fields and porous media, which has significant implications for the control and management of cardiovascular diseases. In particular, the study analyses the impacts of non-dimensional parameters, such as magnetic field, channel permeability, acceleration field, Weissenberg number, and stenosis amplitude, on critical flow variables, such as velocity, resistivity, wall shear stress, and flow rate. Our calculations suggest that a magnetic field is an effective instrument for regulating hemodynamic flow because it increases resistance by up to 8.31% while decreasing flow by up to 8.44%. Channel permeability, on the other hand, improves blood velocity by up to 33.35% while eliminating resistance by up to 23.43%. Furthermore, greater acceleration fields decrease resistivity while increasing velocity, flow rate, and wall shear stress. Additionally, the severity of the stenosis and the Weissenberg number substantially affect flow factors. By raising the stenosis amplitude, resistivity rises, and other flow characteristics diminish, whereas modifying the Weissenberg number causes the reverse effect.

Blood is indeed a suspension of the different type of cells along with shear thinning, yield stress and viscoelastic characteristics, which can be expressed by Newtonian and a lot of non-Newtonian models. Choosing Newtonian fluid as a sample, an unsteady solver for Newtonian fluid is constructed to determine the transient flow of blood in the obscure region. In this probe, the computational unsteady flow of blood in artery with aneurysm and symmetric stenosis has been considered, which is novelty of current research. The results of this investigation can be applied to detect stenotic-aneurysmal diseases and enhance knowledge of the stenotic-aneurysmal artery, which may increase the understanding of medical science. The blood artery is modeled as a circular tube having a 0.3-m radius and a 2-m length along the horizontal axis. The velocity of blood is taken at 0.12 ms-1 so that the geometry satisfies the characteristics of the blood vessel. The governing mass and momentum equations are then solved by finite difference technique of discretization. In this research, important variations in blood pressure and velocity at stenosis and aneurysms in the artery are found. The significant influences on blood flow of the stenotic-aneurysmal artery for pressure and velocity profiles of blood are displayed graphically for the Newtonian model.

Blood flow analysis through arterial walls depicts unsteady non-Newtonian fluid flow behavior. Arterial walls are impacted by various chemical reactions and magnetohydrodynamic effects during treatment of malign and tumors, cancers, drug targeting and endoscopy. In this regard, current manuscript focuses on modeling and analysis of unsteady non-Newtonian Carreau-Yasuda fluid with chemical reaction, Brownian motion and thermophoresis under variable magnetic field. The main objective is to simulate the effect of different fluid parameters, especially variable magnetic field, chemical reaction and viscous dissipation on the blood flow to help medical practitioners in predicting the changes in blood to make diagnosis and treatment more efficient. Suitable similarity transformations are used for the conversion of partial differential equations into a coupled system of ordinary differential equations. Homotopy analysis method is used to solve the system and convergent results are drawn. Effect of different dimensionless parameters on the velocity, temperature and concentration profiles of blood flow are analyzed in shear thinning and thickening cases graphically. Analysis reveals that chemical reaction increases blood concentration which enhance the drug transportation. It is also observed that magnetic field elevates the blood flow in shear thinning and thickening scenarios. Furthermore, Brownian motion and thermophoresis increases temperature profile.

The primary objective of this investigation is to examine the thermal state of an unsteady ternary hybrid-nanofluid flow over an expanding/shrinking cylinder. The influence of radiation along with a non-uniform thermal source/sink is taken into account to expedite heat distribution. Multiple slips are considered at the cylinder interface. The mathematical model is simplified by incorporating appropriate transformations. A numerical solution is obtained using the bvp4c algorithm. The flow characteristics and behavior of the trihybrid nanoliquid exhibit significant changes when the cylinder expands or contracts. The effects of various emerging parameters are analyzed using graphical representations. The velocity field shows an opposite trend when the unsteadiness and mass transfer parameters are increased. The thermal field improves with higher values of the non-uniform source/sink parameter but deteriorates with an increase in the thermal slip parameter. The drag force increases with higher values of the unsteadiness parameter, while it decreases with amplified values of the mass suction and velocity slip parameters. A strong correlation is observed with previous studies which validates and strengthens the credibility of the present analysis.

UNASSIGNED: Nanofluids with aggregation effects mediated by nanoparticles, like geothermal panels and crossflow heat exchangers, ignite new industrial interests. Polymer and conversion processes have transport phenomena in the stagnation zone that must be continuously improved to raise the process quality standard.
UNASSIGNED: Hence, the current computational study examines a T i O 2 - C 2 H 6 O 2 nanofluid\'s unsteady stagnation-point flow performance via a shrinking horizontal cylinder. In addition, the effects of a magnetic field, joule-heating viscous dissipation, nanoparticles aggregation and mass suction on the boundary layer flow are reflected.
UNASSIGNED: ology: The RK-IV with shooting method is applied to resolve the simplified mathematical model numerically in computing software MATHEMATICA. In certain circumstances, comparing the current and prior findings indicates good agreement with a relative error of around 0%.
UNASSIGNED: The implementation of a heat transfer operation may be improved by increasing suction settings. Unsteadiness, nanoparticle volume fraction, magnetic, curvature, and Eckert number (implies the operating Joule heating and viscous dissipation) all influence heat transfer rate. The velocity and temperature profiles both increase as the unsteadiness, magnetic field, and nanoparticle volume fraction parameters increase, whereas the curvature and suction parameters show the opposite behavior. When the values of the suction parameters were changed from 2.0 to 2.5 with φ  = 0.01, the heat transfer rates rose by 4.751%. A comparison shows that the model with aggregation has a better velocity profile, while the model without aggregation has a better temperature profile.

UNASSIGNED: Typical liquids aren\'t great for engineering because of their low heat conductivity. To enhance heat transfer capabilities in industries as diverse as computers, pharmaceuticals, and molten metals, researchers and scientists have developed nanofluids, which are composed of nanoparticles distributed in a base fluid.
UNASSIGNED: Mathematical modeling of micropolar C u - H 2 O nanofluid driven by a deformable sheet in the stagnation area with nanoparticle aggregation, thermal radiation, and the mass suction action has been investigated in this paper. In this case, copper ( C u ) nanoparticles make up the nanofluid.
UNASSIGNED: ology: We have used suitable transformations to arrive at a system of nonlinear ODEs, which we then solve numerically in MATHEMATICA using Runge-Kutta methods of the fourth order coupled with shooting approaches.
UNASSIGNED: Tables and graphs are used to examine the effects of immersed flow and display profiles of physical parameters of interest. This includes velocities, temperatures, skin friction, and Nusselt numbers. The average heat transfer rate increased to 17 . 725 % as the volume percentage of copper nanoparticles in micropolar nanofluid increased from 0.0 to 0.01 . Additionally, the results showed that the local Nusselt number of the micropolar nanofluid increased along with an increase in the unsteady and radiation parameters. However, its value is reduced in an undeniable fashion if a material parameter is present. The impact of radiation on the aggregation of nanoparticles is compared and contrasted with the effects of a non-radiative scenario, and the resulting fluctuations in Nusselt numbers are provided in tables. When the results of this study were compared to data that had already been published about some cases, a lot of agreement was found.

This study was designed to develop a computational fluid dynamics (CFD) method for unsteady analysis of a series of ski jump movements with attitude changes, and to analyse the aerodynamic characteristics of an expert jumper over the entire ski jump movement. Two ski jumpers participated in this study. A sensor-based motion capture suit was used to capture the jumper\'s posture during the actual ski jump. A three-dimensional computer graphics animation was created by superimposing the joint angles obtained from the motion measurements of the 3D shape of the athlete. The unsteady aerodynamic forces acting on the ski jumper, from the takeoff to the landing, were then calculated using CFD. A time-varying spatially uniform flow was specified as the inflow boundary condition of the computational domain. The results indicated that both the lift and drag forces of the expert jumper increase rapidly during the initial flight when the jumper\'s posture changes drastically. Thereafter, drag force decreased considerably, but the decrease in the lift force was less drastic. Later in the flight phase, the lift force acting on the expert jumper increased, and throughout the flight phase, the lift-drag ratio of the expert jumper remained higher than that of the unskilled jumper.

The use of hybrid nanoparticles to increase heat transfer is a favorable area of research, and therefore, numerous scientists, researchers, and scholars have expressed their appreciation for and interest in this field. Determining the dynamic role of nanofluids in the cooling of microscopic electronic gadgets, such as microchips and related devices, is also one of the fundamental tasks. With such interesting and useful applications of hybrid nanofluids in mind, the main objective is to deal with the analysis of the unsteady flow towards a shrinking sheet in a water-based hybrid ferrite nanoparticle in porous media, with heat sink/source effects. Moreover, the impact of these parameters on heat and mass transfers is also reported. Numerical results are obtained using MATLAB software. Non-unique solutions are determined for a certain shrinking strength, in addition to the unsteadiness parameter. The mass transfer and friction factor increase for the first solution due to the hybrid nanoparticles, but the heat transfer rate shows the opposite effect.