Narrow Results

This paper presents a numerical solution to the problem of time-dependent blood flow via a w-shaped stenotic conduit, driven by pulsatile pressure gradient. The problem is formulated in cylindrical coordinates by employing the theoretical model of tangent hyperbolic fluid. The electro-osmotic effects are also taken into consideration. To simplify the non-dimensional governing equations of the flow problem, a mild stenosis assumption is utilized and the impact of the blood vessel wall is mitigated by employing a radial coordinate transformation. An explicit finite difference method is used to solve the resulting nonlinear system of differential equations, considering the auxiliary conditions specified at the boundary of the blood channel. After obtaining the numerical solution to the problem, an examination is carried out for various flow variables, such as axial velocity, temperature field, mass concentration, skin friction, Nusselt number, and Sherwood number. These results are presented graphically, and a concise explanation is provided using physical facts. An increase in flow rate and blood velocity leads to a rise in response, while an increase in stenosis height, Weissenberg number, and power-law exponent leads to a reverse response. Furthermore, the temperature field is significantly affected by the Brinkman number and the Prandtl number.

Transport properties of hydrocarbon liquid-based nanofluids in non-Darcy media have key significance in chemical, thermal and mechanical engineering. Therefore, the key focus of this research is to investigate the transport mechanism in nanofluid using Koo–Kleinstreuer–Li (KKL) thermal conductivity model in non-Darcy media under squeezing and permeable effects. The functional fluid is a homogenous mixture of Cu and kerosene. The problem formation is carried out via nanofluid-enhanced properties and similarity rules. Then numerical scheme was endorsed for the results analysis under increasing physical ranges. It is observed that the velocity $F(\eta )$ increased when the values of ${\alpha }_1$ vary from 1.0 to 4.0. However, quick particles movement is noticed for ${\gamma }_1$ for 1.0–4.0 and $-$1.0 to $-$4.0. Further, the thermal process in Cu/kerosene depreciates for ${\alpha }_1=0.5$, 1.0, 1.5, 2.0, ${\gamma }_1=2$, 4, 6, 8 and ${\gamma }_1=-2.0$, $-$4.0, $-$6.0, $-$8.0, respectively. The stronger permeability of the lower plate highly reduced the fluid movement and depreciation in the movement can be optimized when the fluid sucks from the channel through the lower plate.

This paper focuses on applying the Corcione model to the microchannel. The Corcione model is highly relevant because it provides accurate empirical relationships for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. These qualities are crucial for building and improving different thermal systems. The model presents and discusses two simple empirical correlating equations for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. Hence the aim of this work is to use Corcione’s model to demonstrate the fully developed laminar flow of an electrically conducting nanoliquid through an inclined microchannel. The energy equation takes into account the physical impacts of the heat source/sink, temperature jamp, and viscous dissipation. TiO₂ nanoparticles in water are taken into consideration in this work for enhanced cooling. Using the numerical program Maple, Runge–Kutta–Fehlberg 4th–5th-order method is utilized to solve the present research. Making use of graphs, all of the flow parameters are shown, and the physical consequences on the flow and temperature profiles are thoroughly examined. It is noted that a higher inclined angle enhances the velocity profile whereas a larger temperature jump declines the temperature profile. Furthermore, Corcione’s model often has greater velocities, temperatures, and reduced surface drag forces than the Tiwari–Das model.

In this research, a novel design stochastic numerical technique is presented to investigate the unsteady form magnetohydrodynamic (MHD) slip flow along the boundary layer to analyze the transportation and heat transfer in a solar collector through nano liquids which is a revolution in the field of neurocomputing. Thermal conductivity in variable form is dependent on temperature and wall slips are assumed over the boundary. For mathematical modeling, the solar collector is assumed in the form of a nonlinear stretching sheet and a quite new artificial neural networks (ANNs) based approach is used to solve the current problem in which inverse multiquadric radial basis (IMRB) kernel is sandwiched between a global search solver named genetic algorithms (GAs) and a highly effective local solver named sequential quadratic programming (SQP) i.e. IMRB-GASQP solver. The governing boundary value problem is altered in the form of a system of nonlinear ordinary differential equations (ODEs) through the utilization of similarity transformation and then the obtained system of ODEs is solved using IMRB-GASQP solver by altering the values of distinguished parameters involved in it to observe the fluctuation in the velocity and temperature profiles of nanofluid. The obtained results are effectively compared with the reference solutions using the Adams numerical technique in graphical and tabulated form. An exhaustive error analysis using performance operators is presented while the efficacy of the designed solver using various statistical operators is also part of this research.

Insulating vegetable oils are considered environment-friendly and fire-resistant substitutes for insulating mineral oils. This paper presents the lightning impulse breakdown characteristic of insulating vegetable oil and insulating vegetable oil-based nanofluids. It indicates that Fe₃O₄ nanoparticles can increase the negative lightning impulse breakdown voltages of insulating vegetable oil by 11.8% and positive lightning impulse breakdown voltages by 37.4%. The propagation velocity of streamer is reduced by the presence of nanoparticles. The propagation velocities of streamer to positive and negative lightning impulse breakdown in the insulating vegetable oil-based nanofluids are 21.2% and 14.4% lesser than those in insulating vegetable oils, respectively. The higher electrical breakdown strength and lower streamer velocity is explained by the charging dynamics of nanoparticles in insulating vegetable oil. Space charge build-up and space charge distorted filed in point-sphere gap is also described. The field strength is reduced at the streamer tip due to the low mobility of negative nanoparticles.

Paraffin is an excellent photo-thermal conversion phase change energy storage material, and extensively used in the thermal storage field at the medium-low temperature. However, the low thermal conductivity of paraffin restricts its application in practice. Adding nanoparticles into paraffin is one of the effective methods to improve its thermal conductivity. Nevertheless, the thermal diffusivity, specific heat and volumetric heat capacity of paraffin as well as timeliness were affected after the addition of nanoparticles. In this paper, the influences of volume fraction of Al₂O₃ nanoparticle and timeliness on these thermal parameters of paraffin were investigated. The results show that the thermal conductivity of paraffin-based Al₂O₃ nanofluids increases first and then decreases with time, and the maximum thermal conductivity is 0.34 W/$(\mathrm{\text{m}}\cdot \mathrm{\text{K}})$ for volume fraction 1% on third day. The higher volume concentration, the lower specific heat and volumetric heat capacity, all present downtrend over time, until stable in the range of 0.3 MJ/$(\mathrm{\text{m}}\cdot \mathrm{\text{K}})$ and 0.4 MJ/$(\mathrm{\text{m}}\cdot \mathrm{\text{K}})$. The average enhancement rate of specific heat and volumetric heat capacity are concentrates on −6% to 9%, −10% to 0%, respectively. While increasing the volume concentration, the thermal diffusivity has no obvious regularity, and presents undulatory property over time.

Here our purpose is to explore the entropy generation in nanofluid MHD flow by curved stretching sheet; second-order slip is considered. Additional effects of viscous dissipation, Joule heating, and activation energy are taken. Temperature and concentration boundary conditions are considered convectively. For convergence of series solution NDSolve MATHEMATICA is used. Velocity, Bejan number, concentration, temperature, and entropy generation graphs are sketched for important parameters. For greater estimations of first- and second-order velocity slip parameters fluid velocity reduces. The thermal and solutal Biot numbers enhance the temperature and concentration, respectively. The concentration also has direct relation with activation energy. Entropy generation reduces for chemical reaction parameter and first- and second-order slip parameters.

The thermal efficiency of the heat exchanger is substantial in chemical and mechanical systems. The presence of the non-homogeny magnetic field considerably enhances the heat rate of nanofluid stream. In this exploration, the presence of the non-uniform magnetic intensity on the heat rate of nanofluid stream is noted inside the $180^{\circ }$ elbow pipe. FVM is used to model the flow characteristics and temperature distribution through the $180^{\circ }$ elbow pipe. Our major focus is to demonstrate the main influences of the non-uniform FHD on flow stream and heat transfer of nanofluid in various inlet velocities and magnetic intensities. Achieved outcomes display that growing the magnetic intensity from 1e + 6 to 4e + 6 enhances the average Nusselt number about 30%. Our findings show that increasing the inlet velocity to Re = 100 decreases the magnetic effects about 17% on the heat transfer growth.

Industry and space technology have significant issues managing heat energy and controlling mass dispersion. The purpose of this study is to develop motion caused by boundary layer thickness sheets that are increasingly being used in various engineering fields (civil engineering, mechanical, aeronautical, maritime processes and constructions). The activation energy is a critical factor in chemical reactions due to the existence of many applications in gas-cooled reactors, nuclear thermal rockets and liquid-fluoride reactors. This study presents the numerical analysis of activation energy on three dimensional (3D) nanofluid (NFs) motion via Stretching Surface (SS) with nonlinear thermal radiation effect. This is in contrast to the conventional slip condition, convective condition applied at surface. The governing basic equations are translated into nonlinear ODEs by suitable similarity transformations. The relevant boundary value problem was explored for a numerical solution for applying the MATLAB based on Runge–Kutta–Fehlberg (RKF) scheme via shooting technique. The major outcomes of current work have more concentration ($\varphi ({\eta }_1)$) and Mass Transfer Rate (${\mathrm{\text{Sh}}}_x{\mathrm{\text{Re}}}_x^{-1∕2}$) for various numerical values of Activation Energy ($E_A$). The present solutions determine very good correlation with the previously studied ones in a special case as predicted in the tables.

Presently, due to its extraordinary mechanical, thermal, electrical and biomedical facets nanofluids deliver several prospects to exaggerate the propensity of isothermal systems by augmenting the conductivity features of the host fluids. In various areas of the energy partition, nanoparticles show a remarkable measure in energy storage, energy variation, and energy convertible, i.e. thermoelectric plans, petroleum cells, supercapacitors, stellar cells, rechargeable batteries, light-radiating diode and carbon-based light-radiating diode, smart coatings. In this current conversation, we anticipated an unsteady 3D flow of the Sutterby nanofluid consequence of a bidirectional extended surface. To envision the thermophoresis and Brownian motion properties in Sutterby’s nanofluid, the Buongiorno association is utilized in an additional refined technique. Variable thermal conductivity with heat source/sink property occurred deliberated considering heat transmission techniques. The appropriate transformation is applied for transposing the PDEs into nonlinear ODEs. For numerical results, the bvp4c programmed is prerequisite for elucidating the subsequent Ordinary differential equations. The distinct performance of the Sutterby nanofluid temperature and the concentration field are designated and discussed in the physical parameter’s aspect. It is clear that the temperature of the Sutterby fluid decreases with respect to the ratio of stretching rates parameter and similar developments are observed for the thermophoresis and Brownian motion parameters. Furthermore, the concentration profile declines for sophisticated estimates of the Lewis number and thermophoresis parameters.

The analysis brings out the investigation of the impact of thermal buoyancy on conducting the flow of an unsteady nanofluid within parallel moving walls embedded with a porous matrix. However, the medium is also embedded with permeable materials. Additionally, the impact of a uniform heat source is assumed to affect the designed model. The special attraction of the model is the variation of differently shaped nanoparticles using Hamilton–Crosser conductivity in which the base fluid is concatenated with the gold nanoparticles. The simulation is carried out for the governing equations numerically followed by requisite similarity rules used for the conversion of nonlinear problems of PDEs to ODEs. Further, shooting-based Runge–Kutta fourth-order scheme is imposed for the set of first-order ODEs. The behavior of several characterizing components within their range is presented for both the flow profiles via graphs and numerical results of the rate constants are deployed through the tabular form. Finally, the important outcomes are the particle concentration shows its greater impact in enhancing the fluid velocity neat the plate region and smooth retardation occurs at the central region further, the heat transfer rate retards significantly.

This work considers the analytical analysis of silver-water, silver-blood base nanofluid flow over fluctuating disk with the influence of viscous dissipation over fluctuating disk. The primary goal of this study is an effort to improve the heat transfer ratio, which is a core part of the engineering and industrial sectors. Following a continuity check, the problem is modeled using the conservation rules of momentum and energy. Nonlinear PDEs are produced through modeling, which are then transformed into ODEs using a similarity transformation and thermophysical characteristics. The resultant ODEs are resolved using the Optimal Homotopy Asymptotic Method (HAM). The outcomes of this method are compared to authenticate the outcomes of the obtained results. The Mathematica software is used to run HAM methods, and graphical interpretations are given to highlight the influence of dissimilar contributing factors on the velocity profile and temperature distribution. Nusselt’s number, and the skin friction are examined through graphical representation. Convergence of the problem is checked with the help of graphs and tables by using dual solution of the problem.

This work considers the analytical analysis of graphene oxide ethylene glycol and graphene oxide blood base nanofluid over a vertical sheet. The principal objective of this study is to make an effort to improve the heat transfer ratio, which is the core part of the engineering and industrial sectors. Following a continuity check, the problem is modeled using the conservation rules of momentum and energy. Nonlinear PDEs are produced through modeling, which are then transformed into ODEs using the similarity transformation and thermophysical characteristics. The resultant ODEs are resolved using the Homotopy Asymptotic Method, and graphical interpretations are given to highlight the influence of different contributing parameters such as unsteady parameter, nanoparticle volume fraction, mixed convection parameter, Grashof number and Prandtl number on the velocity profile and temperature distribution. It is noted that increasing the values of nanoparticle volume fraction and stretching parameter slow down the velocity profile. Also, increasing the values of mixed convection parameter and Grashof number (Gr) enhance the velocity profile, and increasing values of Prandtl number and Graship number reduce the temperature distribution. The Nusselt number and the skin friction are examined through graphical representation. It is noted that increasing the value of mixed convection parameter decreases the skin friction of the fluids, and the Nusselt number decreases with the growing value of Prandtl number.

This research paper presents an investigation into the behavior of rarefied flow and heat transfer in a rectangular microchannel utilizing a Cu-water nanofluid. The study employs the thermal lattice Boltzmann method (LBM) with a lattice featuring a double distribution function and a BGK collision model. The simulations are performed using Python software, incorporating slip velocity and temperature jump effects. The primary objective is to analyze the influence of various thermophysical parameters of the coolant fluid on the microchannel, specifically focusing on the characteristics of the Cu-water nanofluid. The study considers laminar flow conditions with nanofluid volume fractions of 2%, 4% and 6%. The findings reveal that both rarefaction effect and Reynolds numbers, as well as the nanoparticle volume fraction, significantly impact the system. Moreover, the investigation evaluates key parameters such as the Nusselt number, skin friction coefficient, temperature jump slip velocity and velocity and temperature profiles. Notably, the nanoparticle volume fraction exhibits minimal influence on the velocity distribution or temperature field, whereas the Nusselt number increases with higher nanoparticle volume fractions. Additionally, the rarefaction effect leads to a reduction in velocity and temperature. At a nanoparticle volume fraction of 2%, increasing the Reynolds number results in elevated velocities and lower temperatures. The skin friction coefficient displays a decreasing trend along the microchannel with increasing Reynolds numbers. Furthermore, an increase in Knudsen numbers corresponds to a decrease in the skin friction coefficient. Finally, an increase in the nanoparticle volume fraction is associated with a decrease in the skin friction coefficient.

The aim of this research paper is to analytically investigate graphene oxide blood base nanofluid with the impact of dynamic viscosity and viscous dissipation. The increased thermal conductivity of nanofluids over regular fluids motivates this research. The basic flow equations are used to model the flow problem in nonlinear partial differential equations (NLPDEs). The dimensionless parameters, classical lie group, and thermo-physical properties are applied to transform the developed NLPDEs into dimensionless ordinary differential equations (ODEs). The resultant ODEs are resolved using the homotopy analysis method (HAM), and graphical and tabular interpretations are used to note the effects of contributing parameters including magnetic parameter, dynamic viscosity, nanoparticle volume friction, Eckert number, and Prandtl number on the velocity profile and temperature distribution. From the obtained results, we see that the velocity profile is decreasing by increasing magnetic parameter, dynamic viscosity, nanoparticle volume friction, and the temperature profile is increasing by increasing dynamic viscosity and Eckert number. The tabular descriptions of convergence of the presented fluid flow are also provided.

This study investigates two-dimensional time-dependent stagnation point nanofluid flow over a permeable stretching or sinking sheet. The electrically conducting fluid allows for the interaction of a transverse magnetic field along with magnetic dissipation and thermal radiation to enrich the flow phenomena. The use of nanofluids is becoming increasingly important in a variety of industrial applications, as well as in engineering and biomedicine. The process of peristaltic pumping, the flow of blood in the artery, the drug delivery process, and besides that, the cooling of electronic devices for the better shape of the product at the final stage of production, the use of nanofluid, are all important. The transformed dimensionless governing equations are obtained by the implementation of various transformation rules, and the model is designed by using different thermophysical properties such as viscosity, conductivity, etc. Finally, the numerical technique RK-fourth-order method is deployed to solve the set of equations and the iteration process is continued up to the desired accuracy of 10${}^{-5}$. The validation of the current result is shown with the earlier investigation in particular cases, and further, the behavior of the physical parameters is presented through graphs. It is observed that the particle concentration has a greater impact in enhancing the velocity distribution for the variation of suction/injection. The behavior of the magnetic parameter vis-à-vis the unsteadiness parameter and the thermal buoyancy presents their greater contribution in enhancing the magnitude of nanofluid velocity.

The phenomenon of natural convection in rectangular cavities of different aspect ratios is considered. The water is considered a base fluid associated with copper nanoparticles. The flow is induced only due to buoyancy force that arises by heating the right side of the cavity. The left side is set cold while the other walls are assumed to be at zero flux temperature. The governing equations of the present communication are simulated by the finite difference method. This study explores the impacts of Rayleigh number (Ra), Prandtl number (Pr), nanoparticles volume fraction ($\varphi$), and aspect ratio (A). Different combinations of these parameters are investigated. Compared to other parameters, Rayleigh number (10${}^4<\mathrm{\text{Ra}}<10^8$), aspect ratio ($1\le A\le 3$), and volume fraction of nanoparticles ($0.01\le \varphi \le 0.1$), A is found more effective on the flow field and isotherms. Regression curves are determined for the mean Nusselt number (Nu_avg) as a function of Ra for different cases. It is found that Nu_avg more precisely fits the exponential function. Also, it is found that Nu_avg decreases as the values of A increase. But, $\varphi$, shows the opposite behavior. It is noticed that when the A of the cavity grows, so does the mean heat transfer Nu. With rising Ra, the local heat transfer Nu_L decreases and the heat transfer rises. In the case of the square cavity, the regression coefficient for Nu_avg is found to be 0.3673 and 0.2514 for an exponential function.

The flow structures of jet impingement dominate heat and mass transfer process, even the whole thermal performance. In this study, we have inspected the flow structures and mechanism of nanofluid jet impingement onto a dimpled target surface with different design parameters. Investigations are performed for the relative depth of dimple ($\delta /D$), the jet-to-plate spacing ($H/d$), nanoparticle volume concentration ($\varphi$), and Reynolds number (Re) ranging to explore the mechanism of flow structure variations. Results indicate that these parameters have a significant effect on the flow structure of nanofluid jet impingement near the dimpled target surface. The flow begins to separate after passing the edge of the dimple along with the curvature of a dimple. $\delta /D$ will affect the form and location of flow separation and reattachment, and $\varphi$ will affect the intensity of separation flow. The length of the flow separation bubble varies in different $H/d$ cases. When $H/d$ increases, the impinging energy and the velocity near the dimple edge decreases. The different Re has little effect on the length of the flow separation bubble and the tendency of the pressure coefficient (Cp). These results can provide further mechanism inspiration for the design of the flow structure of nanofluid jet impingement.

The objective of this paper is to analyze the unsteady incompressible flow of the viscous nanofluid on a contracting surface with viscous dissipation effects. Presented and contrasted are analyses of both multi-wall carbon nanotubes (MWNTs) and single-wall carbon nanotubes (SWNTs). As the common (or base) fluids, kerosene oil and water are utilized. In the existence of first-order thermal and velocity slip conditions, mathematical modeling and analysis are performed. Using the MATLAB software’s bvp4c solver tool, numerical solutions to the governing nonlinear modeled problems were obtained. This technique is particularly effective for developing many solutions to highly nonlinear differential equations. In addition, a comparison is done between this study and previously published works. The temperature, velocity, skin friction coefficient and heat-transfer rate have been explored for various significant factors included in the problem statements. In the unsteadiness parameter regime, dual solutions can be found. As the velocity slip parameter is increased, the flow slows down. In comparison to SWCNTs kerosene, MWCNTs kerosene oil has a greater velocity curve for the nanoparticles volume fraction. Increases in volume fraction decrease skin friction, whereas increases in the unsteadiness parameter speed up the drag force. Furthermore, as the Eckert number intensity increases, so do the temperature profiles in both solutions. Finally, the stability study revealed that the initial solution is robust, whereas the breakage in the second solution in the Nusselt number shows singularity, and thus the second solution is considered unstable.

In this paper, nanofluid flow is considered on curved stretching surface under magnetic influence. Realistic velocity slip together with convective boundary condition is imported. The system is also blessed with radiation and higher order chemical reaction. Active and passive controls of nanoparticles are considered and under both boundary conditions the flow analysis is compared. Leading equations of the system is a set of partial differential equations which are transfigured by similarity variable into a set of highly nonlinear ordinary differential equations (ODEs). The system is solved by the Runge–Kutta fourth-order method (RK-4) with shooting technique. The simulation is done by MAPLE-2021 software. Outcomes are portrayed by several graphs and tables and comparison diagram for different conditions is also included. Velocity lines are compared for suction and injection effect but thermal and concentration profiles are compared under active and passive controls of nanoparticles. The velocity profile changed by 16.55% for higher magnetic profile and the mass transfer changed by 3.57% for actively controlled flow under velocity slip parameter. Chemical reaction parameter detained the concentration profile for both active and passive controls but gave lower magnitude for passively controlled flow.