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This paper focuses on the study of Blasius–Rayleigh–Stokes nanofluid dusty flow with generalized Fourier and Fick laws under the influence of a transitive magnetic field. The Blasius–Rayleigh–Stokes nanofluid dusty flow has significant applications in various fields, including the design of heat exchangers, microfluidic devices and industrial processes involving the transportation of suspended particles in fluids. This paper considers the impact of melting heat transfer at the surface boundary. By employing relevant transformations, the mathematical model is transformed into a system of self-similar equations. The solution to this set of highly nonlinear equations is obtained using the bvp4c numerical method in combination with the response surface methodology (RSM) statistical approach. The results are presented through graphical illustrations and numerically calculated tabulated values. It is observed that the fitted model for the skin friction coefficient Re x 1 ∕ 2 C f optimal. Moreover, the model parameters Pr , Q, β v , M and L are linearly and quadratically significant in explaining the variation presented for skin friction coefficient Re x 1 ∕ 2 C f . This indicates the response skin friction coefficient Re x 1 ∕ 2 C f is minimized to 0.005 at Pr = 2. 2 0 2 7 , Q = 0. 2 5 2 , β v = 0. 2 2 , M = 0. 2 1 7 and L = 0. 2 5 2 and is maximized to 1.387 at Pr = 2. 0 6 6 , Q = 0. 2 5 4 , β v = 0. 0 2 1 , M = 0. 0 5 6 and L = 0. 2 5 2. [ABSTRACT FROM AUTHOR]

This study is focused on examining how solar radiation, thermal convection, and viscous dissipation impact the stagnation point flow in a variable porous space. The colloidal nanoparticles of TiO 2 (titanium oxide) have dispersed in different base fluids taken as H2O (water) and C2H6O2 (ethylene glycol). Boosting heat transfer is made possible by the porous space in hybrid nanofluid flow. The use of porous media leads to increased surface area for heat transfer, which in turn improves heat exchange between the nanofluid and the solid matrix. A suitable set of transformable variables is employed to convert the leading equations in dimensionless form. This set of new equations has been evaluated by employing Mathematica and artificial neural network (ANN). It has been noticed in this work that, the thermal panels have augmented with escalation in volume fractions of solid nanoparticles as well as with positive and negative growth in Eckert number. The range of the parameter Rd , S , Da , Gr , ϕ is considered between 0 and 1. While Ec number range is taken out of this range for better performance. [ABSTRACT FROM AUTHOR]

In this study, we investigate how a magnetic field affects the dynamic behavior of a hybrid nanofluid flow over a curved stretching surface. The unique thermal and rheological characteristics of hybrid nanofluids, which are created by dispersing nanoparticles and micro-sized particles in a base fluid, make them an attractive option for accelerating heat transfer processes. The curved stretching surface taken into consideration in this study is a typical industrial application geometry. This study's main objective is to understand how magnetohydrodynamics (MHD) affects hybrid nanofluid flow over curved surfaces. We investigate the consequences of important parameters such as the magnetic field strength, Reynolds number, and Reynolds number using modern computational approaches. We investigate the paraphernalia of important parameters on the flow and heat transfer characteristics, including the magnetic field strength, Reynolds number, and volume fractions of nanoparticles. Our research shows that adding a magnetic field improves the hybrid nanofluid's thermal performance, making it a promising choice for boosting heat transfer effectiveness in engineering systems. [ABSTRACT FROM AUTHOR]

This study delves into computational fluid dynamics (CFDs) predictions for SiO2–water nanofluids, meticulously examining both single-phase and two-phase models. Employing the finite volume approach, we tackled the three-dimensional partial differential equations governing the turbulent mixed convection flow in a horizontally corrugated channel with uniform heat flux. The study encompasses two nanoparticle volume concentrations and five Reynolds numbers (10,000, 15,000, 20,000, 25,000, and 30,000) to unravel these intricate dynamics. Despite previous research on the mixed convection of nanofluids using both single-phase and two-phase models, our work stands out as the inaugural systematic comparison of their predictions for turbulent mixed convection flow through this corrugated channel, considering the influences of temperature-dependent properties and hydrodynamic characteristics. The results reveal distinct variations in thermal fields between the two-phase and single-phase models, with negligible differences in hydrodynamic fields. Notably, the forecasts generated by three two-phase models—Volume of Fluid (VOF), Eulerian Mixture Model (EMM), and Eulerian Eulerian Model (EEM)—demonstrate remarkable similarity in the average Nusselt number, which are 24% higher than the single-phase model (SPM). For low nanoparticle volume fractions, the average Nusselt number predicted by the two-phase models closely aligns with that of the single-phase model. However, as the volume fraction increases, differences emerge, especially at higher Reynolds numbers. In other words, as the volume fraction of the nanoparticles increases, the nanofluid flow becomes a multi-phase problem, as depicted by the findings of this study. [ABSTRACT FROM AUTHOR]

The homogeneous and heterogeneous reactions can provide important insights into the design and optimization of nanofluid-based heat transfer systems for various applications, such as in thermal management, energy conversion, and cooling. Understanding such pivotal role of homogeneous and heterogeneous reactions in the nanofluid flow modeling, this study aims to explore the consequences on the nanofluid flow comprising graphene oxide/water mixture through a permeable channel impacted by incorporating uniform homogeneous–heterogeneous reactions and heat generation/absorption respectively. The novelty of the presented model is translated by incorporating the thermal conductivity model that integrates the volume fraction of particle, diameter, and nanolayer impacts. The nanofluids possess multi-directional applications including nano drug delivery, cooling of computer microchips, optical devices, etc. The fluid system is formulated using Tiwari and Das nanofluid flow model. The ordinary differential equations (ODEs) are acquired by adopting apposite transformations and numerically computed utilizing the bvp4c method. Moreover, the impacts of the resulting physical parameters on the distributions of temperature, velocity, and nanoparticle volume fraction are examined using graphical representations. It is comprehended that nanofluid velocity declined for the porosity and magnetic parameters. Nevertheless, an upsurge in the fluid temperature is witnessed for the heat generation/absorption parameter. In addition, the heat transfer rate is more prominent in the case of a strong magnetic field. The validity of the envisioned model is also a highlight of this investigation. [ABSTRACT FROM AUTHOR]

The heat transfer improvement by using CuO/water nanofluid (NF) in a wavy channel is evaluated numerically using the turbulent two-phase mixture and the κ - ε models. The numerical work is a 2-dimensional model created and analyzed in Gambit and Ansys Fluent software, respectively. The flow Reynolds (Re) numbers of 8000 – 40,000, wavelength ranging from 0 – 0.4 m, and solid volume fraction (SVF) of 0 % to 4 % are investigated. In all cases, a constant heat flux of q′′=5000 W/m2 is applied on the outer surface of the heat exchanger. The heat transfer and fluid flow were analyzed by the flow visualization method and heat transfer evaluation indexes. The results show that by increasing the Re number, the vortices increase and more turbulence are generated in the vicinity of the waves near the channel inlet. As the amplitude of the channel waves increased, the velocity at the top of the wave increased, and the resulting pressure gradient behind the wave is intensified and the reverse flow is generated. The improving effect of using NF is more prominent where the effect of other enhancing factors is weak. For wall amplitude of 0.1 m, by increasing the SVF from 1 – 4 % the average Nu number (Nuavg) increased by 35 % and 22 % in Re = 8,000 and 40,000, respectively.

Efficient cooling is crucial for maintaining the reliability and performance of industrial and engineering systems that generate excess heat. Entropy generation analysis, established on the second law of thermodynamics, plays a vital role in identifying inefficiencies within these systems and improving their overall efficiency. This study focuses on a theoretical investigation of the entropy generation, considering the cumulative impact of surface slipperiness, Brownian motion, applied magnetic field, thermophoresis on the nanofluid flow toward a convective heated stretching surface. The governing model partial differential equations undergo a transformation through similarity transformation, resulting in a nonlinear ordinary differential equation. This equation is subsequently solved numerically by employing the Runge–Kutta–Fehlberg integration scheme in conjunction with the shooting method. The obtained results reveal the influence of various parameters on the temperature, velocity, Nusselt number, skin friction, Sherwood number, Bejan number, nanoparticle concentration, and entropy generation. Upon analysis, it was notable that the introduction of a magnetic field, higher Biot numbers, Eckert numbers, and elevated Brownian motion led to an increase in the entropy generation within the system. Conversely, the presence of thermophoresis and reduced surface slipperiness resulted in a decrease in entropy. These results are presented through graphical representations, tables, and quantitative discussions, providing valuable insights for optimizing the cooling and performance of industrial and engineering systems. [ABSTRACT FROM AUTHOR]

AbstractIn this work, we use the sophisticated differential transform method (DTM) to derive solutions to the complicated momentum, heat, and mass transfer equations that characterize Darcy-Forchheimer nanofluid flow over a stretching surface with convective boundary conditions. The investigation includes the nuanced effects of heat sources and chemical reactions and also addresses the synergistic effects of Brownian motion and thermophoresis. By applying an appropriate similarity transformation, the governing partial differential equations (PDEs) are gracefully transformed into an elegant system of nonlinear coupled ordinary differential equations (ODEs), a problem that is ingeniously solved using DTM. The veracity of our results is underpinned by a careful validation against previous scientific work that illuminates the path to scientific clarity. As the mathematical tapestry unfolds, the enchanting interplay of physical parameters on fluid dynamics is revealed, manifesting in visually captivating graphs and illuminating tables. Of particular note is the transformative influence of the magnetic parameter, which stages a ballet in which an increase in skin friction and the Nusselt number causes a diminuendo. Meanwhile, the solutal concentration decreases as the Brownian motion, Lewis number, and chemical reaction parameters increase, while it waltzes in reverse harmony with the thermophoresis parameter. Beyond equations and diagrams, this investigation promises to cast a luminous beacon on practical realms, imparting invaluable insights for industries ensconced in the realm of heat exchangers, the alchemy of lubricant refining processes, and the grand tapestry of scientific and engineering domains. [ABSTRACT FROM AUTHOR]

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A pillow plate heat exchanger (PPHE) is one of the types of heat exchangers that haven't received the attention they deserve despite their high efficiency and operational capability. A unique feature of PPHEs is their pillow-shaped structure, which is achieved through hydroforming. In light of this, scholars have been interested in analyzing and optimizing the thermo-hydraulic properties of PPHEs. In this study, the interior of the PPHE was occupied with a permeable substance with a high porosity percentage (0.9034 ≤ ɛ ≤ 0.9586 and 0.00015 ≤ dp ≤ 0.00065) and saturated with Ag-water (0 ≤ϕ ≤ 0.06) nanofluid, which has a profound influence on the heat transfer rate of PPHEs. In order to analyze the determinants affecting the heat transfer rate of PPHEs under these conditions, the governing equations were solved using the finite volume method and also the Brinkman-Forchheimer-extended Darcy equation. According to the results, heat transfer is enhanced in PPHE when using a permeable medium with high porosity and a small pore size. That is, PPHEs transfer heat more efficiently when they are placed in a denser porous medium because heat conduction is boosted. Moreover, due to the increased thermal conductivity of the nanoparticles, the application of nanoparticles to the base fluid also enhanced heat transfer and Nusselt number. However, decreases in friction factor and entropy generation were observed with increasing porosity, pore size, and Darcy number, due to reduced flow resistance. A decrease in Richardson number also results in a decrease in friction factor and entropy generation. At the wake region of welding spots, the velocity has reached its lowest values; consequently, this led to a reduction in the heat transfer rate. Nevertheless, within dense porous media, at the lower hydraulic diameter points, the conduction contributes to heat transfer improvement. The porous medium acts as a heat sink and absorbs the heat from the welding spot. This allows the heat to be dissipated away from the welding spot, which reduces the velocity and heat transfer rate. The nanofluid, on the other hand, helps to increase the thermal conductivity of the medium, resulting in more heat being transferred to the surrounding material. Consequently, the results demonstrated that PPHEs' thermal and thermodynamic performance could be significantly improved by using a porous medium saturated with nanofluid.

The significant impact of nanotechnology has turned the ordinary into the excellent in the ever-changing environment of science and technology. Recent times have seen a dramatic transformation as advances in science and technology continue to push us into the domain of nanoscale innovation. Fluid flow over a range of geometries is involved in the physical processes of heat and mass transfer subject to the constraints. These phase change systems are also converted into the latest technology by improving the thermal conductivity of the fluids through the mixing of nanoparticles in the ordinary base fluid. This approach makes things finer and quicker from the perspective of efficiency and structure. It has many applications in various domains especially in nano-medicines, chemotherapy, microprocessors, refrigeration, and biotechnology. In this work, nanofluid flow through a wavy cylinder is considered in the existence of thermal radiation, activation energy, and motile microorganisms. The physical model is computationally solved by developing a system of PDE's (partial differential equations) and then transformed into ODE's (ordinary differential equations) by the smooth implementation of similarity variables. The resultant ODE's numerically treated by the bvp4c built package of MATLAB and get the required results. These results are discussed and graphically visualized in the analysis section. For the validation of results, the statistical approach is implemented on the acquired results and shows the fitted model, contour plots, surface plots, residual plots, and streamlines of the involved parameters and their impacts on the model. The impact of involving physical quantities on flow velocity, thermal, concentration, and microorganism's density profiles also discussed. From the results, it is noted that the velocity profile increases by increasing the counts of mixed convection. Thermal distribution enhanced due to boosting the values of thermophoresis and Brownian motion. The concentration of nanoparticles increased by increasing the magnetic field strength. The larger values of peclet number minimize the density of microorganisms. Skin friction coefficient is increased by around 28% and mass transport going to be increased by 36% due to the existence of microorganisms. The analysis of variance shows that our model is significant and the fitted summary also shows the fitness of model.

This research presents an innovative alteration to the solar collector's design by integrating a 4-lobed tube with helical tape. The choice of a working fluid, a combination of water and alumina nanoparticles, is purposeful, aiming to reduce irreversibility. Extensive numerical simulations, along with thorough benchmark verification, meticulously assess the system's performance, demonstrating strong alignment with established benchmarks.This study delves into the interaction among pivotal parameters—D* (diameter ratio), Re (Reynolds number), and N (revolution number)—and their impact on essential performance metrics, encompassing ηII (second law performance), Xd (exergy drop), and Φx (exergy drop ratio). With the elevation of all three parameters, the intensified swirl flow facilitates improved heat absorption by the nanofluid, resulting in reduced entropy generation and subsequently, a decrease in exergy drop. More precisely, the increments in Re, N, and D* lead to significant reductions in the value of Xd, with approximately 52.1 %, 4.02 %, and 5.03 %, respectively. When N = 4, D*=0.02, the amount of ηII for Re = 2e4 is 8.38 times greater than that of Re = 4e3. Increasing D* and N leads to substantial improvements in ηII, with approximately 50.02 % and 30.15 % enhancements, respectively. The highest ηII, reaching 0.582, is attained when D*=0.048, N = 7, and Re = 2e4.

In this article, we investigate the heat transfer on nanoparticles Jeffrey Hamel flow problem between two rigid plane walls. Water is used as a main fluid using four different types of nanoparticles, namely aluminum, cuprous, titanium, and silver. The results of nonlinear transformational equations with boundary conditions are solved analytically and numerically. The perturbation iteration scheme (PIS) is used for the analytic solution, while for determining the numerical results, the Rang-Kutta of the four-order scheme (RK4S) is used. The effects on the behavior of non-dimensional velocity and temperature distributions are presented in the form of tables and graphs for different values of emerging physical parameters (Reynolds number, Prandtl number, Eckert number and open angles).The solid component of nanoparticles has an influence on the heat transfer and flow characteristics that is more visible when compared to other types of particles. The temperature distribution increases with the increase of the Reynolds number, Bruntel number, Eckert number, but the velocity distribution decreases with the increase of the Reynolds number. Finally, the obtained findings demonstrate PIS efficacy, accuracy, and convenience in solving the problem of nanofluid flow. [ABSTRACT FROM AUTHOR]

Nanofluids with immersed metallic nanoparticles possess a higher thermal conductivity. The extent of this enhancement is largely dependent on the amount of the volume fraction, composition, nanoparticles' shape, and size. The current study emphasizes nanofluid (gold-ethylene glycol) flow with different shapes past a horizontal infinite permeable conduit. The porous walls exhibit the fluid to move in or out of the channel as the walls expand or contract. The flow problem is modeled in a Cartesian coordinate system by employing the Tiwari-Das nanofluid model. Heat transfer is enhanced with the inclusion of Cattaneo–Christov combined with heat generation/absorption effect and temperature-dependent thermal conductivity. The Hamilton–Crosser model is adopted here for the cylindrical and platelet shapes nanoparticles. By invoking appropriate transformation, the equations are transmuted into ordinary differential equations and are solved numerically by employing the bvp4c approach. The influence of the key parameters is illustrated graphically. A protuberant decline is observed in the cylindrical shape nanoparticles in the thermal field on augmenting the thermal relaxation parameter. The drag force coefficient elevates on incrementing the volume fraction of nanoparticles. A significant correlation is noticed in the findings of the comparison with the existing literature. [ABSTRACT FROM AUTHOR]

A pillow plate heat exchanger (PPHE) is one of the types of heat exchangers that haven't received the attention they deserve despite their high efficiency and operational capability. A unique feature of PPHEs is their pillow-shaped structure, which is achieved through hydroforming. In light of this, scholars have been interested in analyzing and optimizing the thermo-hydraulic properties of PPHEs. In this study, the interior of the PPHE was occupied with a permeable substance with a high porosity percentage (0.9034 ≤ ɛ ≤ 0.9586 and 0.00015 ≤ dp ≤ 0.00065) and saturated with Ag-water (0 ≤ ϕ ≤ 0.06) nanofluid, which has a profound influence on the heat transfer rate of PPHEs. In order to analyze the determinants affecting the heat transfer rate of PPHEs under these conditions, the governing equations were solved using the finite volume method and also the Brinkman-Forchheimer-extended Darcy equation. According to the results, heat transfer is enhanced in PPHE when using a permeable medium with high porosity and a small pore size. That is, PPHEs transfer heat more efficiently when they are placed in a denser porous medium because heat conduction is boosted. Moreover, due to the increased thermal conductivity of the nanoparticles, the application of nanoparticles to the base fluid also enhanced heat transfer and Nusselt number. However, decreases in friction factor and entropy generation were observed with increasing porosity, pore size, and Darcy number, due to reduced flow resistance. A decrease in Richardson number also results in a decrease in friction factor and entropy generation. At the wake region of welding spots, the velocity has reached its lowest values; consequently, this led to a reduction in the heat transfer rate. Nevertheless, within dense porous media, at the lower hydraulic diameter points, the conduction contributes to heat transfer improvement. The porous medium acts as a heat sink and absorbs the heat from the welding spot. This allows the heat to be dissipated away from the welding spot, which reduces the velocity and heat transfer rate. The nanofluid, on the other hand, helps to increase the thermal conductivity of the medium, resulting in more heat being transferred to the surrounding material. Consequently, the results demonstrated that PPHEs' thermal and thermodynamic performance could be significantly improved by using a porous medium saturated with nanofluid. [ABSTRACT FROM AUTHOR]

Abstract Casson fluids are used to understand the rheological characteristics of pigment-oil suspensions, polymeric gels, emulsions, heavy oil, etc. Hence in this article, numerical work is carried out to investigate a steady MHD flow of a Casson nanofluid with the Cattaneo-Christov model over a stretching sheet in the presence of a porous medium with heat generation, and suction/injection. The effects of activation energy and chemical reactions are also considered. The concept of MHD is significant because of its numerous applications, including power generators, cooling process, sensors, and magnetic drug targeting. The governing equations of the model are reduced to a system of nonlinear coupled ordinary differential equations by appropriate transformations and are solved numerically via the bvp5c MATLAB package. The effects of the pertinent parameters on the velocity, temperature, and fluid concentration fields along with the skin friction, heat, and mass transfer rates are discussed in detail through figures and tables. It is reported that the velocity field decreases with an escalation in the magnetic field, porosity, and suction. However, the heat transfer rate enhances due an enhancement in suction and the Biot number, whereas it declines with the increasing values of the Brownian motion, thermophoresis, heat generation and thermal relaxation parameters. Furthermore, activation energy increases the fluid concentration. [ABSTRACT FROM AUTHOR]

Current studies have a significant application in various fields; motile microorganism, such as bacteria, can be used for targeted drug delivery. This is because they can be engineered to carry drugs to specific locations in the body. For example, bacteria can be modified to express genes that code for targeting ligands, which are molecules that bind to specific receptors on cells. This could help to prevent the bacteria from multiplying and causing disease. The main aim of the current work is to perform the numerical analysis of three-dimensional radiative, steady viscoelastic nanofluids flow towards an exponentially stretchable porous surface. The impact of nth-order chemical reaction and motile microbes are also disclosed looks at how multiple slips affect the Buongiorno model for magnetohydrodynamic viscoelastic nanofluids with radiation across a permeable stretched sheet. The appropriate suitable are used to transform nonlinear partial differential equations into ordinary differential equations. The numerical solution of the resulting system of equations is handled numerically by employing the bvp4c algorithm built-in MATLAB Software which comes of three-stage Lobatto IIIa formula. Dimensionless values such as temperature, concentration, velocity, and the non-Newtonian nano-fluid density profile are explored, as are non-dimensional numbers such as the local Nusselt, local friction coefficient, Sherwood, and motile microbe. Present results signifies enhancement in the temperature profiles as well as the thickness of the thermal boundary layer by increasing Brownian motion (Nb) and thermophoresis parameters (Nt), whereas decrement is noted against the viscoelastic parameter (K). As the value of the magnetic parameter ranges 0.0≤M≤ 0.2 the relative increment noted in skin friction coefficient is about 1.9 %, while decrement is found in curves of velocity field. Our findings are compared with the data available in the literature and found to be in good consensus.

The thermal efficiency of the nanofluid flow along the 180-elbow pipe is investigated under effects of double source of non-uniform magnetic field. To model the nanofluid stream with double magnetic sources, computational fluid dynamic is used. Effects of magnetic intensities and velocity of nanofluid on the hydrodynamic of the chosen model is also investigated in this research. The results of simulation indicate that the vortices are generated near the magnetic field and these vortices extend the thermal layer into the main stream and consequently, thermal efficiency of nanofluid stream is enhanced in 180-degree elbow. The results of various magnetic intensities also show that the increasing the magnetic intensities changes the location of maximum heat transfer from 1st magnetic source to 2nd one.

This study aims to analyze the two-dimensional incompressible, steady MHD-mixed convective nanofluid flow with homogenous–heterogeneous (hh) reaction and Cattaneo–Christov heat flux (CCHF) past a rotating cone. The uniqueness of the presented model is the consideration of the surface-catalyzed reaction while considering the hh reactions on the surface of the cone in the existence of a permeable medium. Owing to this supposition, the rate of reaction is provoked in the least possible time. Moreover, irreversibility analysis is also performed for the suggested mathematical model in the wake of the second law of thermodynamics. The impacts of slip conditions and heat sink/source are also assessed here. The numerical model of these governing equations is solved using the MATLAB bvp4c package that addresses the system of ODES extracted from the governing PDEs. Graphs are used to evaluate the important consequences of the main arising parameters versus the concerned fields. The results revealed that in the presence of a high magnetic field, the temperature is enhanced. Moreover, the Entropy generation is boosted for magnetic and diffusion parameters. The results presented for this model are also corroborated by associating them with the published study. [ABSTRACT FROM AUTHOR]

Abstract The combined effects of Stefan blowing and Thompson–Troian slip on mixed convection flow of a nanoliquid over a flat plate with first-order compound response are examined. In several industries and engineering sectors, nanofluid plays a vital role in augmenting heat transport properties. Moreover, nanoliquids are used in chemical manufacturing, cooling of electronic machinery, and biomedical disciplines. The fluids with slip consequences have a wide variety of applications. As the Thompson–Troian slip model permits the alteration of the amounts of slip close to the areas of elevated shear speed and shear anxiety, the effects of this slip model are examined in this article. Using appropriate transformations, the partial differential equations (PDEs) of the model are changed to ordinary differential equations (ODEs), and the reduced ODEs are numerically solved. This study has noteworthy effects on the flow, the heat transfer, and the accumulation transport characteristics. With a rise in the slip velocity and the critical shear rate, the fluid velocity increases, while the temperature field decreases for a rise in the velocity slip. It is also observed that when the Lewis number increases its value from 0.3 to 0.4, the heat transfer rate at the plate increases by almost 30.88%, and the accumulation velocity transport at the plate rises by 56.92%. Interestingly, dual solutions exist for some specific range of values of the relevant parameters. The results of this study will be of use to scientists and engineers to understand better the flow and heat transfer characteristics. [ABSTRACT FROM AUTHOR]

The reviews in the literature reveal that nanofluids are more efficient for heat transfer than regular base fluids. The liquids that contain suspended nanoparticles have gained significant attention in recent years due to their potential enhancement of heat transfer in various applications including electronics cooling, power generation, and refrigeration. The present research work aims to examine the MHD radiative oscillatory nanofluid flow in a porous medium through an asymmetric wavy channel. The partial differential equations with physical boundary conditions represent the mathematical model of the flow problem. The governing equations are solved by the analytical method. H2O-Water and C2H6O2-ethylene glycol (EG) as base fluids are used with four different types of nanoparticles, namely gold (Au), copper (Cu), alumina (Al2O3), and silver (Ag). Graphs for velocity and temperature profiles are drawn for various shapes (cylindrical, brick, and platelet). Several plots illustrate the velocity, temperature, shear stress and heat transfer rate. Viscosity and thermal conductivity are evidently observed to be the most important physical quantities responsible for varying velocity and temperature profiles. [ABSTRACT FROM AUTHOR]

The laminar movement in an expanding and contracting permeable pipe or surface has recently attracted the attention of many scholars owing to its application in engineering and biological processes. The objective of the current study is to examine the influence of chemical processes on magnetized nanofluid flow over extending or shrinking permeable pipes with a heat reservoir. The flow equations are renovated into first ODEs by introducing the new variable and then numerically solved by RK4 with a shooting procedure. The effect of emerging factors on the flow features is observed using graphs and elaborated in detail. From the analysis, the temperature is raised when the heat source is increased in both cases of wall expansion or contraction but declines in the case of heat sinks. In the case of a heat source, the temperature rises as the Hartmann and Prandtl numbers are enhanced, but in the case of a heat sink, the temperature falls. In the presence of heat sinks and injections, when the thermophoresis factor is increased, the concentration of nanoparticles is increased in both wall expansion and contractions. In both situations of wall extension or contraction, along with injection, the concentration of nanoparticles is a decreasing function of N b , while the concentration of nanoparticles is an increasing function in the case of a heat source. Additionally, for the confirmation of the RK4 code, the total average square residue error and average square residue error are also presented. For the stability analysis, the current work is compared with published work, and excellent agreement is established. The novelty of the present study is to investigate the effect of chemical reaction on magnetized nanofluid flow over extending and shrinking porous pipes with heat generation and absorption. [ABSTRACT FROM AUTHOR]

In this paper, the effects of volume fraction, Reynolds number and dilation rate on the permeable walls of the vessel in the gold-copper-nanofluid heat transfer model in two-dimensional of blood are investigated. For this purpose, we consider blood as the base fluid in which units of gold or copper nanoparticles are injected. The mathematical model of this phenomenon is in the form of nonlinear ordinary differential equation of the fourth order. In this paper, the Adomian decomposition method is used to numerically solve this nonlinear model with boundary conditions. Comparing the numerical solutions obtained from the Adomian decomposition method with the analytical solutions obtained from the homotopy analysis method (HAM), shows that the numerical and analytical solutions are in good agreement. Also, according to the obtained results, it can be understood that with increasing the number of gold-copper nanoparticles in the base fluid, what will be the thermal properties. [ABSTRACT FROM AUTHOR]

We have investigated the nanofluid flow in a converging and diverging channel of heated and inclined plane walls. The wellknown Buongiorno model has been undertaken for the transport of nanoparticles in a base fluid. The upper (lower) wall of the channel has the geometry and it is presented by an equation of the straight line y=mx+a0 (y=-mx-a0), in which m is the slope of the upper wall, a0 is the half width of the channel inlet (exit) for diverging (converging) flow, x and y are representing the Cartesian Coordinates. Note that the walls of the channel are uniformly and equally heated and the nanoparticle concentration at the walls is also constant. On the contrary, the flow problem is strictly described in Cartesian Coordinates. The problem is formulated for the upper half of the channel and later on the results are generalized for the lower half. The new observations are shown in different graphs. The four governing PD E’ s are simplified with the help of proper and appropriate similarity transformations and they constituted a system of ODE’s, whereas, it is equipped with several dimensionless parameters. Note that the convective terms in energy and concentration equations are disappeared in view of these similarity variables. The effects of all parameters are investigated on flow, heat and mass transfer characteristics. Moreover, effects of all parameters are seen on skin friction, rates of heat and mass transfer. In addition, classical models of nanofluid flow inside a converging and diverging channel in plane polar coordinates will be the special cases of the current modeled problem. Furthermore, the perturbation solution of the modeled equations is also determined for small values of the parameter. Note that slope m and Pr number are used as a perturbation parameters for the momentum equation and energy, species concentration equations and these solutions are valid for small values of all other parameters involved in the problem. In addition, exact solutions of the final ODE are also found for special ranges of parameters value. Moreover, the comparison is shown between the different solutions of the problem and classical solutions in tables and graphs. The temperature (concentration) profiles are increased (decreased) with the increasing of Nb, and Nt, however, both of them are increased with m. Moreover, the linear (non-linear) profiles of skin friction (rate of heat transfer) are decreased(increased) with the increasing of both Re (Pr,m) and m (Nb). In addition, the rate of mass transfer is increased linearly (non-linearly) against the increasing value of Nt (Pr) and Nb (Nb=Nt). Note that the temperature (concentration) profiles are effectively improved (declined) with the increase of thermophoretic forces, moreover, it is also rapidly increased (decreased) with the increase of concentration of nanoparticles (and their rapid fluctuations) in a converging and diverging channel.

In the present study, the combined influence of chemical reaction, thermal radiation, thermophoresis, and Brownian motion on mixed convective heat and mass transfer in the boundary layer of moving magneto nanofluid due to a permeable stretching surface with a heat generation through a porous medium is investigated. The velocity, temperature, and mass concentration of the stretching surface are assumed to have nonlinear variations with the distance. The PDEs governing the study are converted into nondimensional ODEs containing a set of physical parameters. The resulting equations are solved computationally and the impacts of the thermo-physical factors are discussed. To proceed and build on the computational analysis for this work, the computational results are validated by comparing special cases of the present study to those in some earlier studies, and good agreement is obtained. The results show that the thermal boundary layer thickness is less than those for the momentum and mass transfer with factors of mixed convection, chemical reaction, nanoparticles volume fraction, the nonlinearity of the surface, and porous medium. In this view, these factors have a significant impact on many engineering applications such as in the cores of nuclear reactors, the manufacturing of polymers, metal layers, paper sheets, and biochemistry industries.

Nanofluid and its higher thermal performance are displayed more promising outcomes when the flow medium is assumed to be a porous medium. Additionally, the radius size of nanoparticles plays a significant role in enhancing this thermal performance. So, present analysis aims to investigate the time-dependent flow of copper-water nanofluid in porous medium on an expanding sheet in presence of buoyancy force and slip phenomenon under various nanoparticle's radii. The flow is assumed to be boundary layer, two-dimensional, viscous, incompressible, laminar and unsteady. Governing coupled PDEs are changed into ODEs by suitable transformations and the converted ODEs are solved numerically. The study discloses that velocity rises with larger radius of nanoparticles and enlargement in assisting buoyancy force, whereas with unsteadiness of the flow, less permeability of porous material and boundary slip it drops. Also, magnitude of wall-drag force grows with larger radius of nanoparticles and flow unsteadiness. Importantly, for higher value of nanoparticle's radius surface-drag force massively enhances when permeability of porous medium is less. Temperature increment exhibits for boundary slip and less permeability of the porous material. Lastly, wall cooling rate intensifies with flow unsteadiness and higher value of nanoparticle's radius.

The purpose of the current study is to investigate the non-Newtonian unsteady Williamson fluid on a stretching/shrinking surface along with thermophoresis and Brownian effects. Basically, the model consists of a time-dependent magnetic field. The fluid is considered to be electrically conducting due to the effect of the external magnetic field. The values of magnetic Reynolds number are so small that the induced magnetic field is assumed to be negligible. In the concentration equation, the effects of Brownian motion and thermophoresis are discussed. Employing the similarity transformations, the governing nonlinear Partial Differential Equations (PDEs) are converted into the Ordinary Differential Equations (ODEs). The resulting ODEs are solved with the combined effects of the Successive Over Relaxation (SOR) method and Finite Difference Method (FDM). The impact of all the including parameters such as suction parameter, injection parameter, stretching/shrinking parameter, the ratio of viscosity, local Weissenberg number, unsteadiness parameter, Eckert number, Prandtl number, Lewis number, Nusselt number, Brownian motion parameter, shear stress, heat transfer rate, and mass transfer rate are analyzed using graphs and tables. Results show that the values of fluid velocity are better for S = 8 ,   − S = 0 ,   λ = 0.3 ,   β * = 0.9 ,   W i = 0.3 , and A a = 2.0 . It is also depicted from the results that the values of boundary layer thickness are better for S = 0 ,   − S = − 8 ,   λ = 0.3 ,     β * = 0.1 ,   W i = 1.5 , and A a = 0.25 . From the above numeric results, it is concluded that the fluid velocity is reduced and the thermal boundary layer thickness is enhanced by the enhancement of the stretching parameter. [ABSTRACT FROM AUTHOR]

A hydromagnetic nanofluid flow past a permeable cone with heat and mass transfer has been investigated. An incompressible, steady, laminar flow was used to study the entropy generation. The main aim was to find the physical parameters responsible for the enhancement of the entropy generation. The presence of nanoparticles in a base fluid helps to improve the heat transfer characteristics. Based on the obtained results, we can predict the entropy variation due to the variation in the flow parameters. The enhancement in the slip velocity and suction/injection parameters is shown to enhance the system efficiency. It was found that the enhancement of diffusion leads to maximum irreversibility and minimum efficiency. The MATLAB built in bvp4c solver technique was used to solve transformed ordinary differential equations with convective boundary conditions. [ABSTRACT FROM AUTHOR]

In this research, the laminar, incompressible, unsteady oscillatory flow and convective heat transfer of nanofluid around a porous cuboid were studied two-dimensionally using particle resolved calculations. Several cuboids of different sizes and porosities and with a constant temperature were subjected to a nanofluid flow with a sinusoidal velocity profile. The effects of the Reynolds number (Re = 100–900), the volume fraction of nanoparticles, the aspect ratio of the porous cuboid, the Darcy number and the amplitude and frequency of the inlet velocity on the flow field and heat transfer were investigated. To evaluate the system's optimal performance, performance evaluation criteria (PEC) were also investigated. The results showed that increasing the Reynolds number improved thermal performance. Increasing the volume fraction of nanoparticles increased the Nusselt number; however, the pressure drop coefficient increased more strongly. The heat transfer and pressure drop coefficient increased in line with the growth of the porous cuboid aspect ratio. When the Darcy number was increased, the Nusselt number first increased and then decreased and the pressure drop coefficient continuously decreased. A higher amplitude of the inlet velocity profile augmented the heat transfer and pressure drop coefficient. An increase in the amplitude and frequency of the inlet velocity profile widened the range of drag and lift coefficients. Furthermore, flow at different inlet velocity frequencies (f* = 0–10) behaved differently; as a result, the maximum rate of heat transfer and pressure drop was obtained at f*=5. However, considering the ratio of the Nusselt number to the pressure drop coefficient and PEC parameter, the optimum frequency was f*=9. [ABSTRACT FROM AUTHOR]

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power‐law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power‐law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power‐law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to propose a kernel-based method for solving the problem of squeezing Cu–Water nanofluid flow between parallel disks. Our method is based on Gaussian Hilbert–Schmidt SVD (HS-SVD), which gives an alternate basis for the data-dependent subspace of "native" Hilbert space without ever forming kernel matrix. The well-conditioning linear system is one of the critical advantages of using the alternate basis obtained from HS-SVD. Numerical simulations are performed to illustrate the efficiency and applicability of the proposed method in the sense of accuracy. Numerical results obtained by the proposed method are assessed by comparing available results in references. The results demonstrate that the proposed method can be recommended as a good option to study the squeezing nanofluid flow in engineering problems. [ABSTRACT FROM AUTHOR]

This work investigates a three-dimensional Magnetohydrodynamic (MHD) nanofluid flow with heat and mass transfer over a porous stretching sheet. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation and solved by Galerkin Finite Element Methods (FEM). The effects of thermal radiation, viscous dissipation and chemical reaction on the fluid flow are considered. The behaviour and properties of pertinent flow parameters on the velocity, temperature and concentration profiles are presented and discussed graphically. The effects of the friction coefficient parameter, Nusselt and Sherhood numbers are also shown and considered using tables. The work is in good agreement in comparison with the recent work in literature.

A two-dimensional numerical investigation on laminar forced convection is carried out to estimate the thermal and fluid field behavior of Al2O3-water nanofluid in a circular pipe with constant heat flux. In this study, the finite element method (FEM) is employed to analyze the continuity, momentum, and energy governing equations by using COMSOL Multiphysics 3.5a. Computations of heat transfer rates were performed for a range of Reynolds numbers (Re ≤ 2000), and (Pr= 5.42). The effects of Reynolds number and fraction volume of nanoparticle (ɸ≤ 5%) on the mean coefficient of convection (havg), pressure drop (ΔP), and thermal-hydraulic performance are investigated. The computations indicate that Al2O3 nanoparticle usage augments the average coefficient of heat convection significantly, and which is increased by (10%) with maximum pressure loss (15%) for (ɸ=5%) and high Reynolds number when compared to the base fluid. The present model is validated with empirical Shah Equation and the results showed a good agreement.

A novel mathematical model is envisaged to scrutinize the Darcy Forchheimer 3D Powell Eyring nanofluid flow in a porous medium. Flow is taken under the influence of zero mass flux and convective boundary conditions at the surface and a chemical reaction in the mass equation. The heat transfer flow is scrutinized with non-linear thermal radiation. Entropy generation analysis of the envisioned model is also conducted. The Homotopy Analysis method to yield the series solutions for the envisioned model. The graphs are plotted to witness the characteristics of several parameters versus velocity, heat, and mass distributions and are well cogitated accordingly. The findings show that the velocity is decreasing the function of Darcy-Forchheimer number. Further, the Biot number large values boost the fluid temperature. The outcomes obtained in the analysis are substantiated when compared with a published result in the literature. An outstanding matching is achieved in this regard.

We have investigated the nanofluid flow in a converging and diverging channel of heated and inclined plane walls. The wellknown Buongiorno model has been undertaken for the transport of nanoparticles in a base fluid. The upper (lower) wall of the channel has the geometry and it is presented by an equation of the straight line y = mx + a 0 (y = - mx - a 0 ), in which m is the slope of the upper wall, a 0 is the half width of the channel inlet (exit) for diverging (converging) flow, x and y are representing the Cartesian Coordinates. Note that the walls of the channel are uniformly and equally heated and the nanoparticle concentration at the walls is also constant. On the contrary, the flow problem is strictly described in Cartesian Coordinates. The problem is formulated for the upper half of the channel and later on the results are generalized for the lower half. The new observations are shown in different graphs. The four governing PD E' s are simplified with the help of proper and appropriate similarity transformations and they constituted a system of ODE's, whereas, it is equipped with several dimensionless parameters. Note that the convective terms in energy and concentration equations are disappeared in view of these similarity variables. The effects of all parameters are investigated on flow, heat and mass transfer characteristics. Moreover, effects of all parameters are seen on skin friction, rates of heat and mass transfer. In addition, classical models of nanofluid flow inside a converging and diverging channel in plane polar coordinates will be the special cases of the current modeled problem. Furthermore, the perturbation solution of the modeled equations is also determined for small values of the parameter. Note that slope m and Pr number are used as a perturbation parameters for the momentum equation and energy, species concentration equations and these solutions are valid for small values of all other parameters involved in the problem. In addition, exact solutions of the final ODE are also found for special ranges of parameters value. Moreover, the comparison is shown between the different solutions of the problem and classical solutions in tables and graphs. The temperature (concentration) profiles are increased (decreased) with the increasing of Nb , and Nt , however, both of them are increased with m. Moreover, the linear (non-linear) profiles of skin friction (rate of heat transfer) are decreased(increased) with the increasing of both Re (Pr , m) and m (Nb). In addition, the rate of mass transfer is increased linearly (non-linearly) against the increasing value of Nt (Pr) and Nb (Nb = Nt). Note that the temperature (concentration) profiles are effectively improved (declined) with the increase of thermophoretic forces, moreover, it is also rapidly increased (decreased) with the increase of concentration of nanoparticles (and their rapid fluctuations) in a converging and diverging channel. [ABSTRACT FROM AUTHOR]

The study is intended to give a brief overview of recent papers on spectral methods in different types of fluid flow especially nanofluid flow. The survey does not presume to be exhaustive; hence some selection is necessary. The papers reviewed herein relate to the recent use of some spectral based algorithms, notably the spectral relaxation method, the spectral local linearization method, the spectral quasi-linearization method, the successive linearization method, the piecewise successive linearization method and the spectral homotopy analysis method, etc. We review the important papers and problems where these methods have been used. The paper is divided into sections related to the use of each method. In addition to reviewing the journal articles in the main body of the paper, we also give details of important books published on spectral methods in fluid dynamics.

In this study, we investigate steady-state convective boundary layer fluid flow of heat and mass transfer features of a nanofluid moving over a nonlinearly stretching sheet in detail. The nanofluid physical model of the problem comprises with effects of thermophoresis and Brownian motion. The mathematical model scrutinizes mass, momentum and heat transfer equations are reduced to ordinary differential equations over infinite domain using suitable similarity variables. Haar wavelet collocation method is used to solve the resulting coupled nonlinear ordinary differential equations with an infinite domain. The obtained results are validated with available numerical findings and the solutions are more efficient which confirm and verify the wavelet method. The impact of several interesting physical aspects viz. thermophoresis parameter, stretching parameter, Brownian motion and Schmidt number on nanoparticle volume fraction and temperature profile curves are graphically demonstrated. The derived quantities of various parameters on the rate of heat and mass transfer are depicted in tabular forms. It predicts that the increase in Brownian motion and thermophoresis parameter reduces the local Nusselt number. The local Sherwood number increases with an increase in the parameters of Brownian motion and thermophoresis. For both temperature and volume fraction profiles decreases due to an increase in the Schmidt number.

Here, we study the effect of mixed convection and thermal radiation on unsteady boundary layer of heat transfer and nanofluid flow over permeable moving surface through a porous medium. The effect of heat generation is also discussed. The equations governing the system are the continuity equation, momentum equation and the heat transfer equation. These governing equations transformed into a system of nondimensional equations contain many physical parameters that describe the study. The transformed equations are solved numerically using an implicit finite difference technique with Newton's linearization method. The thermo-physical parameters describe the study are the mixed convection parameter α, 0 ≪ α ≪ 10 , the Radiation parameter Rd, 0 ≪ R d ≪ 1.0 , porous medium parameter k, 0 ≪ k ≪ 1.0 , the nanoparticles volume ϕ , 0 ≪ ≪ 0.2 , the suction or injection parameter fw, − 1 ≪ f w ≪ 1 , the unsteadiness parameter At, 1 ≪ A t ≪ 2 and the heat source parameter λ = 0.5.The influence of the thermo-physical parameters is obtained analytically and displayed graphically. Comparisons of some special cases of the present study are performed with previously published studies and a good agreement is obtained. [ABSTRACT FROM AUTHOR]

Solar collectors are systems for absorbing the sun's radiant energy and converting it into heat. The working principle of solar collectors are relying on the solar radiation incident upon the transparent surface, and the collected radiation heat is stored within the operating fluid. However, the conventional operating fluid is less than satisfactory in term of promoting the thermal efficiency of solar collector. Consequently, the aim of this paper is to investigate the use of nanofluid as an operating fluid in a single end evacuated solar collector. The expectation is that the flow behavior of nanofluid can lead to the improvement of thermal efficiency of solar collector. The design of solar collector is carried out using Gambit software and the heat transfer characteristics are simulated by nanofluid flow with 1%, 3% and 5% volumes by ANSYS Fluent software. The results demonstrate good agreement with existing experimental results. The numerical analysis shows the improvement of collector performance compared to pure water fluid. The results show that by increasing the nanoparticles volume fraction the efficiency of the collector improves significantly. [ABSTRACT FROM AUTHOR]

The present study explores the flow of nanofluid between a cone and a disk with the thermophoresis and Brownian motion impact. The flow is due to an expanding disk and a rotating cone. In the current study, radiative heat flux is considered. Using proper similarity transformations, the governing differential equations of momentum, temperature and concentration are transformed into a set of nonlinear ordinary differential equations (ODEs). The Runge-Kutta Fehlberg fourth fifth-order (RKF-45) technique and the shooting strategy are employed to solve the reduced ODEs. The impact of various parameters is illustrated through graphs and used to comprehend flow profile behaviour easily. The obtained results demonstrate that the velocity profiles enhance as improve in values of the Reynolds number. The rise in radiation, thermophoresis and Brownian motion parameters increases the thermal profile due to the potency of Brownian movement which results in a compelling nanoparticle interaction and boosts the fluid's thermal efficiency. Increasing values of the thermophoresis parameter reduces the heat transmission rate at the disk. As the Brownian motion parameter elevates, the concentration profile reduces, but the concentration profile increases as the thermophoresis parameter is raised. [ABSTRACT FROM AUTHOR]

Two dimensional incompressible turbulent nanofluid flow in a sinusoidal wavy channel is numerically investigated. Finite volume method and Rhie and Chow interpolation in a collocated grid arrangement are used for solving governing equations. The effects of the volume fraction of nanoparticles, Reynolds number, phase lag, frequency and amplitude of the wavy walls on the heat transfer rate are studied. The present work showed good agreement with existing experimental and numerical results. Increasing the frequency and amplitude of the wave and nanoparticles volume fraction has great effect on heat transfer rate.

The purpose of the current study is to investigate the non-Newtonian unsteady Williamson fluid on a stretching/shrinking surface along with thermophoresis and Brownian effects. Basically, the model consists of a time-dependent magnetic field. The fluid is considered to be electrically conducting due to the effect of the external magnetic field. The values of magnetic Reynolds number are so small that the induced magnetic field is assumed to be negligible. In the concentration equation, the effects of Brownian motion and thermophoresis are discussed. Employing the similarity transformations, the governing nonlinear Partial Differential Equations (PDEs) are converted into the Ordinary Differential Equations (ODEs). The resulting ODEs are solved with the combined effects of the Successive Over Relaxation (SOR) method and Finite Difference Method (FDM). The impact of all the including parameters such as suction parameter, injection parameter, stretching/shrinking parameter, the ratio of viscosity, local Weissenberg number, unsteadiness parameter, Eckert number, Prandtl number, Lewis number, Nusselt number, Brownian motion parameter, shear stress, heat transfer rate, and mass transfer rate are analyzed using graphs and tables. Results show that the values of fluid velocity are better for S=8, −S=0, λ=0.3, β*=0.9, Wi=0.3, and Aa=2.0. It is also depicted from the results that the values of boundary layer thickness are better for S=0, −S=−8, λ=0.3, β*=0.1, Wi=1.5, and Aa=0.25. From the above numeric results, it is concluded that the fluid velocity is reduced and the thermal boundary layer thickness is enhanced by the enhancement of the stretching parameter.

Heat sinks are always in the center of electronic cooling researchers' attention. Microchannels, due to their increased surface and better thermal performance than that of normal heat sinks were used in electronic cooling devices. In this numerical investigation, the first and second laws of the thermodynamic impact of twisted porous ribs on the microchannel were studied. The effects of the Reynolds number and volume fraction of nanoparticles were investigated. The range of Reynolds number was 250 to 1000. All types of the microchannel in this study consisted of a clear microchannel, a twisted porous ribbed microchannel with two and three layers of twisted porous ribs. The results show that by inserting porous ribs, the local cross-section decreases, and the local Reynolds number increases. Also, twisted porous ribs are the cause of nanofluid flow circulation and make the heat transfer coefficient greater. Increasing the porous layer from one layer to three layers has an increasing effect on the heat transfer coefficient, and the friction factor and increasing the φ is the reason for increasing the friction factor. Finally, the microchannel with triple layers of twisted porous ribs has better performance in total entropy generation, and by inserting twisted porous ribs, the entropy generation decreases. Unlabelled Image • The first and second laws of the thermodynamic impact of twisted porous ribs on the microchannel were studied. • The effects of the Reynolds number and volume fraction of nanoparticles were investigated. • The twisted porous ribs are the cause of nanofluid flow circulation. • Microchannel with triple layers of twisted porous ribs has better performance in total entropy generation. [ABSTRACT FROM AUTHOR]

The aim of the current investigation is to explore the heat transfer of nanofluid flow in a channel with non-parallel walls. Two different nanoparticles, namely, Cu and Ag, with water as the base fluid are considered. The equations governing the flow are obtained using an appropriate similarity transform and solved analytically with the optimal homotopy asymptotic method (OHAM). Here, OHAM was first used to solve the problem to ensure a much more rapid convergence of the solution only after one iteration, with high efficiency. Comparative analysis was carried out to ensure the authenticity of the results. The effects of the involved parameters on fluid velocity, temperature, skin friction coefficient, and Nusselt number are presented in graphical and tabular forms with comprehensive discussions in this paper. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic analysis of the nanofluid flow is extremely noteworthy in industrial applications. This study investigates the application of the nonhomogeny magnetic source on the migration of fluid with nanoparticles within the angled junction. In this work, Ferro particles are injected into the water flow to intensify the influence of the FHD on nanomaterial flow. To perform computational study on nanofluid in the junction, the FVM with SIMPLEC model was selected. According to our results, the existence of the nonhomogeny magnetic field produces the circulation in the vicinity of the junction and decreases the mineral sedimentation on the junction wall. In existence of two magnetic sources, Nu augments by 20% when the Reynolds number of nano flow is augmented from 50 to 100. When results of four sources of nonhomogeny FHD sources are compared with that of two magnetic sources, it is detected that the mean Nusselt number approximately increases 57 % inside the domain. [ABSTRACT FROM AUTHOR]

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number. [ABSTRACT FROM AUTHOR]

This study presents a computational investigation on heat and flow behaviors between non parallel plates with the influence of a transverse magnetic field when the medium is filled with solid nanoparticles. The nonlinear governing equations are treated analytically via Differential Transform Method (DTM). Thereafter, obtained DTM results are validate with the help of numerical fourth order Runge-Kutta (RK4) solution. The main aim of this research work is to analyze the influence of varying physical parameters, in particular Reynolds number, nanofluid volume fraction, and Hartmann number. It was found that the presence of solid nanoparticles in a water base liquid has a notable effect on the heat transfer improvement within convergent-divergent channels. The comparison of DTM results with numerical RK4 solution also shows the validity of the analytical DTM technique. In fact, results demonstrate that the DTM data match perfectly with numerical ones and those available in literature.

A two-dimensional numerical investigation on laminar forced convection is carried out to estimate the thermal and fluid field behavior of Al2O3-water nanofluid in a circular pipe with constant heat flux. In this study, the finite element method (FEM) is employed to analyze the continuity, momentum, and energy governing equations by using COMSOL Multiphysics 3.5a. Computations of heat transfer rates were performed for a range of Reynolds numbers (Re ≤ 2000), and (Pr= 5.42). The effects of Reynolds number and fraction volume of nanoparticle (ɸ≤ 5%) on the mean coefficient of convection (havg), pressure drop (∆P), and thermal-hydraulic performance are investigated. The computations indicate that Al2O3 nanoparticle usage augments the average coefficient of heat convection significantly, and which is increased by (10%) with maximum pressure loss (15%) for (ɸ=5%) and high Reynolds number when compared to the base fluid. The present model is validated with empirical Shah Equation and the results showed a good agreement. [ABSTRACT FROM AUTHOR]

In this study, the Runge Kuta numerical method (RK4), was used to find an accurate solution for the velocity and temperature fields of an unsteady flow of grapheme oxide nanofluid, in a rotating system, within a channel with lower porous wall in presence of imposed external uniform magnetic field. First of all, a local similarity solution for the transformed governing equations was achieved. The nonlinear partial differential equations (PDEs) and boundary conditions were changed to dimensionless form. Thereafter, the numerical approach was employed for obtaining the solution of resulted coupled nonlinear ordinary differential equations. The effect of various parameters including Eckert number, Magnetic parameter and etc. on temperature and velocity distributions were investigated. Finally, the entropy generation rate was calculated. To study the accuracy of solutions, RVIM –analytical method- was used for validation procedures. [ABSTRACT FROM AUTHOR]