Narrow Results

Recent studies indicate that nanofluids are crucial for solar heat exchange operations and solar energy collectors. Furthermore, the importance of energy and mass transfer in entropy creation is significantly increased in a number of industrial and engineering processes, such as mechanical power collectors, air conditioning, food processing, refrigeration, and heat exchangers. As a result of this advancement, this research is aimed to explore the comparative study on bioconvective Darcy–Forchheimer flow of an incompressible hydromagnetic Ree–Eyring nanofluid over a chemically activated expanding sheet in suction and injection cases while including the consequences of radiation, energy generation, and convective boundary conditions. Boundary layer approximation is utilized to represent this investigation’s primary partial differential equations (PDE). Then, using the appropriate transformation, the models are rebuilt into nonlinear ordinary differential equations (ODE). Utilizing the BVP5C inbuilt MATLAB package, the numerical solutions for this examination are established. Further, the graphical and tabular representations allow us to analyze the impacts of several relevant features on the microorganism’s density, concentration, entropy creation, velocity, temperature, friction factor, Sherwood, and Nusselt number distribution. The outcomes reveal that the velocity field of the liquid movement is declined by applying positive amounts of the Darcy–Forchheimer and magnetic parameters, respectively. Boosting values of the radiation, thermal ratio parameter, and temperature Biot number assist an increase in the thermal field. It reveals the augmented entropy generation with the rising values of bioconvection Lewis number and Brinkman number. Furthermore, the mass transfer rate increases with larger values of the Brownian parameter and chemical reaction parameter.

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme.

Thermal transmission is very significant in the industrial and engineering sectors. This research aims to investigate the MHD stagnation point movement of methanol and water-driven $\mathrm{\text{Cu}}-{\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ hybrid nanofluid flow via an exponentially extending cylinder. An inclined magnetic field’s control, suction or injection and viscous dissipation impacts are used and considered in the flow paradigm, as no prior research has been performed on it. This motivated the authors to perform a computational analysis of the distinct base fluid (water and methanol)-driven hybrid nanofluid flow with the aforementioned impacts, which gives distinctiveness to the flow model. The basic partial differential equation flow mechanism has been streamlined to nondimensional ordinary differential equations by the inclusion of distinct dimensionless factors, which are simulated employing the BVP4c methodology. The impacts of dimensionless variables, namely the Eckert factor, suction/injection term, Biot factor, velocity ratio term and magnetic factor, on the flow speed, thermal distribution, rate of shearing stress and thermal transmission are delineated in figures and demonstrated with tables. The major findings specify that methanol-based hybrid nanofluid ($\mathrm{\text{Cu}}-{\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$/methanol) has a significantly higher thermal transmission rate when compared with the water-based hybrid nanofluid ($\mathrm{\text{Cu}}-{\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$/water). Furthermore, it has been shown that the methanol-based hybrid nanofluid has an absolute friction drag that is up to 26.5% larger than that of nanofluid. The thermal gradient reduces with the enhancement of $\mathrm{\text{Ec}}$ and $M$. Moreover, the fluid temperature upsurges as $\mathrm{\text{Ec}}$ and $\mathrm{\text{Bi}}$ elevate. These outcomes significantly advance fluid dynamics and nanofluid research, offering opportunities for improved thermal transmission in numerous industrial and engineering sectors. A noteworthy validation with previously published work has also been performed.

The flow characteristics of Williamson nanofluids flow caused by a permeable vertical plate are investigated in this research. Influence of magnetic field on mixed convection flow in the presence of thermal radiation and heat source/sink is further studied. To develop the mathematical model of Williamson nanofluids, we employ the Brownian motion and thermophoresis impacts. By using Sparrow–Quack–Boerner local nonsimilarity method, the governing equations are transformed into a set of ordinary differential equations. Additionally, the obtained equations are numerically tackled by employing an efficient Runge–Kutta–Fehlberg method with MATLAB. The effect of emerging parameters on dimensionless velocity, temperature and concentration as well as the skin friction coefficient, the local Nusselt number and a local Sherwood number are explored with the help of graphs. The results indicate that as the value of buoyancy parameter increases, the nanofluid temperature and concentration decrease, whereas the velocity distribution increases. Further, the skin friction coefficient is increased with the higher buoyancy parameter. On the other hand, the rate of heat transfer is decreased by Brownian motion parameter. A comparison with the previous data in the literature shows good agreement with the obtained results.

This work analyzes the two-dimensional flow of an incompressible magneto-hydrodynamic fluid over linear stretching sheet in the presence of suction or injection and convective boundary conditions. A scaling group transformation method is applied to the flow governing equations. The system remains invariant due to the relation between the transformation parameters. Upon finding three absolute invariants, third-order ordinary differential equations (ODEs) corresponding to momentum equation and second-order ODEs corresponding to energy and diffusion equations are derived. Shooting technique (R-K fourth-order) is applied to work out the flow equations numerically. MATLAB is used for the simulation and the results are exhibited through graphs. The computational results are validated with the published research work and a modest concurrence was found. The main outcome of this study is found to be that raising values of $f_{\mathrm{\text{si}}}$ and ${\mathrm{\Gamma }}_1$ decline the friction, whereas ${\mathrm{\Gamma }}_1$ and ${\mathrm{\Gamma }}_2$ show the opposite (increasing). The rising values of $f_{\mathrm{\text{si}}}$ and $M$ in addition to $M$ and ${\mathrm{\Gamma }}_2$ show a decline in friction factor. The Nusselt number values are improved as raising values of $Pr$ versus $f_{\mathrm{\text{si}}}$ and $Pr$ versus $M$. It is very clear the monotonically increasing $M$ versus $f_{\mathrm{\text{si}}}$ and strictly increasing $f_{\mathrm{\text{si}}}$ versus $M$ cases. It is very clear the mass-transfer rate is smoothly improved $L{e}_1$ versus $L{e}_2$ and strictly increased $L{e}_1$ versus ${\mathrm{\Gamma }}_1$.

This investigation includes a three-dimensional Darcy–Forchheimer flow model and the heat transfer phenomenon of H₂O-CNTs nanofluid for a two-way stretchable surface. Xue’s proposed thermal conductivity model is employed. The numerical analysis scheme is applied to solve the transformed PDEs. The outline of velocities, temperature, surface drag forces and Nusselt number against relevant variables are portrayed. From this study, it has been noted that with an increase in Eckert numbers along both directions, two patterns were obtained for temperature curves, the initial temperature outlines increased and after that they decreased. Moreover, the width of the thermal boundary layer for H₂O-MWCNT nanofluid was more compared to H₂O-SWCNT nanofluid. To validate the existing code, numerical outcomes were compared to the earlier published data.

This paper investigates the second-order slip effect under multiple convective conditions. Nanofluid flow is taken over a permeable stretching cylinder. Suction and injection of nanofluid together with Brownian motion and thermophoresis is also incorporated in this research. Renovation of leading partial differential equations is done with the help of appropriate similarity transfiguration. Obtained nonlinear Ordinary differential equations (ODEs) are solved by Runge–Kutta 4^th order (RK-4) method with shooting technique. MAPLE-2019 software is used to simulate the system with a degree of precision of $10^{-6}$. Several graphs and tables are included to showcase the findings in this investigation. Heat transfer allocation was changed by 17.52% for injection to suction of nanofluid in the system but mass transfer is changed by 9% approximately for the same situation. Skin friction co-efficient diminished in case of higher value of Reynolds number by 2.52% for suction of nanofluid and 2.68% for injection of nanofluid. Upshots of several parameters are compared under suction and injection.

This study investigates the effects of complete slip conditions on the peristaltic pumping of a Casson nanofluid with suction and injection in a vertical due to the crucial role that nano liquids play in a variety of technological and medical fields, particularly in peristalsis, a mechanism that transports liquids. The Casson fluid belongs to a class of non-Newtonian fluids that, through a particular stress threshold magnitude, exhibit elastic solid behavior before changing to liquid behavior. These fluids have several uses in engineering, food preparation, drilling and other fields. After establishing the governing conservation equations, the resulting flow model is effectively simulated using the realistic assumptions of a long wavelength and a low Reynolds number. The temperature distributions, velocity, pressure rate per wavelength and nanoparticle concentration of the resulting flow problem have been solved analytically. The effects of all physical factors on temperature, velocity, concentration fields, pressure rate, frictional force and pressure gradient are graphically examined using Wolfram MATHEMATICA software. There are a variety of biofluids that cannot be classified as liquids. For example, blood contains WBC, RBC and plasma. It is essential to model biofluids (blood) as nanofluids given the physical properties of these biofluids. According to reports, one of the finest yield stress models is the Casson model, and blood exhibits a similar behavior. We took these facts into consideration when thinking about Casson nanofluid flow in a vertical layer under peristalsis. Additionally, the suction and injection mechanisms can be used to represent the exchange of carbon dioxide in bold. In order to understand how blood flows through small blood vessels, this model must be examined. The obtained results show that the Newtonian case and those found in the literature have a very good agreement. Since the liquid moves faster and more effectively when the value is increased, it becomes clear that this increases the strength of the velocity.  In other words, nanoperistaltic pumps can maintain a pressure differential that increases or decreases at all operating flow rates with an increasing thermophoresis effect. Furthermore, it is obvious that the pressure reduction in a Casson fluid is greater than in a Newtonian fluid.

Inquisitive researchers have studied the movement of peristaltic nanofluids due to the enlightening impact of nanoliquids in various technological and therapeutic fields, particularly in the fluids transport mechanisms known as peristalsis. The Casson fluid belongs to a group of non-Newtonian fluids that, according to a particular stress threshold, exhibit elastic solid behavior before changing to liquid behavior. These fluids are known as viscoelastic fluids and have several uses in engineering, food preparation, drilling and other fields. The Casson nanofluid model is used in this investigation. In order to better understand this, this study examines the peristaltic motion of a Casson nanofluid in a vertical layer with suction/injection. The resulting flow model is successfully simulated under the realistic assumptions of long wavelength and low Reynolds number after obtaining the governing conservation equations. By using workable transformations, the derived partial differential equations are mathematically converted into a dimensionless form. Analytical solutions have been found for the resulting flow problem’s temperature distribution, velocity, pressure rate per wavelength and concentration of nanoparticles. Using Wolfram Mathematica software, the impacts of all physical characteristics on temperature, velocity, concentration fields, pressure rate, frictional force and pressure gradient are graphically studied. The influences of thermophoresis parameter Nt raise the temperature and diminish fluid concentration. By raising the suction and injection parameter k values, the velocity in the directions of x and y is decreased. The pressure rate enhances by raising the Reynolds number and diminishes by enhancing the Grashof number.

We intend to analyze the influences of heat dissipation and heat generation on steady nanofluid stagnated flow along an extending surface along with thermal boundary layers. Water-based Cu and Al₂O₃ nanoparticles are considered. Moreover, the mechanism of injection/suction has been analyzed for such flows. Fundamental governing equations for the flow of an isotropic in-compressible thermally radiative single-phase nanofluid are defined by the set of nonlinear Partial Differential Equations (PDEs) which are transmuted to Ordinary Differential Equation (ODEs) and dealt with numerically by using Runge–Kutta (RK) fourth-order adopting shooting technique that gives approximate simulations. The numerical findings are illustrated as graphical and tabular representations after a careful parametric examination of determined parameters is carried out. The current outcomes specify that the velocity profiles decrease under the influence of magnetic strength while heat distribution positively changes under the effect of magnetic strength, heat source, radiative term and Biot number quantity. The temperature profiles behave negatively with the thermal Grashof number and Prandtl number. Moreover, the comparative simulations of the ongoing study with existing the literature for ensuing the obtained simulations have been worked out.

In this paper, a pulsatile flow of a biviscous fluid in a circular tube of varying cross-section has been considered for investigation. The study helps to draw the characteristics of blood, the pressure drop and the wall shear stress on the inner wall of small blood vessels and capillaries where suction/injection velocity arises and Reynolds number is very low. The effects of Reynolds number, apparent viscosity coefficient and leakage parameter on the streamlines, pressure drop and wall shear stress have been discussed and shown graphically for suction and injection, respectively. The wall of the tube is supposed to be permeable and a normal velocity of the fluid at the wall is prescribed to consider the fluid exchange across the wall. Both analytic and numerical solutions are given. Using the perturbation technique, we analyze the problem for low Reynolds numbers and small oscillation amplitude. Lastly, the simulations are given to demonstrate the effectiveness and excellent tracking performance of the proposed control scheme.

Pseudoplastic fluids are non-Newtonian fluids with intriguing uses in current research and industry. Among many other extant models, the Sutterby fluid model is an essential viscoelastic fluid model that demonstrates shear thinning and shear thickening properties in high polymer aqueous solutions by manifesting viscous and elastic aspects during deformation. The magneto hydrodynamic effects of Sutterby nanofluid on porous elastic surfaces in the presence of chemical processes are examined in this theoretical study. By using similarity transformation, the mathematical model of a governed problem is converted into a collection of differential equations. A shooting strategy is used to solve these nonlinear coupled ordinary differential equations. The velocities, temperatures, and chemical species concentrations of fluids are graphically shown. Physical quantities of importance, such as local heat and mass flow, are visually represented using bar charts. Heat and mass transport, as well as chemical species concentration, decrease with Hartman number in both suction and injection. Chemical concentration of governed fluid rises for homogeneous reactions but drops for heterogeneous reactions. Temperature and concentration of fluid increases for thermophoresis parameter but decreases for Brownian motion parameter, also the effects of injection are much stronger and higher than suction.

We have examined the impacts of the suction and/ or injection on the magnetohydrodynamic convection fluctuating flow of secondary order fluids through the absorbent medium into a perpendicular channel by non-uniformed walls’ temperature. The fluid is subjected to a transversal magnetic domain as well as the velocity slips near the left side plate. The systematic resolutions of the non-dimensional equations were found and the impacts of the governed variables on velocity, temperatures, concentration profiles, skin frictions, rates of temperature and mass transports were explored. It is motivating to note that skin friction enhances channel plates as permeability enlarges. The magnitude of the velocity retards with an enhancement in Hartmann number and enlarges with an increase in the permeability parameter.

The phenomenon of free convection above an isothermal vertical cone in the flow of Newtonian fluid suspended with solid nanoparticles like silver (Ag) and magnesium oxide (MgO) is numerically analyzed in this paper. Here, a convectively heated vertical cone is immersed in the infinite nanofluid with a porous medium. The fluid motion occurs due to the thermal gradient and force of gravity in the system. Energy transportation is studied with help of the empirical theory of Cattaneo–Christov. The physical effects included in the problem are heat source, stratification, chemical reaction, and motile microorganism. Further, the total entropy rate is computed. The flow, temperature, concentration, and microorganism distribution are explored in view graphical abstracts which are computed numerically by integration of the governing non-linear system of equations using the bvp4c technique. The outcomes are validated by relating them to earlier available data in the field, which is a remarkable feature of the proposed model. In this feature, an admired balance has been attained. The investigation proves that the buoyancy ratio characteristic and bioconvection Rayleigh number reduce the fluid velocity. Further, the concentration and microorganism stratification parameter effect diminish the motile microorganism and concentration distribution.

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.

In recent days, entropy generation has attracted the attention of several researchers due to its applications in manufacturing electronic devices, heat exchangers, conservation of energy, and generation of power. Further, activation energy is an essential requirement in automobile and chemical industries, nuclear reactors, and so on. This paper investigation aims to examine the entropy generation and the mass and energy transfer in the magneto-hydro dynamic movement of convective Carreau-Yasuda nano liquid past a porous stretching sheet with the consequences of activation energy, energy source, and binary chemical reaction. Also, the analysis of the impact of viscous and Joule dissipation in the presence of suction/injection into the Buongiorno model is an essential objective of this study. By introducing a similarity variable, the partial differential equations are altered into a system of ordinary differential equations. Numerical solutions to the modified equations are determined by utilizing a BVP5C MATLAB package. The findings are presented visually for several relevant flow characteristics and explained carefully. The thermophoresis parameter and activation energy parameter optimize the concentration of nanoparticles. These outcomes further indicate that as the larger Brinkmann and permeability parameters the entropy generation is broadened. It is discovered that an augmentation in thermal and solutal Grashof numbers is associated with greater velocity distribution.

Cross-diffusion effects are essential in industry because they can improve process efficiency, optimize product development, improve environmental sustainability, and drive technological advancements. The effects of cross-diffusion, aligned magnetization, and radiation are considered and adequately reported on the micropolar fluid boundary layer. The momentum, energy, and species reaction models are utilized to quantitatively represent the flow equations containing the thermophysical parameters at an aligned angle. The described fluid models are transformed into ordinary systems of derivatives. The solution to the resulting equations is determined via Fehlberg Runge–Kutta. The impacts of related terms are presented on various plots. The investigation revealed that the aligned angle strengthens magnetic field parameters, which can also lower the flow. For injection cases, microrotation has a parabolic distribution. An inclined value of radiation term contributed to improving the temperature profile. Temperature and concentration profiles rise and decrease with the Soret number, affecting heat, and species transport rates. The porosity and the thermal buoyancy parameter exhibit conflicting behaviors for both the coefficient of plate drag and the couple stress.

This study investigates the convective heat transfer characteristics in the vicinity of a stagnation point for the flow of Maxwell nanofluid over a porous rotating disk. The analysis takes into account the complex inert-active effects arising from nonlinear thermal radiation, activation energy, and the presence of a Darcy–Forchheimer medium. Through numerical simulations, the enhancement of heat transfer due to the addition of nanoparticles is explored, considering their impact on heat transport. The rotational and porous characteristics of the disk, coupled with nonlinear thermal radiation and activation energy effects, are crucial factors in shaping the overall heat transfer behavior. The study aims to provide valuable insights into the complicated interactions of these phenomena, contributing to the understanding of advanced heat transfer processes and their potential applications in various engineering systems. Using suitable variables to convert the system of leading equations to dimensionless form has then been evaluated by employing the bvp4c approach. It has been revealed that Radial flow has retarded with an upsurge in Deborah number, inertial factor, and porous factor while has upsurge with growth in rotational factor. Angular velocity has declined with higher values of Deborah number, and porous factor and has upsurged with escalation in inertial and rotational factors. Azimuthal flow has weakened with an upsurge in porous factor and has augmented with growth in Deborah number, inertial factor, and rotational factor. Thermal profiles have augmented with an upsurge in rotational, porous, inertial, thermophoresis, Brownian, and radiation factors, and Deborah number has declined with growth in the Prandtl number. Concentration distribution has declined with an upsurge in Schmidt number, Brownian motion factor, rotation factor, and porous factor, while has grown with the escalation in chemically reactive, thermophoresis, inertial factors, and Deborah number.

Unsteady hydromagnetic Couette flow of a viscous, incompressible and electrically conducting fluid between two parallel porous plates taking Hall current into account in a rotating system is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel and is permeated by a uniform transverse magnetic field which is fixed relative to the moving plate. Solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. Asymptotic behavior of the solution valid for small and large values of time t is analyzed to gain some physical insight into the flow pattern. Numerical values of primary and secondary velocities and that of shear stress at the moving plate due to primary and secondary flows are displayed graphically for various values of Hall current parameter m, rotation parameter K², magnetic parameter M², suction/injection parameter S and time t.