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The document is a correction notice for a scientific article titled "Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection." It includes corrections to figures, text, equations, and nomenclature used in the original publication. The corrections aim to clarify and improve the accuracy of the scientific content presented in the article. The corrections were approved by the Academic Editor, and the original publication has been updated accordingly. [Extracted from the article]

The present article investigates viscous fluid flow’s heat and mass transfers over a stretching/shrinking sheet using the single and multi-wall carbon nanotube models. The analysis considers the effects of thermal radiation, induced slip, mass transpiration, and inclined magnetic force. The effect of the carbon nanotube model on fluid flow has not been considered in previous studies. By exploiting the similarity variable, the governing nonlinear partial differential equations are converted into nonlinear ordinary differential equation. The derived equations are solved analytically, and we obtained an exact solution for the velocity and energy conservation equation. The physical parameters of interest such as induced slip parameter, suction/injection, magnetic field, thermal radiation, and shear stress are analyzed and presented graphically. In particular, we show that the fluid flow in a single wall carbon nanotube transfers more energy than the multivalued nanotubes.

Hybrid nanofluids have caught the attention of scholars and investigators in the present technological period due to their improved thermophysical features and the desire to boost heat transfer rates compared to those of conventional fluids. The present paper is mainly concerned with heat transmission in cone-disk geometry in the presence of a magnetic field, activation energy, and non-uniform heat absorption/generation. In this work, the cone-disk (CD) apparatus is considered to have a rotating cone (RC) and a stretching disk, along with iron oxide and cobalt ferrite-based hybrid nanofluid. Appropriate similarity transformations are employed to change the physically modeled equations into ordinary differential equations (ODEs). Heat transfer rates at both surfaces are estimated by implementing a modified energy equation with non-uniform heat absorption/generation. The outcomes illustrated that the inclusion of such physical streamwise heat conduction variables in the energy equation has a significant impact on the well-known conclusions of heat transfer rates. To understand flow profile behavior, we have resorted to the RKF-45 method and the shooting method, which are illustrated using graphs. The findings provide conclusive evidence that wall stretching alters the flow, heat, and mass profile characteristics within the conical gap. The wall deformation caused by disk stretching was found to have a potential impact of modifying the centripetal/centrifugal flow characteristics of the disk, increasing the flow velocity and swirling angles. A rise in activation energy leads to an improved concentration field. [ABSTRACT FROM AUTHOR]

The main objective of this study is to explore the inventive conception of the magnetohydrodynamic flow of a hybrid nanofluid over-porous stretching/shrinking sheet with the effect of radiation and mass suction/injection. The hybrid nanofluid advances both the manufactured nanofluid of the current region and the base fluid. For the current investigation, hybrid nanofluids comprising two different kinds of nanoparticles, aluminium oxide and ferrofluid, contained in water as a base fluid, are considered. A collection of highly nonlinear partial differential equations is used to model the whole physical problem. These equations are then transformed into highly nonlinear ordinary differential equations using an appropriate similarity technique. The transformed differential equations are nonlinear, and thus it is difficult to analytically solve considering temperature increases. Then, the outcome is described in incomplete gamma function form. The considered physical parameters namely, magnetic field, Inverse Darcy number, velocity slip, suction/injection, temperature jump effects on velocity, temperature, skin friction and Nusselt number profiles are reviewed using plots. The results reveal that magnetic field, and Inverse Darcy number values increase as the momentum boundary layer decreases. Moreover, higher values of heat sources and thermal radiation enhance the thermal boundary layer. The present problem has various applications in manufacturing and technological devices such as cooling systems, condensers, microelectronics, digital cooling, car radiators, nuclear power stations, nano-drag shipments, automobile production, and tumour treatments. [ABSTRACT FROM AUTHOR]

Understanding of dusty fluids for different Brinkman numbers in porous media is limited. This study examines the Darcy–Brinkman model for two-dimensional magneto-hydrodynamic fluid flow across permeable stretching/shrinking surfaces with heat transfer. Water was considered as a conventional base fluid in which the copper (Cu), silver (Ag), and titanium dioxide ( T i O 2 ) nanoparticles were submerged in a preparation of a ternary dusty nanofluid. The governing nonlinear partial differential equations are converted to ordinary differential equations through suitable similarity conversions. Under radiation and mass transpiration, analytical solutions for stretching sheets/shrinking sheets are obtained. Several parameters are investigated, including the magnetic field, Darcy–Brinkman model, solution domain, and inverse Darcy number. The outcomes of the present article reveal that increasing the Brinkman number and inverse Darcy number decreases the velocity of the fluid and dusty phase. Increasing the magnetic field decreases the momentum of the boundary layer. Ternary dusty nanofluids have significantly improved the heat transmission process for manufacturing with applications in engineering, and biological and physical sciences. The findings of this study demonstrate that the ternary nanofluid phase's heat and mass transpiration performance is better than the dusty phase's performance. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of small boundary perturbation on the laminar motion of a conducting fluid in a rectangular duct under applied transverse magnetic field. A small boundary perturbation of magnitude Є is applied on cross-section of the duct. Using the asymptotic analysis with respect to Є, we derive the effective model given by the explicit formulae for the velocity and induced magnetic field. Numerical results are provided confirming that the considered perturbation has nonlocal impact on the asymptotic solution.

The study of inclined magnetohydrodynamics (MHD) mixed convective incompressible flow of a fluid with hybrid nanoparticles containing a colloidal combination of nanofluids and base fluid is presented in the current research. Al2O3-Cu/H2O hybrid nanofluid is utilized in the current analysis to enhance the heat transfer analysis. The impact of radiation is also placed at energy equation. The main research methodology includes that the problem provided equations are first transformed into non-dimensional form, and then they are obtained in ordinary differential equations (ODEs) form. Then using the solutions of momentum and transfers equations to solve the given ODEs to get the root of the equation. The main purpose includes the resulting equations are then analytically resolved with the aid of suitable boundary conditions. The results can be discussed with various physical parameters viz., stretched/shrinked-Rayleigh number, stretching/shrinking parameter, Prandtl number, etc. Besides, skin friction and heat transfer coefficient can be examined with suitable similarity transformations. The main significance of the present work is to explain the mixed convective fluid flow on the basis of analytical method. Main findings at the end we found that the transverse and tangential velocities are more for more values of stretched/shrinked-Rayleigh number and mass transpiration for both suction and injection cases. This is the special method it includes stretched/shrinked-Rayleigh number, it contributes major role in this analysis. The purpose of finding the present work is to understand the analytical solution on the basis of mixed convective method. [ABSTRACT FROM AUTHOR]

The present study investigates the effect of mass transpiration on heat absorption/generation, thermal radiation and chemical reaction in the magnetohydrodynamics (MHD) Darcy–Forchheimer flow of a Newtonian fluid at the thermosolutal Marangoni boundary over a porous medium. The fluid region consists of H2O as the base fluid and fractions of TiO2–Ag nanoparticles. The mathematical approach given here employs the similarity transformation, in order to transform the leading partial differential equation (PDE) into a set of nonlinear ordinary differential equations (ODEs). The derived equations are solved analytically by using Cardon's method and the confluent hypergeometric function. The solutions are further graphically analyzed, taking into account parameters such as mass transpiration, chemical reaction coefficient, thermal radiation, Schmidt number, Marangoni number, and inverse Darcy number. According to our findings, adding TiO2–Ag nanoparticles into conventional fluids can greatly enhance heat transfer. In addition, the mixture of TiO2–Ag with H2O gives higher heat energy compared to the mixture of only TiO2 with H2O. [ABSTRACT FROM AUTHOR]

In this research, we investigated the wall jet problem for a hybrid nanofluid with MHD, thermal radiation, velocity slip, and convective boundary conditions. After converting the governing partial differential equations into nonlinear ordinary ones, by using the proper similarity transformations, they were theoretically solved in view of the hypergeometric function. Comparing the present results with those in the literature, a very good agreement was obtained for fixed values of the included parameters. For some included parameters, regions of physical solutions were presented. By deducing the critical and terminated values of the suction/injection parameter, dual solutions for the reduced skin friction coefficient have been determined. It was found that the hybrid nanofluid temperature is efficiently heated by increasing values of the moving wall, absolute value of the Biot number, and thermal radiation parameters. However, it is cooled by enlarging values of the velocity slip and suction parameters. [ABSTRACT FROM AUTHOR]

The current study experimentally investigates the heat transfer augmentation on the novel axial corrugated heat exchanger tube in which the spring tape is introduced. Air (Pr = 0.707) is used as a working fluid. In order to augment the thermohydraulic performance, a corrugated tube with inserts is offered. The experimental study is further extended by varying the important parameters like spring ratio (y = 1.5, 2.0, 2.5) and Reynolds number (Re = 10 000–52 000). The angular pitch between the two neighboring corrugations and the angle of the corrugation is kept constant through the experiments at β = 1200 and α = 600 respectively, while two different corrugations heights (h) are analyzed. While increasing the corrugation height and decreasing the spring ratio, the impact of the swirling effect improves the thermal performance of the system. The maximum thermal performance is obtained when the corrugation height is h = 0.2 and spring ratio y = 1.5. Eventually, correlations for predicting friction factor (f) and Nusselt number (Nu) are developed. [ABSTRACT FROM AUTHOR]

Detailed The analytical solution of the unsteady boundary layer flow due to impulsive porous stretching sheet is solved by means of an Adomian Decomposition Method (ADM). The ADM alongside Pade approximants are connected to tackle the nonlinear partial differential equation with different boundary conditions got in demonstrating the unsteady boundary layer flow. Apparently, this yields better accuracy when compared to results from other prime methods. The present results are in good match with the pioneering work of other authors. The impact of parameters like mass suction/injection parameter and Darcy number on the velocity profile were examined. The present results can be found very useful in a wide range of applications in extrusion process and related process in fluid dynamics and heat transfer problems. [ABSTRACT FROM AUTHOR]

The main objective of this article is to explore analytical solution for fourth order highly nonlinear differential equation. The stretching/shrinking is a non-linear (at least quadratic) function along the direction of stretching/shrinking. The stretching/ shrinking of a sheet with a velocity profiles are comparatively dependent on the distance from the velocity axes. The system of partial differential equations is transformed into the system of highly nonlinear ordinary differential equation via similarity transformation. Velocity profiles as a function of stretching/shrinking related parameters, Chandrasekhar number and viscoelastic parameter are discussed graphically. The analytical solutions of system of boundary layer equations emerging from the stretching/shrinking sheet problems were investigated and also the outcomes are in good agreement with the classical results on this topic. The outcomes have conceivable mechanical applications in fluid based frameworks including stretchable materials, in polymer extrusion process, metal spinning and other industrial processes. [ABSTRACT FROM AUTHOR]

The problem of mixed convective flow of a couple stress fluid in a vertical channel in the presence of first order chemical reaction and heat generation/absorption is studied. Two walls of the channel are considered with asymmetirc heating conditions along with flux boundary conditions on temperature and concentrations. The governing nonlinear differential equations are solved numerically. The effect of physical parameters like couple stress, heat generation/absorption, chemical reaction, thermal buoyancy and concentration buoyancy are evaluated numerically. Also heat transfer parameters such as Nusselt number, Sherwood number and skin friction factors are analyzed. [ABSTRACT FROM AUTHOR]