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The heat transfer characteristics of an unsteady magnetohydrodynamic flow through non-conducting infinite vertical parallel plates are presented in this investigation. The flow is subjected to an induced magnetic field, and the base fluid water contains carbon nanotubes (CNTs), in particular multi-wall carbon nanotubes, to present the behaviour of the nanofluid. The aim is to examine the effect of the applied magnetization and CNT concentration on the heat transport performance of the system. However, suitable transformation rules are adopted for the re-designing of the proposed design model into its non-dimensional form. This transformed system is then solved analytically following the standard transformations. The influence of key parameters, including the Hartmann number (Ha), the angle of inclination of the magnetic field, thermal buoyancy, heat source, and the concentration of CNTs in the nanofluid, on the flow phenomena is analysed. The consequences reveal that the occurrence of the inclined magnetic field affects the flow and heat transfer characteristics significantly. Additionally, the introduction of CNTs to the nanofluid enhances the heat transfer performance due to their unique thermal properties. The study demonstrates that enhanced Ha and CNT concentration augments the heat transfer rate.

Closed-form expressions for the dimensionless velocity, shear stresses, and the flow vorticity fields corresponding to the isothermal unsteady Poiseuille flows of a fractional incompressible viscous fluid over an infinite flat plate are established. The fluid motion induced by a pressure gradient in the flow direction is also influenced by the flat plate that oscillates in its plane. The vorticity field is dependent on two spatial coordinate and time, and it is an arbitrary trigonometric polynomial in the horizontal coordinate. The exact solutions, obtained by generalized separation of variables and Laplace transform technique, are presented in terms of the Wright function and complementary error function of Gauss. Their advantage consists in the fact that the values of the fractional parameter can be chosen so that the predicted material properties by them to be in agreement with the corresponding experimental results. In addition, they describe motions for which the nontrivial shear stresses are influenced by history of the shear rates. It is found that the flow vorticity is stronger near the plate, but it could be attenuated in the case of fractional model.

The study aims to investigate the heat transfer efficiency in a hybrid nanofluid flow consisting of silver–molybdenum tetra sulphide (Ag–MoS4) with variable magnetism. The Yamada–Ota model is incorporated to account for viscous dissipation and heat source/sink effects, providing a comprehensive understanding of the fluid flow characteristics. However, the dissipative heat along with thermal radiation combined with the hybrid particles enriches the flow properties. The proposed model is simplified to its corresponding non-dimensional form for using proper similarity rules, and the set of transformed problems is handled numerically by employing the in-house MATLAB function bvp5c. The research utilizes a new statistical approach based on response surface methodology (RSM) and sensitivity evaluation to enhance the overall heat transmission performance. The work is conducted to obtain the relevant data on heat transfer rate. The concentration of nanoparticles, thermal radiation, and heat source are selected as the key parameters affecting the heat transfer efficiency. RSM is employed to optimize these parameters and determine the optimal conditions for enhanced heat transfer rate. Furthermore, the sensitivity analysis is performed to evaluate the efficiency of individual parameters on heat transportation. The findings of this study demonstrate that the hybrid nanofluid flow of Ag–MoS4 exhibits improved heat transfer efficiency compared to conventional fluids. Further, the Yamada–Ota conductivity model is also influential in enhancing the heat transfer properties.

The goal of this research is to compute the numerical solution of the thermally stratified kerosene oil‐based ternary nanofluid flow with metallic nanoparticles including Nickel (Ni), Tantalum (Ta), and Zinc (Zn) influenced by an angled magnetic field between two parallel plates. The upper plate is assumed to be permeable and the lower is along the horizontal axis. The oxidation resistance and great thermal chemical stability of these nanoparticles make them ideal for usage in high temperature applications. This study also finds applications in chemical processing, microfluidic devices, and targeted drug delivery. In the energy equation, modified Fourier law and non‐uniform heat source‐sink are considered. The surface‐catalyzed reactions are considered with the variable diffusion coefficients. In addition, the irreversibility analysis is also performed. The flow model is supported by the slip and the thermal stratification conditions at the surface. The Tiwari and Das model is utilized to elucidate the characteristics of liquid flow, and it involves applying appropriate transformations to transmute the flow model into ordinary differential equations. These equations are computed via the bvp4c scheme. Graphs are generated to illustrate the impact of varied quantities on the flow and temperature profiles. Additionally, the surface drag coefficient and surface heat transfer rate are evaluated and summarized. It is worth mentioning that the thermal stratified and surface‐catalyzed parameters have reduced the temperature and concentration distributions respectively. The entropy generation is higher near the lower impermeable plate and lower near the upper permeable plate when the porosity parameter is enhanced. Additionally, it is noticed that 6% of the volume fraction of nanoparticles has a greater surface drag coefficient and heat transmission rate than 3% of the volume fraction of nanoparticles. This indicates that a higher volume fraction improves the surface drag and the heat transmission rate. [ABSTRACT FROM AUTHOR]

The term "thermal conductance" is used to describe a material's ability to transport or conduct heat. Materials with high thermal conductivity are employed as heating elements, while those with poor thermal conductivity are used for insulation purposes. It is known that the thermal conductivity of pure metals decreases as temperature increases. In this study, the primary focus is on the physical assessment of thermal conductivity, entropy, and the improvement rate of thermal density in a magnetic nanofluid. To achieve this, nonlinear partial differential equations are transformed into ordinary differential equations. These equations are further solved using a computational method known as the Keller box technique. Various flow parameters, such as the Eckert number, density parameter, magnetic-force parameter, thermophoretic number, buoyancy number, and Prandtl parameter, are examined for their impact on velocity, temperature distribution, and concentration distribution. For the asymptotic results, the appropriate range of parameters, such as 1.0 ≤ ξ ≤ 5.0, 0.0 ≤ n ≤ 0.9, 0.1 ≤ Ec ≤ 2.0, 0.7 ≤ Pr ≤ 7.0, 0.1 ≤ Nt ≤ 0.5, and 0.1 ≤ Nb ≤ 0.9, is utilized. The key findings of this study are related to the assessment of heat transfer in a magnetic nanofluid considering thermal conductivity, entropy generation, and temperature density. It is observed that the temperature distribution increases as entropy generation increases. From a physical perspective, thermal conductivity acts as a facilitating factor in enhancing heat transfer. The study concludes by emphasizing the consistency achieved through a comparison of the latest findings with previously reported analyses. [ABSTRACT FROM AUTHOR]

This study investigates the effects of activation energy and chemical reactions on the boundary layer flow around a wedge that is moving in a nanofluid. To represent the problem, nonlinear partial differential equations are utilized. These equations can be reduced to nonlinear coupled ordinary differential equations using similarity transformations. These equations are numerically solved using the Keller Box technique, and then their numerical and pictorial solutions are studied using MATLAB. The study looks at the relationship between the velocity, temperature, and concentration profiles and important factors such as the Prandtl number, constant moving parameter, activation energy, and reaction rate. The parametric range of factors such as 0.1 ≤ λ ≤ 1.0, 0.1 ≤ Le ≤ 3.0, 0.1 ≤ E ≤ 2.0, 0.1 ≤ Pr ≤ 7.0, 0.1 ≤ Nt ≤ 0.5, 0.1 ≤ Nb ≤ 1.0, 0.1 ≤ σ ≤ 3.4, 0.1 ≤ δ ≤ 2.5, and 0.1 ≤ β ≤ 2.0 is utilized. Furthermore, a comprehensive investigation is conducted into the remedies for skin friction and heat transmission rate. It is deduced that a growing magnitude in moving fluid velocity is noted for lower Prandtl, moving factor, reaction factor, and greater activation energy. It is depicted that the maximum enhancing magnitude in temperature and concentration with good distributions is examined for each pertinent factor. The growing magnitude of heat transport is noted for lower Lewis and temperature-difference factors but increases as pressure-gradient and Brownian factor rise. [ABSTRACT FROM AUTHOR]

The importance of this investigation is to examine the heat and mass transportation of magneto nanofluid movement along a heated sheet with exponential temperature-dependent density, entropy optimization, thermal buoyancy, activation energy, and chemical reaction aspects. The influence of these factors in cutting tools by means of machining and nanofluid lubrication is a significant process in cutting zone, chip cleaning, lubricating, and cooling productivity in milling. The corresponding energy activation and chemical process are essential to understand the thermal behavior of nanofluid. The appropriate transformations are used to solve nonlinear partial differential equations within the framework of ordinary differential equations using stream functions and similarity variables. The Keller box method is employed to efficiently solve these equations computationally under the Newton–Raphson approach. Through tables and figures, the fluid velocity, temperature distribution, and concentration consequences are sketched using various controlling parameters. It is seen that the fluid temperature function increases with noticeable amplitude as the Eckert factor, variable density, chemical-reaction, and activation energy increase. It is found that the noticeable enhancement in heat and mass transportation is deduced for maximum Brownian motion and thermophoresis. This work is important in various applications such as cutting fluids, drilling, brake oil, engine oil, minimum quantity lubrication, enhanced oil recovery, and controlled friction between the tool-chip and tool-work during machining operations. [ABSTRACT FROM AUTHOR]

The blood flow over a stenotic artery is important investigation in mathematical fluid mechanics due to its significance in biomedical sciences. The present investigation aims to examine how nanoparticles affect circulation in a stenotic artery. We examine the significance of magnetized Casson nanofluid flow over a stenotic artery under consideration of the mathematical flow problem. By using the suitable self-similarity variables, the partial differential equation is transformed into ordinary differential equations. Then, the non-dimensional equations are solved using the MATLAB software in the Bvp5c scheme. By increasing the magnetic properties of the circulatory system's cells, which is a scheme that was previously utilized by raising the magnetic field parameter, there was a predictable decrease in the blood flow. Covering the stenosed artery with a greater amount of copper nanoparticles improves its heat transmission efficiency. The present technique may help distribute medications throughout the circulatory system. [ABSTRACT FROM AUTHOR]

The present investigation focused on the influence of magnetohydrodynamic Gold-Fe3O4 hybrid nanofluid flow over a stretching surface in the presence of a porous medium and linear thermal radiation. This article demonstrates a novel method for implementing an intelligent computational solution by using a multilayer perception (MLP) feed-forward back-propagation artificial neural network (ANN) controlled by the Levenberg-Marquard algorithm. We trained, tested, and validated the ANN model using the obtained data. In this model, we used blood as the base fluid along with Gold-Fe3O4 nanoparticles. By using the suitable self-similarity variables, the partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). After that, the dimensionless equations were solved by using the MATLAB solver in the Fehlberg method, such as those involving velocity, energy, skin friction coefficient, heat transfer rates and other variables. The goals of the ANN model included data selection, network construction, network training, and performance assessment using the mean square error indicator. The influence of key factors on fluid transport properties is presented via tables and graphs. The velocity profile decreased for higher values of the magnetic field parameter and we noticed an increasing tendency in the temperature profile. This type of theoretical investigation is a necessary aspect of the biomedical field and many engineering sectors. [ABSTRACT FROM AUTHOR]

The thermal radiation and Fourier flux have drawn the attention of scientists and experts due to their extensive applications in the fields of medicine, manufacturing modern airplanes, water distillation, more efficient electronic devices, more efficient batteries, radiating treatment, and the textile industry. Through careful consideration of this, the mathematical investigation of natural convection and Fourier flux on the flow of energy and diffusion transmission of a body of cone and cylinder revolution, located in a saturated medium, has been described for the dual situations (flow over a cone and a cylinder). After then, the Runge–Kutta technique was used to explain the leading mechanism. Possessions of governing physical measures of local Nusselt and Sherwood numbers as well as velocity, thermal and diffusion figures are provided with support of tables and diagrams. It is motivating to declare that mass transfer rate is advanced in cone kind of revolution matched to cylinder kind of revolution with rising N R , N t , Q S . Also, the heat transmission rate is upper in cylinder revolution equated to cone revolution. [ABSTRACT FROM AUTHOR]

The axisymmetric unsteady two-phase flow problem is explored. The flow domain is defined by two co-axial circular cylinders and is axial symmetric. The Dirichlet-type boundary condition is used on the inner cylindrical surface, whereas the Robin-type boundary condition is used on the outer cylindrical surface. The velocities are computed analytically using a new form of the Weber transform that is suited for these boundary conditions. The effect of the slip parameter on velocities is investigated using numerical simulations and graphical representations. The studied problem is new in the literature because there do not exist any analytical studies regarding the problems with boundary conditions of Dirichlet type on the inner cylinder (the no-slip on the wall) and boundary conditions of Robin type on the outer cylinder (the mixture slipping on the wall). A new integral transform of Weber type has been employed to determine analytical solutions for such problems, together with the Laplace transform. The studied problem could generate analytical solutions for more two-phase flow problems in annular domains since the translational motions of the inner cylinder and the outer cylinder are given by arbitrary functions of the time t. [ABSTRACT FROM AUTHOR]

Fins are utilized to considerably increase the surface area available for heat emission between a heat source and the surrounding fluid. In this study, radial annular fins are considered to investigate the rate of heat emission from the surface to the surroundings. The effects of a ternary nanofluid, magnetic field, permeable medium and thermal radiation are considered to formulate the nonlinear ordinary differential equation. The differential transformation method, one of the most efficient approaches, has been used to arrive at the analytical answer. Graphical analysis has been performed to show how nondimensional characteristics dominate the thermal gradient of the fin. The thickness and inner radius of a fin are crucial factors that impact the heat transmission rate. Based on the analysis, it can be concluded that a cost-effective annular rectangular fin can be achieved by maintaining a thickness of 0.1 cm and an inner radius of 0.2 cm. [ABSTRACT FROM AUTHOR]

We investigate the divisor class group of the kernels of three dimensional Jacobian derivations onA = k[x,y,z] that are regular in codimension one, wherekis an algebraically closed field of characteristicp>0. These correspond to intersections in affine 5-space of pairs of hypersurfaces,, withf,ginA. Our calculations focus primarily on pairs wherefandgare quadratic forms. We show that in this case the class group is a direct sum of up to three copies ofℤp, is never trivial, and is generated by those hyperplane sections whose forms are factors of linear combinations offandg. [ABSTRACT FROM AUTHOR]

Efficient dissipation of heat is crucial in various heat transfer applications. Hybrid nanofluids outperform conventional coolants in both absorbing and transferring heat, rendering them ideal for cooling purposes in machinery, electronics, and various industrial processes. Given these intriguing properties of coolant-based hybrid nanofluid, this numerical study aims to analyze the unsteady flow of hybrid nanofluid around a rotating sphere with thermal stratification, and variable heat source and sink effects. This investigation incorporates aluminum alloys AA7072 and AA7075 as nanoparticles in the Fluorinert liquid named FC-72 base liquid. The AA7072 alloy is a composition of silicon, ferrous, and copper added to aluminum and zinc in the ratios of 98:1. Similarly, AA7075 comprises a combination of aluminum ∼90, zinc ∼6, magnesium ∼3, and copper ∼1, together with magnesium and silicon ferrous. What sets this model apart is its incorporation of variable porosity and permeability, along with temperature-dependent viscosity and thermal conductivity. The governing equations are converted into systems of differential equations, and a boundary value problem solver for ordinary differential equations of fourth order using the collocation (bvp4c) technique is employed to obtain the numerical solution. Two alternative scenarios for porous media — (i) constant porosity and permeability, and (ii) variable porosity and permeability — are determined for relevant parameters versus the velocity and temperature profiles. Additionally, the heat transfer rate is computed versus numerous parameters. It is perceived that secondary velocity profiles decrease more significantly with higher estimates of the variable viscosity parameter when a constant porous medium is assumed. Furthermore, the heat transfer rate of the FC-72-based hybrid nanofluid increases with higher estimates of the rotation parameter and the particle volume fraction of aluminum alloys. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the behavior of micropolar Eyring-Powell ferrofluids over a stretchable surface, considering heterogeneous-homogeneous chemical reactions, thermal radiation, and magnetic dipole effects. The governing partial differential equations are transformed into ordinary differential equations (ODEs) using similarity transformations, which are then solved using the shooting method with Runge-Kutta updates. The effects of various parameters on the flow and temperature fields are computed and visualized using MATLAB 2023. The results show that the velocity field decreases with increasing ferro-magnetic parameter β and fluid material parameter ß, while the temperature field increases with thermal radiation R, but decreases with higher dissipation parameter λ1 and Prandtl number Pr. The results are in excellent agreement with previously published data, validating the accuracy of our approach. [ABSTRACT FROM AUTHOR]