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Steady flow of incompressible Maxwell–Sutterby fluid at stretching sheet is discussed in the presence of stagnation point region. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied to the fluid flow. Temperature-dependent properties with radiation influence are considered in this analysis. The heat source or sink and melting impact are also debated in this analysis. A differential model of mathematics is developed by employing a governing constitutive equation. The differential equations' model is condensed and becomes ordinary differential equations by implementing the appropriate transformations. Furthermore, these equations are elucidated by the numerical scheme. The physical influence of physical parameters is exhibited in the graphs and tabular form. The escalating values of M cause a shear thinning attitude in the fluid; as a result, devaluation in the velocity is detected in the case of a / c = 0. 5 , while it depicted the counter behavior for a / c = 1. 5. The skin friction is heightened with improving values of Re because R e boosted which improved the viscosity of liquid as well as heightened the friction at sheet. The enhancing values of M p cause a decrement in skin friction. The melting parameter is enriched which reduces the viscosity of fluid due to temperature boosting as well as friction reduction. The diminution in skin friction is found for enhancing the values of β. [ABSTRACT FROM AUTHOR]

The increasing number of ways in which carbon nanotubes (CNTs) may be used in business and technology has led to an explosion of interest in these tiny tubes. As a result, the Yamada–Ota model is used to investigate the unsteady, non-axisymmetric MHD Homann stagnation point of carbon nanotubes passing over a convective surface with nonlinear radiation. Consisting of single-walled and multi-walled carbon nanotubes that are suspended in water (H2O). The length of the nanomaterial is between 3 μ m ≤ L ≤ 7 0 μ m nanometers, while its radius is between 1 0 nm ≤ R ≤ 4 0 nm. The method of similarity transformation is altered so that it may be used to get the dimensionless system of differential equations from the mathematical model that is envisioned for PDEs. After that, approximate solutions are obtained using MATHEMATICA and the Shooting with RK-IV technique. In this paper, we provide a graphical discussion and a physical interpretation of the results of measures of practical significance as a function of key factors. The results indicated that an increase in the volume fraction led to a corresponding rise in the heat transfer rate. However, it is reduced by the magnetic energy that is supplied to it. Carbon nanoliquids with a single wall have a greater melting point than nanoliquids with multiple walls. Industrial and technological uses of the issue under examination span several fields, including aviation and health. The results of the interface velocity and heat transfer rate at the surface, as well as the solution of each profile, are shown graphically, along with an analysis of the effects of MHD on the flow and heat transfer characteristics of the fluid under the influence of radiation. [ABSTRACT FROM AUTHOR]

An analysis is carried out to investigate the influence of the magnetic field over Carreau fluid flow and heat transfer in a liquid film on an unsteady stretching surface. The governing equations are converted to a system of boundary value problem (BVP) by using the similarity transforms. The differential equations are solved numerically using the modified Laplace decomposition method (MLDM) and the obtained results are compared with the existing schemes. An excellent agreement between them illustrates the accuracy of MLDM to the suggested model. The influence of the dimensionless governing parameters like magnetic field number, Prandtl number, unsteadiness parameter, Weissenberg parameter, and radiative number on velocity and temperature profiles is discussed in tabular form and shown through illustrative graphs. [ABSTRACT FROM AUTHOR]

This paper examines the heat transfer characteristics of magnetohydrodynamics (MHD), suction, and Marangoni convection under the stretching/shrinking Ag–Cu hybrid nanofluid surface flow. First, the governing partial differential equations (PDEs) were transformed into ordinary differential equations (ODEs), and the numerical result was obtained using the boundary value problem solver (bvp4c) in MATLAB. The development of the Nusselt number, the velocity profile and the temperature profile was plotted, discussed and inspected. Next, this paper undergoes stability analysis and heat transfer rate comparison between water, nanofluid and hybrid nanofluid. The dual solutions were observed, and the upper branch solution is determined to be stable. Compared to water, the heat transfer rates of Ag–Cu hybrid nanofluid and Cu nanofluid were accelerated by 2.84% and 2.75%, respectively. [ABSTRACT FROM AUTHOR]

This paper discusses the impacts of velocity, temperature, and solutal slip on the mass and heat transfer characterization of MHD mixed convection Casson fluid flow along an exponential permeable stretching surface with chemical reaction, Dufour and Soret effects. The Casson fluid is supposed to flow across an exponentially stretched sheet, together with the exponential temperature and concentration fluctuations of the fluid. As governing equations, the momentum, energy and species concentration equations are constructed and represented as PDEs. Following that, these equations were converted via the similarity transformation into ODEs. Finally, the ODEs are numerically solved using the Keller-box method with MATLAB software's algorithm. Expressions are produced for the fluid flow, temperature and concentration gradients. We also determined the physical variables from which the friction factor, rate of mass and heat transfer are attained for engineering purposes. Using graphs and tables, the impacts of altered physical characteristics on flow amounts are explored. The consistency and validity of our outcomes revealed a significant degree of agreement when comparing them to previously published studies. The findings reveal that raising the Soret and Dufour parameter enhances the velocity profile at the wall, but the converse is true for increasing the velocity slip factor. [ABSTRACT FROM AUTHOR]

The heat transfer through the thermal radiation is very significant in many industrial processes, biomedical engineering, technological devices and thermal therapeutic process. These comprise nuclear power plants, propulsion of rockets, missiles, satellites and space vehicles, photochemical reactors, solar collector performance, heat exchangers. The boundary layer flow and the heat transport of dusty liquid over a stretching cylinder are discussed. The impact of nonlinear thermal radiation is explored. Cattaneo–Christov heat flux model is considered to formulate the energy equation. The resulting equations of the physical system are converted into a system of nonlinear ordinary coupled differential equations with the help of suitable similarity transformations and numerically solved by using Runge–Kutta–Fehlberg's method along with shooting technique. The influence of nondimensional parameters is analyzed and interpreted graphically. The heat transfer rate and local coefficient of skin friction are also calculated for diverse nondimensional constraints and plotted. [ABSTRACT FROM AUTHOR]

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement. [ABSTRACT FROM AUTHOR]

In this paper, a steady solution is presented for the equations that represent the MHD rarefied gas fluid flow and heat transfer due to a permeable stretching sheet with second-order velocity slip and thermal slip phenomenon. By using nondimensional transformations, the system of partial differential equations governing the problem is transformed into another system of nonlinear ordinary differential another equations. Novel solutions are investigated for the resulting ordinary differential equation which describe the momentum equation. The numerical results obtained agreed very well with previously reported cases available in the literature. Additionally, the effects of the magnetic parameter, first- and second-order velocity slip parameter, conductivity parameter, thermal slip parameter and the suction (injection) parameter on both the velocity and temperature profiles and on the local skin-friction coefficient are discussed and presented through tables and graphs. [ABSTRACT FROM AUTHOR]