Due to excessive heating, various physical mechanisms are less effective in engineering and modern technologies. The aligned electromagnetic field performs as insulation that absorbs the heat from the surroundings, which is an essential feature in contemporary technologies, to decrease high temperatures. The major goal of the present investigation is to use magnetism perpendicular to the surface to address this issue. Numerical simulations have been made of the MHD convective heat and amplitude problem of electrical fluid flow down a horizontally non-magnetized circular heated cylinder with reduced gravity and thermal stratification. The associated non-linear PDEs that control fluid motion can be conveniently represented using the finite-difference algorithm and primitive element substitution. The FORTRAN application was used to compute the quantitative outcomes, which are then displayed in diagrams and table formats. The physical features, including the phase angle, skin friction, transfer of heat, and electrical density for velocity description, the magnetic characteristics, and the temperature distribution, coupled by their gradients, have an impact on each of the variables in the flow simulation. In the domains of MRI resonant patterns, prosthetic heartvalves, interior heart cavities, and nanoburning devices, the existing magneto-hydrodynamics and thermodynamic scenario are significant. The main findings of the current work are that the dimensionless velocity of the fluid increases as the gravity factor $R_g$ decreases. The prominent change in the phase angle of current density ${\alpha }_m$ and heat flux ${\alpha }_t$ is examined for each value of the buoyancy parameter at both $\alpha =\pi /6$ and $\pi$ angles. The transitory skin friction and heat transfer rate shows a prominent magnitude of oscillation at both $\alpha =\pi /6$ and $\pi /2$ positions, but current density increases with a higher magnitude of oscillation.

The study considers the case of the unequal diffusion coefficients of reactant $A$ (bulk fluid) and reactant $B$ (catalyst at the wall) with the dispersion of both nanoparticles and gyrotactic microorganisms of Erying-Powell fluid flow over a surface with non-uniform thickness in the presence of variable fluid properties and stratification. The numerical solution of the transformed governing equations is obtained by using the Runge-Kutta method and shooting techniques. The outcome of this study is that the increasing values of temperature-dependent thermal conductivity parameter lead to the augmentation of the kinetic energy which thereafter causes a significant enhancement of the fluid temperature.

In this study, we propose new illustrative and effective modeling to point out the behaviors of the Hepatitis-B virus (Hepatitis-B). Not only do we consider the mathematical modeling, equilibria, stabilities, and existence–uniqueness analysis of the model, but also, we make numerical simulations by using the Adams–Bashforth numerical scheme. However, we apply the parameter estimation method to determine our model parameters and find the curve that best fits the model. Additionally, in this study, the stability analysis of the aforementioned model is considered, and also the sensitivity analysis of R₀ is examined. The results point out that the order of the fractional derivative has an essential effect on the dynamical process of the constructed model for Hepatitis-B.

The core purpose of this work is the formulation of a mathematical model by dint of a new fractional modeling approach to study the dynamics of flow and heat transfer phenomena. This approach involves the incorporation of the Prabhakar fractional operator in mathematical analysis to transform the governing system from a conventional framework to a generalized one. This generalized model evaluates the improvement in thermal efficacy of vacuum pump oil because of the inclusion of aluminum alloy nanoparticles. The flow of the under-observation nanofluid starts due to the combined effects of natural convection and the ramped velocity function at the boundary. Meanwhile, an analysis of the energy equation is conducted by taking the Newtonian heating mechanism into consideration. The characteristics of platelet-, brick-, cylinder-, and blade-shaped alloy nanoparticles are incorporated into the primary system using shape-dependent relations for thermal conductivity and viscosity. Both the classical and generalized models are solved to derive the exact solutions by first inserting some dimension-independent quantities and then operating the Laplace transform on the succeeding equations. These solutions are utilized for the development of graphical illustrations to serve the purpose of covering all features of the problem under consideration. Furthermore, changes in energy and flow functions due to the dominant influences of the relevant contributing factors are delineated with appropriate physical arguments. In addition, the numerical results of the skin friction coefficient and Nusselt number are displayed via multiple tables to analyze the disturbance in shear stress and discuss the contribution of the fractional parameters, the volume concentration of the considered nanoparticles, and the shape factor in the boost of the thermal potential of the considered nanofluid. The findings imply that aluminum alloy nanoparticles have the ability to produce a 44% enhancement in the thermal effectiveness of vacuum pump oil. Moreover, the flow velocity is reduced as the loading range of the nanoparticles rises.

The Navier–Stokes (NS) equations involving MHD effects with time-fractional derivatives are discussed in this paper. This paper investigates the local and global existence and uniqueness of the mild solution to the NS equations for the time fractional differential operator. In addition, we work on the regularity effects of such types of equations which are caused by MHD flow.

This discussion intends to scrutinize the Darcy–Forchheimer flow of Casson–Williamson nanofluid in a stretching surface with non-linear thermal radiation, suction and heat consumption. In addition, this investigation assimilates the influence of the Brownian motion, thermophoresis, activation energy and binary chemical reaction effects. Cattaneo–Christov heat-mass flux theory is used to frame the energy and nanoparticle concentration equations. The suitable transformation is used to remodel the governing PDE model into an ODE model. The remodeled flow problems are numerically solved via the BVP4C scheme. The effects of various material characteristics on nanofluid velocity, nanofluid temperature and nanofluid concentration, as well as connected engineering aspects such as drag force, heat, and mass transfer gradients, are also calculated and displayed through tables, charts and figures. It is noticed that the nanofluid velocity upsurges when improving the quantity of Richardson number, and it downfalls for larger magnitudes of magnetic field and porosity parameters. The nanofluid temperature grows when enhancing the radiation parameter and Eckert number. The nanoparticle concentration upgrades for larger values of activation energy parameter while it slumps against the reaction rate parameter. The surface shear stress for the Williamson nanofluid is greater than the Casson nanofluid. There are more heat transfer gradient losses the greater the heat generation/absorption parameter and Eckert number. In addition, the local Sherwood number grows when strengthening the Forchheimer number and fitted rate parameter.