Levenberg–Marquardt Backpropagation for Numerical Treatment of Micropolar Flow in a Porous Channel with Mass Injection

In this research work, an effective Levenberg–Marquardt algorithm-based artificial neural network (LMA-BANN) model is presented to find an accurate series solution for micropolar flow in a porous channel with mass injection (MPFPCMI). The LMA is one of the fastest backpropagation methods used for solving least-squares of nonlinear problems. We create a dataset to train, test, and validate the LMA-BANN model regarding the solution obtained by optimal homotopy asymptotic (OHA) method. The proposed model is evaluated by conducting experiments on a dataset acquired from the OHA method. The experimental results are obtained by using mean square error (MSE) and absolute error (AE) metric functions. The learning process of the adjustable parameters is conducted with efficacy of the LMA-BANN model. The performance of the developed LMA-BANN for the modelled problem is confirmed by achieving the best promise numerical results of performance in the range of E-05 to E-08 and also assessed by error histogram plot (EHP) and regression plot (RP) measures.

Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non-Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

Homogeneous And Heterogeneous Reactions on The Peristalsis of Bingham Fluid with Variable Fluid Properties Through a Porous Channel

The exploration addresses the effect of variable viscosity and thermal conductivity on the peristaltic mechanism of Bingham fluid. A two-dimensional non-uniform porous channel is considered for the fluid flow, which is assumed to be inclined. The impact of heat, slip conditions, wall properties, homogeneous and heterogeneous reactions are examined. The resulting nonlinear differential equations are solved by employing the perturbation method. The solutions acquired are analyzed and sketched through graphs that show that the variable viscosity renders a critical role in regulating the velocity of the fluid in the channel's central part. The stream function has been analyzed to observe the trapping phenomenon. Further, the obtained results find its application in understanding the flow of blood in micro arteries.

Parametric Study of Unsteady Flow and Heat Transfer of Compressible Helium–Xenon Binary Gas through a Porous Channel Subjected to a Magnetic Field

A numerical analysis of unsteady fluid and heat transport of compressible Helium–Xenon binary gas through a rectangular porous channel subjected to a transverse magnetic field is herein presented. The binary gas mixture consists of Helium (He) and Xenon (Xe). In addition, the compressible gas properties are temperature-dependent. The set of governing equations are nondimensionalized via appropriate dimensionless parameters. The dimensionless equations involve a number of dimensionless groups employed for detailed parametric study. Consequently, the set of equations is discretized using a compact finite difference scheme and solved by using the 3rd-order Runge–Kutta method. The model’s computed results are compared with data from past literature, and very favorable agreement is achieved. The results show that the magnetic field, compressibility and variable fluid properties profoundly affect heat and fluid transport. Variations of density with temperature as well as pressure result in an asymmetric mass flow profile. Furthermore, the friction coefficient is greater for the upper wall than for the lower wall due to larger velocity gradients along the top wall.