Features of double stratification on stagnation point flow of Walter's B nanoliquid driven through Riga surface are examined in the current study. Via solutal stratification, radiation and thermal effects, heat and mass phenomena are evaluated. The novelty of the proposed investigation is focused on the important effect of melting phenomenon and EMHD Lorentz force along with stratification and heat generation over the rheology of the liquid flow. The influence of Brownian and thermophoresis particle deposition is included in transport equations involved in the analysis. Transformation is incorporated by the basic laws of mass, energy and linear momentum to acquire nonlinear differential system of equations. Utilizing Optimal Homotopy Analysis Method through BVPh2.0.0, optimum value of convergence control factors is estimated. Graphical findings for the dimensionless temperature, velocity and concentration for different pertinent parameters are explained. Numerical values of physical interest like skin friction coefficient, local Sherwood number and local Nusselt number are computed and visualized graphically. The heat generation and advanced modified Hartmann number improve the speed of flow. It is also observed that weaker thermal stratification upraises the rate of heat transport, and mass transport rate lessens for stronger mass stratification. In addition, contour graphs of velocity for ratio parameter A describe the accurate perception of flow. The intensity of temperature and concentration field is low owing to double stratification, whereas the stronger radiation corresponds the significantly rise in temperature. Reliability of outcomes assured by means of probable error analysis.

A study of dual stratification on stagnation point Walters' B nanofluid flow via radiative Riga plate: a statistical approach

This paper aims to analyze the features of MHD Darcy-Forchheimer nanofluid flow over a nonlinear stretching sheet. A viscous incompressible nanofluid saturates the porous medium via Darcy-Forchheimer relation. Heat and mass transfer is analyzed through Brownian motion factor and Thermophoresis. A non-uniform magnetic field is induced to enhance the electric conductivity of the nanofluid. The model emphasis on small magnetic Reynolds number and boundary layers formulation. The governing Partial differential Equations are converted into nonlinear Ordinary differential equations using similarity transformations and thereafter solved utilizing homotopy analysis method. Graphs are sketched for different values of various fluid parameters. Drag force, heat flux and mass flux are interpreted numerically. The porosity factor results in rising the skin friction due to high resistance offered by porous medium. The heat and mass flux are reduced for a stronger porosity factor, which is an important finding for industrial applications of nanofluids. The temperature profile shows augments for increasing values of both the Brownian diffusion and Thermophoresis.

Magnetohydrodynamic Darcy–Forchheimer nanofluid flow over a nonlinear stretching sheet

This article is concerned with the nanofluid flow in a rotating frame under the simultaneous effects of thermal slip and convective boundary conditions. Arrhenius activation energy is another important aspect of the present study. Flow phenomena solely rely on the Darcy–Forchheimer-type porous medium in three-dimensional space to tackle the symmetric behavior of viscous terms. The stretching sheet is assumed to drive the fluid. Buongiorno’s model is adopted to see the features of Brownian diffusion and thermophoresis on the basis of symmetry fundamentals. Governing equations are modeled and transformed into ordinary differential equations by suitable transformations. Solutions are obtained through the numerical RK45-scheme, reporting the important findings graphically. The outputs indicate that larger values of stretching reduce the fluid velocity. Both the axial and transverse velocity fields undergo much decline due to strong retardation produced by the Forchheimer number. The thermal radiation parameter greatly raises the thermal state of the field. The temperature field rises for a stronger reaction within the fluid flow, however reducing for an intensive quantity of activation energy. A declination in the concentration profile is noticed for stronger thermophoresis. The Forchheimer number and porosity factors result in the enhancement of the skin friction, while both slip parameters result in a decline of skin friction. The thermal slip factor results in decreasing both the heat and mass flux rates. The study is important in various industrial applications of nanofluids including the electro-chemical industry, the polymer industry, geophysical setups, geothermal setups, catalytic reactors, and many others.

https://www.mdpi.com/2073-8994/12/5/741/pdf

Significance of Thermal Slip and Convective Boundary Conditions in Three Dimensional Rotating Darcy-Forchheimer Nanofluid Flow

Characteristics of chemical reaction and convective boundary conditions in Powell-Eyring nanofluid flow along a radiative Riga plate.

In this paper, it has been discussed the fractional model of Brinkman type fluid (BTF) holding hybrid nanoparticles. Titanium dioxide ( T i O 2 ) and silver (Ag) nanoparticles were liquefied in water ( H 2 O ) (base fluid) to make a hybrid nanofluid. The magnetohydrodynamic (MHD) free convection flow of the nanofluid ( Ag - T i O 2 - H 2 O ) was measured in a bounded microchannel. The BTF model was generalized using constant proportional Caputo fractional operator (CPC) with effective thermophysical properties. By introducing dimensionless variables, the governing equations of the model were solved by Laplace transform method. The testified outcomes are stated as M-function. The impact of associated parameters were measured graphically using Mathcad and offered a comparison with the existing results from the literature. The effect of related parameters was physically discussed. It was concluded that constant proportional Caputo fractional operator (CPC) showed better memory effect than Caputo-Fabrizio fractional operator (CF) (Saqib et al., 2020).

Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates

In this article, the stagnation point flow of Walters-B fluid induced by a Riga plate is investigated. Heat transfer properties are investigated with thermal radiation effect and Newtonian heating. An electromagnetic actuator is a Riga-plate where a span wise associated array of irregular electrodes and permanent magnets mounted on a flat surface. Lorentz force is parallel to a surface which is generated by this array and it reduces exponentially in the direction normal to the surface. The non-linear ordinary differential equations through the fundamental laws of mass, linear momentum and energy are obtained using the suitable transformation. The optimal values of convergence control parameters are computed by means of Optimal homotopy analysis method (OHAM) via BVPh2.0. Graphical results for the dimensionless velocity and temperature are presented and discussed for various physical parameters. Local skin friction and Local Nusselt numbers are computed analytically using OHAM.

Impact of radiation in a stagnation point flow of Walters’ B fluid towards a Riga plate

The choice behavior model is the model which describes the spiritual process of thinking which is concerned with the process of judging the merits of the numerous options and making the decision to determine one of them for action. The aim of this paper is to analyze the one specific type of choice behavior model for the learning process of the paradise fish. The existence and uniqueness results of the solution of the proposed choice behavior model are investigated via the fixed point tool.

On analytic model for two-choice behavior of the paradise fish based on the fixed point method

This paper deals with a specific type of traumatic avoidance for the learning process of normal dogs enclosed into a small compartment with a steel grid floor. Our aim is to analyze the behavior of the dogs in such situations and to construct a suitable mathematical model for it. The existence and uniqueness results of the proposed traumatic avoidance learning model are being investigated by the use of the Banach fixed point theorem.

On the solution of the traumatic avoidance learning model approached by the Banach fixed point theorem

The analysis of iterative differential equations is often related to the various applications of calculus, which support all mathematical sciences. These equations are critical when it comes to interpreting the infection models. Furthermore, the inclusion of self-mapping raises the complexity of determining the existence of solutions for the iterative differential equations. This paper considers a particular type of second-order iterative differential equations and uses the Banach fixed point theorem to find the existence and uniqueness of the proposed differential equation’s solution. We discuss the Hyers-Ulam and Hyers-Ulam-Rassias type stability of a solution to the proposed iterative boundary-value problem and present three illustrative examples to support our main results.

A unique solution of the iterative boundary value problem for a second-order differential equation approached by fixed point results

Chemical graph theory is a branch of mathematics that combines graph theory and chemistry and discusses the effect of research on “serious” or “pure” mathematics. A range of new graph ideas can be identified in the current development of mathematical chemistry and chemical graph theory. These advances include chemical kinetics as well as biomacromolecules. On star graphs, a few researchers have studied fractional differential equations. They used star graphs because their approach requires a common point that has edges with other nodes, whereas there are no edges between them. Our aim is to broaden the approach by using the idea of an ethane graph, which is an organic chemical compound with the chemical formula C 2 H 6 and having more than one junction nodes. In this work, we analyze the existence of solutions on such graphs for the fractional boundary value problem in the sense of Caputo fractional derivative. Inspired by a graph describing ethane’s chemical compound, we assume a graph with labeled vertices of 0 or 1 and describe fractional differential equations on each edge of this graph. We use the notable fixed point theorems to find the existence and uniqueness of a solution to the proposed fractional differential equation. An example is also presented to support our main results.

Ali Turab

Papers

Impact of radiation in a stagnation point flow of Walters’ B fluid towards a Riga plate

On analytic model for two-choice behavior of the paradise fish based on the fixed point method

On the solution of the traumatic avoidance learning model approached by the Banach fixed point theorem

A unique solution of the iterative boundary value problem for a second-order differential equation approached by fixed point results

The novel existence results of solutions for a nonlinear fractional boundary value problem on the ethane graph