An Implicit Numerical Approach for 2D Rayleigh Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

In this research work, our aim is to use the fast algorithm to solve the Rayleigh–Stokes problem for heated generalized second-grade fluid (RSP-HGSGF) involving Riemann–Liouville time fractional derivative. We suggest the modified implicit scheme formulated in the Riemann–Liouville integral sense and the scheme can be applied to the fractional RSP-HGSGF. Numerical experiments will be conducted, to show that the scheme is stress-free to implement, and the outcomes reveal the ideal execution of the suggested technique. The Fourier series will be used to examine the proposed scheme stability and convergence. The technique is stable, and the approximation solution converges to the exact result. To demonstrate the applicability and viability of the suggested strategy, a numerical demonstration will be provided.

Thermal slip and homogeneous/heterogeneous reaction characteristics of second-grade fluid flow over an exponentially stretching sheet

This paper deals with an unsteady magnetohydrodynamic two-dimensional second-grade fluid flow towards a permeable exponentially stretching surface with heterogeneous–homogeneous reactions. The nonuniform heat source/sink, thermal slip, and thermal radiation effect are also considered to analyze the thermal attributes. The modeled equations of motions are converted into nonlinear ordinary differential equations (ODEs) by suitable transformations. A MATLAB Bvp4c approach is employed for the numerical solution of ODEs. The outcomes of various parameters are scrutinized by graphs. The quantities of interests such as Nusselt number and the skin friction are presented and discussed. The resistance effects take place due to higher estimations of second-grade parameter, as a result, the velocity field declines. The temperature field raises with the increment of radiation parameter. The concentration of nanoparticles decaying when heterogeneous-homogeneous reactions become larger. Moreover, from the tabulated data, it is noticed the growing estimations of K and M boosts the coefficient of skin friction.

Enhancement of heat and mass transfer of a physical model using Generalized Caputo fractional derivative of variable order and modified Laplace transform method

In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.

Mechanical and thermal energies transport flow of a second grade fluid with novel fractional derivative

In this study, an unsteady natural convection flow of second-grade fluid over a vertical plate with Newtonian heating by constant proportional Caputo non-integer order derivative is presented. After developing a dimensionless flow model, the set of governing equations are solved with the help of integral transform, namely the Laplace transform and closed solutions are obtained. Also, some graphs of temperature and velocity field are drawn to see the subjectively of fractional parameter [Formula: see text] and other involved parameters of interest. It also shows dual nature for small and large time behavior due to the power-law kernel. Further, a comparative analysis between the temperature as well as the velocity fields with existing literature has been presented. Further, as a result, it is concluded that constant proportional Caputo derivative shows more decaying nature of the fluid flow properties than classical Caputo and Caputo-Fabrizio fractional derivatives.

Entropy Optimized Second Grade Fluid with MHD and Marangoni Convection Impacts: An Intelligent Neuro-Computing Paradigm

Artificial intelligence applications based on soft computing and machine learning algorithms have recently become the focus of researchers’ attention due to their robustness, precise modeling, simulation, and efficient assessment. The presented work aims to provide an innovative application of Levenberg Marquardt Technique with Artificial Back Propagated Neural Networks (LMT-ABPNN) to examine the entropy generation in Marangoni convection Magnetohydrodynamic Second Grade Fluidic flow model (MHD-SGFM) with Joule heating and dissipation impact. The PDEs describing MHD-SGFM are reduced into ODEs by appropriate transformation. The dataset is determined through Homotopy Analysis Method by the variation of physical parameters for all scenarios of proposed LMT-ABPNN. The reference data samples for training/validation/testing processes are utilized as targets to determine the approximated solution of proposed LMT-ABPNN. The performance of LMT-ABPNN is validated by MSE based fitness, error histogram scrutiny, and regression analysis. Furthermore, the influence of pertinent parameters on temperature, concentration, velocity, entropy generation, and Bejan number is also deliberated. The study reveals that the larger β and Ma, the higher f′(η) while M has the reverse influence on f′(η). For higher values of β, M, Ma, and Ec, θ(η) boosts. The concentration ϕ(η) drops as Ma and Sc grow. An augmentation is noticed for NG for higher estimations of β,M, and Br. Larger β,M and Br decays the Bejan number.

Unsteady MHD Plane Couette-Poiseuille Flow of Fourth-Grade Fluid with Thermal Radiation, Chemical Reaction and Suction Effects

This study investigates the unsteady MHD flow of a fourth-grade fluid in a horizontal parallel plates channel. The upper plate is oscillating and moving while the bottom plate is stationary. Solutions for momentum, energy and concentration equations are obtained by the He-Laplace scheme. This method was also used by Idowu and Sani [12] and there is agreement with our results. The effect of various flow parameters controlling the physical situation is discussed with the aid of graphs. Significant results from this study show that velocity and temperature fields increase with the increase in the thermal radiation parameter, while velocity and concentric fields decrease with an increase in the chemical reaction parameter. Furthermore, velocity, temperature and concentric fields decrease with an increase in the suction parameter. It is also interesting to note that when S4 = 0, our results will be in complete agreement with Idowu and Sani [12] results. The results of this work are applicable to industrial processes such as polymer extrusion of dye, draining of plastic films etc.