Numerical Solution for Unsteady Acceleration MHD Third-Grade Fluid Flow in a Rotating Frame Through Porous Medium Over Semi-Infinite Boundary Condition with a Presence of Heat Transfer

The aim of this work is to present a suitable numerical solution for unsteady non-Newtonian third-grade fluid which rotates at z -axis and pass through a porous medium. The fluid flows in magnetic field with constant acceleration and the semi-infinite boundary condition are highlighted. The fluid problem is also deal with heat transfer. The nonlinear partial differential equation is discretised using the finite difference method (FDM). The linear system obtained for three different domains (lengths). Consequently, the asymptotic interpolation method is merged to solve problems of large sizes. This hybrid method yielded results that satisfied the boundary condition that reaches zero as length grows to infinite length. For velocity profile and temperature distribution, a comparison of FDM and hybrid method is shown. It is discovered that the hybrid method produces better results than FDM for this infinitely large problem. Several analyses have been carried out to investigate the effect of various fluid parameter values. The findings reveal that as the porosity parameter increases, the velocity decreases. The Grashof and Prandtl numbers demonstrate the relationship to the temperature distributions. The effects of the magnetic field and the non-Newtonian parameters were also illustrated, as these parameters influence the velocity distribution of the fluid flow.

Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment

The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement.

Thermodynamic Analysis of Magnetohydrodynamic Third Grade Fluid Flow with Variable Properties

This article aims to computationally study entropy generation in a magnetohydrodynamic (MHD) third grade fluid flow in a horizontal channel with impermeable walls. The fluids viscosity and thermal conductivity are assumed to be dependent on temperature. The flow is driven by an applied uniform axial pressure gradient between infinite parallel plates and is considered to be incompressible, steady and fully developed. Adomian decomposition method (ADM) is used to obtain series solutions of the nonlinear governing equations. Thermodynamic analysis is done by computing the entropy generation rate and the irreversibility ratio (Bejan number). The effects of the various pertinent embedded parameters on the velocity field, temperature field, entropy generation rate and Bejan number are analysed through vivid graphical manipulations. The analysis shows that an appropriate combination of thermophysical parameters efficiently achieves entropy generation minimization in the thermomechanical system. The analysis shows that entropy generation minimization is achieved by increasing the magnetic field and the third grade material parameters, and therefore designs and processes incorporating MHD third grade fluid flow systems are far more likely to give optimum and efficient performance.

Numerical Investigation of Thin Film Flow of a Third-Grade Fluid on a Moving Belt Using Evolutionary Algorithm-Based Heuristic Technique

This paper presents a stochastic heuristic approach to solve numerically nonlinear differential equation (NLDE) governing the thin film flow of a third-grade fluid (TFF-TGF) on a moving belt. Moreover, the impact on velocity profile due to fluid attribute is also investigated. The estimate solution of the given NLDE is achieved by using the linear combination of Bernstein polynomials with unknown constants. A fitness function is deduced to convert the given NLDE along with its boundary conditions into an optimization problem. Genetic algorithm (GA) is employed to optimize the values of unknown constants. The proposed approach provided results in good agreement with numerical values taken by Runge–Kutta and more accurate than two popular classical methods including Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The error is minimized 10[Formula: see text] times to 10[Formula: see text] times.