Exploring the magnetohydrodynamic stretched flow of Williamson Maxwell nanofluid through porous matrix over a permeated sheet with bioconvection and activation energy

The evolution of compact density heat gadgets demands effective thermal transportation. The notion of nanofluid plays active role for this requirements. A comparative account for Maxwell nanofluids and Williamson nanofluid is analyzed. The bioconvection of self motive microorganisms, non Fourier heat flux and activation energy are new aspects of this study. This article elaborates the effects of viscous dissipation, Cattaneo–Christov diffusion for Maxwell and Williamson nanofluid transportation that occurs due to porous stretching sheet. The higher order non-linear partial differential equations are solved by using similarity transformations and a new set of ordinary differential equations is formed. For numerical purpose, Runge–Kutta method with shooting technique is applied. Matlab plateform is used for computational procedure. The graphs for various profiles .i.e. velocity, temperature, concentration and concentration of motile micro-organisms are revealed for specific non-dimensional parameters. It is observed that enhancing the magnetic parameter M, the velocity of fluid decreases but opposite behavior happens for temperature, concentration and motile density profile. Also the motile density profile decrease down for Pe and Lb. The skin friction coefficient is enhanced for both the Williamson and Maxwell fluid.

The Impact of Variable Fluid Properties on Biomagnetic Maxwell Fluids Past a Stretching Sheet with Slip Velocity and Heat Generation/Absorption

The impact of variable fluid properties (viscosity and thermal conductivity) and magnetic dipole on biomagnetic Maxwell fluid past a stretching sheet with slip velocity and heat generation/absorptionhave been studied. Similarity transformation technique is adopted to obtain the self-similar coupled nonlinear ordinary differential equations. Using similarity variable, the basic governing equations with boundary conditions are transformed and solved in bvp4c technique with MATLAB software. The contribution of different pertinent parameters such as viscosity, thermal conductivity and ferromagnetic parameter on the flow profiles with physical quantities are analyzed and examined through graphically. Results shown that with increasing ferromagnetic parameter, slip parameter, Maxwell parameter, velocity decreases but temperature increases. For accuracy of the proposed model to compare our numerical results in numerically and graphically with the previousliterature under some limiting cases and a good agreement is found. Dhaka Univ. J. Sci. 69(2): 109-115, 2021 (July)

Power Law Kernel Analysis of MHD Maxwell Fluid with Ramped Boundary Conditions: Transport Phenomena Solutions Based on Special Functions

In this paper, a new approach to find exact solutions is carried out for a generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate, which is analyzed for ramped-wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters the effects of radiation. An innovative definition of the time-fractional operator in power-law-kernel form is implemented to hypothesize the constitutive mass, energy, and momentum equations. The Laplace integral transformation technique is applied on a dimensionless form of governing partial differential equations by introducing some non-dimensional suitable parameters to establish the exact expressions in terms of special functions for ramped velocity, temperature, and constant-concentration fields. In order to validate the problem, the absence of the mass Grashof parameter led to the investigated solutions obtaining good agreement in existing literature. Additionally, several system parameters were used, such as as magnetic value M, Prandtl value Pr, Maxwell parameter λ, dimensionless time τ, Schmidt number “Sc”, fractional parameter α, andMass and Thermal Grashof numbers Gm and Gr, respectively, to examine their impacts on velocity, wall temperature, and constant concentration. Results are also discussed in detail and demonstrated graphically via Mathcad-15 software. A comprehensive comparative study between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach

Fractional-order mathematical modelling of physical phenomena is a hot topic among various researchers due to its many advantages over positive integer mathematical modelling. In this context, the appropriate solutions of such fractional-order physical modelling become a challenging task among scientists. This paper presents a study of unsteady free convection fluid flow and heat transfer of Maxwell fluids with the presence of Clay nanoparticle modelling using fractional calculus. The obtained model was transformed into a set of linear nondimensional, partial differential equations (PDEs). The finite difference scheme is proposed to discretize the obtained set of nondimensional PDEs. The Maple code was developed and executed against the physical parameters and fractional-order parameter to explain the behavior of the velocity and temperature profiles. Some limiting solutions were obtained and compared with the latest existing ones in literature. The comparative study witnesses that the proposed scheme is a very efficient tool to handle such a physical model and can be extended to other diversified problems of a complex nature.

Analytical Solution of Fractional Oldroyd-B Fluid via Fluctuating Duct

This investigation focuses on the mixed initial boundary value problem with Caputo fractional derivatives. The studied pour an incompressible fractionalized Oldroyd-B fluid prompted by fluctuating rectangular tube. The explicit expression of the velocity field and shear stresses for the fractional model are obtained by utilizing the integral transforms, i.e., double finite Fourier sine transform and Laplace transform. Furthermore, the confirmation of the analytical solutions is also analyzed by utilizing the Tzou’s and Stehfest’s algorithms in the tabular form. In limited cases, ordinary Oldroyd-B fluid similar solutions and classical Maxwell and fractional Maxwell fluid are derived. The flow field’s graphs with the influences of relevant parameters are also mentioned.

Role of Newtonian heating on a Maxwell fluid via special functions: memory impact of local and nonlocal kernels

The impact of Newtonian heating on a time-dependent fractional magnetohydrodynamic (MHD) Maxwell fluid over an unbounded upright plate is investigated. The equations for heat, mass and momentum are established in terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transforms. The change in the momentum profile due to variability in the values of parameters is graphically illustrated for all three C, CF and ABC models. The ABC model has proficiently revealed a memory effect.