Characterization of Marangoni Forced Convection in Casson Nanoliquid Flow with Joule Heating and Irreversibility

The Marangoni forced convective inclined magnetohydrodynamic flow is examined. Marangoni forced convection depends on the differences in surface pressure computed by magnetic field, temperature, and concentration gradient. Casson nanoliquid flow by an infinite disk is considered. Viscous dissipation, heat flux, and Joule heating are addressed in energy expressions. Thermophoresis and Brownian motion are also examined. Entropy generation is computed. The physical characteristics of entropy optimization with Arrhenius activation energy are discussed. Nonlinear PDE’s are reduced to highly nonlinear ordinary systems with appropriate transformations. A nonlinear system is numerically computed by the NDSolve technique. The salient characteristics of velocity, temperature, concentration, entropy generation, and Bejan number are explained. The computational results of the heat-transfer rate and concentration gradient are examined through tables. Velocity and temperature have reverse effects for the higher approximation of the Marangoni number. Velocity is a decreasing function of the Casson fluid parameter. Temperature is enhanced for higher radiation during reverse hold for concentration against the Marangoni number. The Bejan number and entropy generation have similar effects for Casson fluid and radiation parameters. For a higher estimation of the Brinkman number, the entropy optimization is augmented.

Nonlinear mixed convective nanofluid flow along moving vertical rough plate

The objective of the current research paper is to investigate the effects of surface roughness on magnetohydrodynamic nonlinear mixed convection nanofluid flow over vertically moving plate. The highly coupled dimensional nonlinear partial differential equations (NPDE) are converted into dimensionless NPDE along with the boundary conditions with the help of non-similar transformations. The resulting set of dimensionless nonlinear PDE’s are solved by using Quasilinearization technique and implicit finite difference method. Impacts of various dimensionless parameters, namely, Brownian diffusion (Nb), nonlinear mixed convection ( ), nanoparticle buoyancy ratio (Nr), Lewis number (Le), thermophoresis (Nt), frequency (n), magnetic (M) and small parameter ( ) are studied in detail on profiles as well as gradients. The results reveal that increasing values of increase the velocity profile, while increasing values of Nr decrease the same. Further, increasing values of and n exhibit sinusoidal variations on skin-friction coefficient, heat and nanoparticle mass transfer rates. Moreover, the presence of nonlinear mixed convection parameter has significant effects on fluid flow compared to its absence. In addition to this, rate of heat transfer is analyzed in presence and absence of nanoparticles.

Mahgoub Deterioration Method and its Application in Solving Duo-combination of Nonlinear PDE’s

This paper aims to solve Duo-combination of non linear partial differential equations by a latest approach called Mahgoub deterioration method (MDM). The latest technique is mix of the Mahgoub transform furthermore the, Adomian deterioration method. The generalized solution has been proved. Mahgoub deterioration method (MDM) is a very successful tool for finding the correct solution of linear and non linear partial differential equations. The continuance and uniqueness of solution is based on MDM.