Numerical Analysis of Boundary Layer Flow Adjacent to a Thin Needle in Nanofluid with the Presence of Heat Source and Chemical Reaction

Abstract

The steady boundary layer flow of a nanofluid past a thin needle under the influences of heat generation and chemical reaction is analyzed in the present work. The mathematical model has been formulated by using Buongiornos’s nanofluid model which incorporates the effect of the Brownian motion and thermophoretic diffusion. The governing coupled partial differential equations are transformed into a set of nonlinear ordinary differential equations by using appropriate similarity transformations. These equations are then computed numerically through MATLAB software using the implemented package called bvp4c. The influences of various parameters such as Brownian motion, thermophoresis, velocity ratio, needle thickness, heat generation and chemical reaction parameters on the flow, heat and mass characteristics are investigated. The physical characteristics which include the skin friction, heat and mass transfers, velocity, temperature and concentration are further elaborated with the variation of governing parameters and presented through graphs. It is observed that the multiple (dual) solutions are likely to exist when the needle moves against the direction of the fluid flow. It is also noticed that the reduction in needle thickness contributes to the enlargement of the region of the dual solutions. The determination of the stable solution has been done using a stability analysis. The results indicate that the upper branch solutions are linearly stable, while the lower branch solutions are linearly unstable. The study also revealed that the rate of heat transfer is a decreasing function of heat generation parameter, while the rate of mass transfer is an increasing function of heat generation and chemical reaction parameters.

Thermally Stratified Darcy Forchheimer Flow on a Moving Thin Needle with Homogeneous Heterogeneous Reactions and Non-Uniform Heat Source/Sink

“…In order to obtain ODEs for Equations (3)-(7), the following non dimensional parameters are used [48,49]:…”

Darcy–Forchheimer flow of Ree–Eyring fluid over an inclined plate with chemical reaction: A statistical approach

“…Pal and Mondal 3 made an attempt to numerically examine unsteady nanofluid flow through a vertical plate submerged in a porous medium with chemical reaction. Salleh et al 4 and Kiyani et al 5 analyzed different nanofluid flows via various geometries, including a thin needle with chemical reaction and discovered that the chemical reaction parameter minimizes fluid concentration and the Brownian motion parameter lowers the heat transfer rate. Yadav 6 noticed that there is an inverse proportional relation between the chemical reaction parameter and Rayleigh (R)-Darcy (D) number in his examination of the (convective) unstableness in various fluid flows in porous case.…”

Mixed Convection Flow Along Vertical Thin Needles Containing Gyrotactic Microorganism with Variable Heat, Mass and Motile Microorganism Flux

“…The Buongiorno mathematical model of nanofluid due to moving slender needle was used by Ahmad et al [48]. Salleh et al [49] then studied stability analysis to understand the additional impact of the heat source and chemical reaction in a nanofluid flow towards a slender needle. Very recently Waini et al [50] and Khan et al [51] studied hybrid nanofluid flow through the thin needle.…”