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.
Highlights
In recent decades, the performance of heat transfer of conventional fluids like ethylene glycol, lubricants, oil, kerosene and water, etc., has become less favorable in certain applications
The influence of chemical reaction and heat generation on mixed convection flow of a Casson nanofluid towards a permeable stretching sheet has been studied by Ibrahim et al [25]
The literature shows that researchers have devoted their attention to the study of boundary layer flow near a slender needle in nanofluid. These situations are caused by the usage of nanofluid that enhance the heat transfer rate
Summary
The performance of heat transfer of conventional fluids like ethylene glycol, lubricants, oil, kerosene and water, etc., has become less favorable in certain applications. The influence of chemical reaction and heat generation on mixed convection flow of a Casson nanofluid towards a permeable stretching sheet has been studied by Ibrahim et al [25]. The literature shows that researchers have devoted their attention to the study of boundary layer flow near a slender needle in nanofluid. These situations are caused by the usage of nanofluid that enhance the heat transfer rate. The novelty of the present work is to analyze the problem of the steady laminar nanofluid flow adjacent to a slender needle by considering the additional effects of chemical reaction and heat source. The graphical results are presented and discussed for the varying effect of emerging parameters
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