Abstract
We considered the steady flow of Buongiorno’s model over a permeable exponentially stretching channel. The mathematical model was constructed with the assumptions on curved channels. After applying the boundary layer approximation on the Navier–Stocks equation, we produced nonlinear partial differential equations. These equations were converted into a system of non-dimensional ordinary differential equations through an appropriate similarity transformation. The dimensionless forms of the coupled ordinary differential equations were elucidated numerically through boundary value problem fourth order method. This method gains fast convergence as compared to other method such as the shooting method and the Numerical Solution of Differential Equations Mathematica method. The influence of the governing parameters which are involved in ordinary differential equations are highlighted through graphs while R e s 1 / 2 C f , R e s 1 / 2 N u s , and R e s − 1 / 2 S h s are highlighted through the tables. Our interest of study was to analyze the heat transfer rate of nanofluids. Surprisingly, for momentum boundary layer thickness, thermal boundary layer thickness and solutal boundary layer thickness became larger when λ > 0 , as compared to the case when λ < 0 .
Highlights
Analysis of stretching surfaces play a key role in the field of engineering and industrial due to its practical applications
We developed a mathematical model that we solved usingisis the bvp4c method
We considered the steady flow of Buongiorno’s model over a permeable exponentially stretching channel
Summary
Analysis of stretching surfaces play a key role in the field of engineering and industrial due to its practical applications. An influence of buoyancy on boundary layer flow of a continuous stretching surface was highlighted by Ali [7]. The heat transfer coefficient expansion seems to go beyond the important thermal conductivity effect, and cannot be foreseen by conventional pure fluid relationships, for example, Dittus–Boelter’s He deliberated, seven slip mechanisms: Inertia, Brownian diffusion, thermo phoresis, Magnus impact, diffusion phoresis, fluid drainage, and gravity, and asserted while Brownian diffusion are significant slip systems in nanofluids. Slip condition on the boundary layer flow was introduced by Andersson [28] He pioneered the closed form results of the Navier–Stokes equations over stretching sheets with MHD flow. Using the Andersson [28] idea, Wang [29] pioneered the closed form solution of the Navier–Stokes equations over stretching sheets with a slip condition. This analysis provides innovative insight for applications and complements the existing literature
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