Purpose
– The purpose of this paper is to theoretically study the problem of mixed convection boundary layer flow and heat transfer past a vertical needle with variable wall temperature using nanofluids. The similarity equations are solved numerically for copper nanoparticles in the based fluid of water to investigate the effect of the solid volume fraction parameter of the fluid and heat transfer characteristics. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles and are graphically presented and discussed.
Design/methodology/approach
– The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 1e-10. For the study of the stability the authors also used the bvp4c function in combination with chebfun package from Matlab.
Findings
– It is found that the solid volume fraction affects the fluid flow and heat transfer characteristics. The numerical results for a regular fluid and forced convection flow are compared with the corresponding results reported by Chen and Smith. The solutions exists up to a critical value of λ, beyond which the boundary layer separates from the surface and the solution based upon the boundary-layer approximations is not possible
Originality/value
– The paper describes how multiple (dual) solutions for the flow reversals are obtained. A stability analysis for this flow reversal has been also done showing that the lower solution branches are unstable, while the upper solution branches are stable.
The economic operation of wind turbines is completely dependent upon the local wind conditions. Statistically determined wind velocity distribution is decisive for the expected energy yield. Before the pillars of wind turbines are erected, the expected energy potential should be predicted as precisely as possible to reduce the investments risk. Energy predictions based on local wind conditions measured at the hub height of a planned turbine give the most exactly predictions. However, this involves an expansive and time (years) consuming process. Our issue for fine wind emplacement is based on a Patent Application that claims that the wind potential in any other point of a known area can be inferred provided that we know the wind potential in one point of the area. Our aim is 1) to avoid the obsolete, expansive and inaccurate method to build wind map, and 2) to offer a final simply to be used tool. To solve that problem we must enter in the field of high mathematics of fluid dynamics.
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