Engineering Science and Technology, an International Journal (Dec 2017)
MHD wedge flow of nanofluids with an analytic solution to an especial case by Lambert W-function and Homotopy Perturbation Method
Abstract
In the present work, an analytical investigation on the wedge flow of magnetic nanofluids is performed. A relatively new empirical model is used in an Eulerian framework to study the effectiveness of nanofluids against the pure base fluids. This new Eulerian model is considered mainly due to two significant reasons. First is to indicate some anomalies within the nanofluids system which are overlooked on using the popular classic models (e.g. Maxwell-Garnett relation for thermal conductivity and Brinkman/Einstein model for viscosity). The anomalies simply refer to the effects imposed due to different nanoparticles sizes as well as various thermal boundary conditions (here is to be the direction of heat transfer). The second reason behind the implementation of such a model is to follow some important notes recently revealed via a critical paper. In this regard, the nanoparticles migration due to either Brownian motion or thermophoresis effect is totally disregarded as the corresponding factors can be shown to be negligible for many actual nanofluids. Therefore, further parametric studies may be depreciated subject to a more rigorous physical ground. Before proceeding with nanofluids analysis, an especial case was found to be interesting. This case is referred to the MHD flow around a 90 degree corner where the magnetic parameter is equal to unity. The case is treated analytically firstly in an implicit manner using the inverse operator of Lambert W-function and secondly in an explicit manner using Homotopy Perturbation Method (HPM). Upon reading the existing literature, it may be confirmed that this case has not been noted so far. An insight to the classic convective heat transfer coefficient in Blasius flow is also additionally provided in this paper where this factor is simply obtained purely independent of any solution to energy similarity equation seemingly for the first time in the state of art.
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