Numerical investigation of boundary layer flow past a thin heated needle immersed in hybrid nanofluid

Impact of needle size and distinct flow conditions on thermal performance of TiO2–MWCNTs hybrid nanofluid flow past thin needle using Casson fluid model

“…so that the velocity components obey the relations given in Equation (18) as explained in ref. [27].…”

“…The momentum equation in the radial direction disappears due to the application of boundary layer theory as per which the terms in the axial direction $$\,u,\,{{\partial u} \mathord{/ {\vphantom {{\partial u} {\partial x}}} \kern-\nulldelimiterspace} {\partial x}},\,{{{\partial ^2}u} \mathord{/ {\vphantom {{{\partial ^2}u} {\partial {x^2}}}} \kern-\nulldelimiterspace} {\partial {x^2}}}$$ are presumed to be of O (1) but the terms v and r are taken to be of $$O( \delta )$$ as they are in the radial direction. Here δ represents the thickness of the boundary layer [20, 27].…”

“…To attain a better understanding of the heat exchange phenomenon in boundary layers and to use that information for practical design purposes, it is much needed to take the help of simulations and numerical investigations. The heat exchange involved in the boundary layer flow past the thin needle, stretching/shrinking sheet, or disk using different mathematical or computational methods has been studied widely, some of which are mentioned here [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. A lot of hybrid nanofluids comprising MWCNTs and metal oxide nanoparticles as their constituents exhibit non-Newtonian nature, as discussed in the last paragraph.…”

Similarity and Finite Difference Solution on Biomagnetic Flow and Heat Transfer of Blood‐Fe3O4 through a Thin Needle

“…, where x and r represent the axial and radial directions, respectively (v) Te temperature of the sheet and ambient fuid temperature is T w and T c , respectively, with T w < T c (vi) A magnetic dipole generates a strong magnetic feld of intensity H that is kept the distance d from the cylindrical surface (vii) Te physical efect of radiative heat fux has sufciently small in the direction parallel to the surface such that it can be neglected Our work is motivated by that references [12,[43][44][45][46]. By considering our assumptions and following the aforementioned references, the corresponding continuity, momentum, and energy equations in the cylindrical coordinates take the following form:…”

“…To nondimensionalize equations (1) to (3), we introduced the following transformations as performed in references [44,45]:…”