A mathematical model is presented for laminar, steady natural convection mass transfer in boundary layer flow from a rotating porous vertical cone in anisotropic high-permeability porous media. The transformed boundary value problem is solved subject to prescribed surface and free stream boundary conditions with a Maple 17 shooting method. Validation with a Chebyshev spectral collocation method is included. The influence of tangential Darcy number, swirl Darcy number, Schmidt number, rotational parameter, momentum (velocity slip), mass slip and wall mass flux (transpiration) on the velocity and concentration distributions is evaluated in detail. The computations show that tangential and swirl velocities are enhanced generally with increasing permeability functions (i.e., Darcy parameters). Increasing spin velocity of the cone accelerates the tangential flow, whereas it retards the swirl flow. An elevation in wall suction depresses both tangential and swirl flow. However, increasing injection generates acceleration in the tangential and swirl flow. With greater momentum (hydrodynamic) slip, both tangential and swirl flows are accelerated. Concentration values and Sherwood number function values are also enhanced with momentum slip, although this is only achieved for the case of wall injection. A substantial suppression in tangential velocity is induced with higher mass (solutal) slip effect for any value of injection parameter. Concentration is also depressed at the wall (cone surface) with an increase in mass slip parameter, irrespective of whether injection or suction is present. The model is relevant to spin coating operations in filtration media (in which swirling boundary layers can be controlled with porous media to deposit thin films on industrial components), flow control of mixing devices in distillation processes and also chromatographical analysis systems.

中文翻译：

---

带有Stefan吹气和Navier滑移的各向异性多孔介质中自转锥自相似自然对流传质的数值研究

提出了一个数学模型，用于各向异性高渗透性多孔介质中旋转多孔垂直锥的边界层流中层流，稳态自然对流传质。使用Maple 17射击方法，可以在规定的表面和自由流边界条件下解决变换后的边值问题。包括使用Chebyshev频谱配置方法进行的验证。详细评估了切向达西数，旋流达西数，施密特数，旋转参数，动量（速度滑移），质量滑移和壁质量通量（蒸腾量）对速度和浓度分布的影响。计算表明，随着渗透率函数（即达西参数）的增加，切向速度和旋涡速度通常会提高。圆锥体的自旋速度增加会加速切向流，但会阻碍旋流。壁吸力的升高会同时抑制切向流和涡流。但是，增加喷射量会在切向和旋流中产生加速。随着动量（流体动力）滑移的增加，切向流和涡流均被加速。浓度值和舍伍德数函数值也随动量滑动而增加，尽管这仅在壁注入的情况下才能实现。对于任何注入参数值，都将以较高的质量（绝对）滑移效应引起切向速度的显着抑制。随质量滑移参数的增加，壁（圆锥表面）的浓度也降低，而与是否存在注入或抽吸无关。