This study addresses the development of a mathematical model and theoretical analysis of a free convective three-directional flow of an incompressible second-grade fluid through a highly porous medium bounded by a vertical infinite plate in slip flow regime subjected to a constant suction. The free stream velocity is rumored to be constant while permeability of the medium is presumed to be periodic. It is well known that the assumption of either time dependent or constant permeability of a porous medium leads to two-dimensional flows, of course, the flow comes to be three-dimensional due to variation in permeability of the porous medium. Approximate solutions of velocity and temperature fields, heat flux and skin friction are established by applying the regular perturbation technique. Results are discussed and visualized graphically in the light of physical parameters emerging in the mathematical model of the physical phenomenon with carefully selected and viable data. The significance of current study reveals that presence of slip parameter reduces the thickness of boundary layer causing the enhancement in the main flow velocity component. With increasing permeability parameter fluid velocity is decelerated whereas it is accelerated with increasing Grashof number. With increasing non-Newtonian parameter, a similar response is noted as for the permeability parameter. It is also noted that permeability parameter, Prandtl number, Grashof number and elastic parameter provide mechanism to control the skin friction. In addition, Reynolds number also plays a vital role to control the skin friction. Furthermore, Reynolds number significantly boosts the coefficient of heat transfer, and Prandtl number causes to reduce the thermal boundary layer thickness.

本研究解决了不可压缩的二级流体通过高度多孔介质的自由对流三向流动的数学模型的开发和理论分析，该介质由垂直无限板限定，处于滑流状态，受到恒定吸力。据传自由流速度是恒定的，而介质的渗透率被认为是周期性的。众所周知，多孔介质的时间依赖或恒定渗透率的假设导致二维流动，当然，由于多孔介质渗透率的变化，流动变成了三维。通过应用规则微扰技术建立速度和温度场、热通量和皮肤摩擦的近似解。根据物理现象数学模型中出现的物理参数以及精心选择的可行数据，以图形方式讨论和可视化结果。当前研究的意义表明，滑移参数的存在降低了边界层的厚度，导致主要流速分量的增强。随着渗透率参数的增加，流体速度会减慢，而随着 Grashof 数的增加，它会加速。随着非牛顿参数的增加，注意到与渗透率参数类似的响应。还注意到渗透率参数、Prandtl 数、Grashof 数和弹性参数提供了控制皮肤摩擦的机制。此外，雷诺数对控制皮肤摩擦也起着至关重要的作用。此外，