Imran Muhammad, Yasmin Sumeira, Waqas Hassan, Khan Shan Ali, Muhammad Taseer, Alshammari Nawa, Hamadneh Nawaf N, Khan Ilyas
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan.
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia.
Nanomaterials (Basel). 2022 Feb 16;12(4):663. doi: 10.3390/nano12040663.
The present work discusses the 2D unsteady flow of second grade hybrid nanofluid in terms of heat transfer and MHD effects over a stretchable moving flat horizontal porous plate. The entropy of system is taken into account. The magnetic field and the Joule heating effects are also considered. Tiny-sized nanoparticles of silicon carbide and titanium oxide dispersed in a base fluid, kerosene oil. Furthermore, the shape factors of tiny-sized particles (sphere, bricks, tetrahedron, and platelets) are explored and discussed in detail. The mathematical representation in expressions of PDEs is built by considering the heat transfer mechanism owing to the effects of Joule heating and viscous dissipation. The present set of PDEs (partial differential equations) are converted into ODEs (ordinary differential equations) by introducing suitable transformations, which are then resolved with the bvp4c (shooting) scheme in MATLAB. Graphical expressions and numerical data are obtained to scrutinize the variations of momentum and temperature fields versus different physical constraints.
本文研究了二级混合纳米流体在具有热传递和磁流体动力学(MHD)效应的可拉伸移动水平多孔平板上的二维非定常流动。考虑了系统的熵。还考虑了磁场和焦耳热效应。碳化硅和二氧化钛的微小纳米颗粒分散在基础流体煤油中。此外,还详细探讨和讨论了微小颗粒(球体、砖块、四面体和薄片)的形状因子。通过考虑焦耳热和粘性耗散效应引起的热传递机制,建立了偏微分方程(PDEs)表达式中的数学表示。通过引入合适的变换,将当前的偏微分方程组转换为常微分方程(ODEs),然后在MATLAB中用bvp4c(打靶)方案求解。获得了图形表达式和数值数据,以研究动量和温度场随不同物理约束的变化。