Marwat Dil Nawaz Khan
Department of Mathematics, Faculty of Technologies and Engineering Sciences, Islamia College Peshawar, University Campus, Jamrod Road, Peshawar, Khyber Pakhtunkhwa, 25120, Pakistan.
Sci Rep. 2022 Jun 1;12(1):9134. doi: 10.1038/s41598-022-12908-9.
In this paper, double-diffusive convection in flow of viscous fluid is investigated inside a horizontal channel. It has heated, inclined and rectangular plane walls. The upper wall has non-uniform temperature and variable species concentration. Note that the Jeffery-Hamel flow depends upon the radial component of velocity, whereas, the peripheral velocity is taken zero. However, the current simulation has been accomplished in view of new procedures and we dealt with two non-zero components of velocity. The problem has been described in a set of four PDEs and the relevant BCs, whereas, the whole set of BVP is taken in Cartesian Coordinates. A set of proper transformation is formed, which reduces the system of PDEs into a new system of ODEs. The system of ODEs is solved with the help of several methods in order to check the validity of the solution. An approximate analytical solution is provided for small values of inclination parameter. An accurate numerical solution of the modelled equations is also given. Moreover, skin friction, rate of the two diffusions are investigated for all different cases of assisting (opposing) and converging (diverging) flows. Thus, the current modelled problem perfectly describes the physical problems of real world in such special circumstances.
本文研究了水平通道内粘性流体流动中的双扩散对流。通道具有加热的、倾斜的矩形平面壁。上壁具有非均匀温度和可变的物种浓度。注意，杰弗里 - 哈梅尔流动取决于速度的径向分量，而圆周速度取为零。然而，当前的模拟是按照新的程序完成的，并且我们处理了速度的两个非零分量。该问题用一组四个偏微分方程（PDEs）和相关的边界条件（BCs）进行了描述，而整个边值问题（BVP）采用笛卡尔坐标系。形成了一组适当的变换，将偏微分方程组简化为一个新的常微分方程组（ODEs）。为了检验解的有效性，借助几种方法求解了常微分方程组。针对倾斜参数的小值提供了一个近似解析解。还给出了建模方程的精确数值解。此外，针对所有不同的辅助（反向）和汇聚（发散）流动情况，研究了表面摩擦力和两种扩散速率。因此，当前建模的问题在这种特殊情况下完美地描述了现实世界的物理问题。
