Gupta Diksha, Kumar Lokendra, Singh Bani
Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector 62, Noida, Uttar Pradesh 201307, India.
ScientificWorldJournal. 2014 Feb 4;2014:362351. doi: 10.1155/2014/362351. eCollection 2014.
The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements.
本研究的目的是分析在存在粘性耗散的情况下，不稳定对微极流体在可渗透收缩片上的混合对流边界层流动的影响。在该片上假定有可变的抽吸分布。流动和温度场中的不稳定是由收缩速度和表面温度的时间依赖性引起的。借助相似变换，将控制偏微分方程转化为一组非线性常微分方程，使用变分有限元法对其进行数值求解。借助重要物理参数（即抽吸参数、不稳定参数、浮力参数和埃克特数）的图形表示，研究并分析了它们对速度、微旋转和温度函数的影响。此外，还计算了表面摩擦力和传热速率。在特殊条件下，将流速的精确解与有限元法得到的数值结果进行了比较。两组解之间观察到了极好的一致性。此外，为了验证数值结果的收敛性，随着单元数量的增加进行了计算。
