Dero Sumera, Rohni Azizah Mohd, Saaban Azizan
School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia.
Institute of Information and Communication Technology, University of Sindh, Jamshoro, Pakistan.
Heliyon. 2020 Mar 3;6(3):e03510. doi: 10.1016/j.heliyon.2020.e03510. eCollection 2020 Mar.
A mathematical analysis is performed to study the flow and heat transfer phenomena of Casson based nanofluid with effects of the porosity parameter and viscous dissipation over the exponentially permeable stretching and shrinking surface. The considered nanofluid comprises Casson as a base fluid that contains silver ( and copper ( ) solid nanoparticles. The system of the nonlinear governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by applying similarity transformation. The obtained ODEs are solved by using shooting technique in Maple software. Numerically obtained results reveal dual solutions for various values of pertinent parameters. Due to occurrence of dual solutions, the stability analysis is done in order to find stable solution. Positive signs of smallest eigenvalues point out that the first solution is stable and second unstable. The variation of the velocity and the temperature profiles with coefficient of the skin friction and the Nusselt number are shown graphically. Both temperature profiles and its boundary layer thicknesses increase as volume fraction of nanoparticles of and are increased in the Casson fluid. Velocity profiles and corresponding boundary layer thicknesses decrease by suspension of nanoparticles of silver and copper, whereas the silver nanoparticles show the greater rate of heat transfer enhancement as compared to copper nanoparticles when suspended in Casson fluid.
进行了数学分析，以研究基于Casson的纳米流体在指数渗透拉伸和收缩表面上的流动和传热现象，该过程考虑了孔隙率参数和粘性耗散的影响。所考虑的纳米流体以Casson为基础流体，其中包含银（ ）和铜（ ）固体纳米颗粒。通过应用相似变换，将非线性控制偏微分方程（PDEs）系统转换为常微分方程（ODEs）。使用Maple软件中的打靶技术求解得到的ODEs。数值结果揭示了相关参数在不同取值时的双解情况。由于出现了双解，因此进行了稳定性分析以找到稳定解。最小特征值的正号表明第一个解是稳定的，第二个解是不稳定的。以图形方式展示了速度和温度分布随表面摩擦系数和努塞尔数的变化情况。随着Casson流体中银和铜纳米颗粒体积分数的增加，温度分布及其边界层厚度均增大。银和铜纳米颗粒的悬浮会使速度分布和相应的边界层厚度减小，而当悬浮在Casson流体中时，银纳米颗粒的传热增强速率比铜纳米颗粒更大。
