Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids

• Main Author: Dero, Sumera
• Format: Thesis
• Language: English; English; English; English
• Published: 2020
• Subjects: QA Mathematics
• Online Access: https://etd.uum.edu.my/8930/1/depositpermission-902590.pdf; https://etd.uum.edu.my/8930/2/s902590_01.pdf; https://etd.uum.edu.my/8930/3/s902590_02.pdf; https://etd.uum.edu.my/8930/4/s902590_references.docx; https://etd.uum.edu.my/8930/

Studies of multiple solutions on boundary layer flows have gained much attention in the field of fluid dynamics in the recent years. In this regard, stability analysis is also important to identify the stable and unstable solutions. In this thesis, the possibility of occurrence of multiple solutions has been studied for boundary layer flows over stretching/shrinking sheet in nanofluids. Five different problems have been considered where two of the problems used nanofluid model proposed by Buongiomo and the remaining three problems used nanofluid model proposed by Tiwari and Das. The base fluids considered in this study are viscous fluid, Casson fluid and micropolar fluid. The mathematical models which govern the flows of five different problems have been constructed. Similarity transformations have been employed to transform the governing equations of partial differential equations to nonlinear ordinary differential equations. The resulting system is then solved numerically using shooting method with the aid of shootlib function in Maple software. To validate the results obtained in this study, comparison for specific cases have been done and in good agreement with existing solutions in literature. From this study, it is found that an increase of suction parameters will increase the rate of heat transfer in both stretching and shrinking cases. However, it causes the rate of skin friction to decrease for stretching case but to increase for shrinking case. Further, suction parameter, Casson parameter and Biot number decrease the temperature profiles but radiation, Brownian motion and thermophoresis parameters contribute towards the opposite. The results also displayed the occurrence of multiple solutions in all the problems considered. Therefore, the stability analysis has been performed to identify the stability of multiple solutions by using bvp4c solver in Matlab. The stability analysis indicates that the first solution is stable while the second and third solutions are unstable.