Thermal investigation of Cu-TiO 2 /sodium alginate Casson hybridized nanofluid flow via a stretching (shrinking) disk: Stability analysis
Syed Modassir Hussaina, Hazoor Bux Lanjwanib, M Imran Anwarc d e, Muhammad Amer Qureshif, Saeed Ahmed Rajpuitg, Wasim Jamshedh i j✉, Mohamed Rabea Eidk, Kamel Guedril, Mustafa Bayrami
- aDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
- bDepartment of Mathematics, University of Sindh, Jamshoro, Pakistan
- cDepartment of Mathematics, Govt Postgraduate College Jhang, Higher Education Department, Punjab Lahore, Pakistan
- dDepartment of Mathematics, School of Sciences and Humanities, Nazarbayev University, Astana, Kazakhstan
- eDepartment of Mathematics, University of Sargodha, Sargodha, Pakistan
- fDepartment of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Nizwa, Sultanate of Oman
- gDepartment of Mathematics, Quaid-e-Awam University College Larakana, Larkana, Pakistan
- hCollege of Engineering, Al-Ayen Iraqi University, An Nasiriyah, Iraq
- iDepartment of Computer Engineering, Biruni University, Istanbul, Turkey
- jDepartment of Mathematics, Capital University of Science and Technology (CUST), Islamabad, Pakistan
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Abstract
This study evaluates the thermal characteristics of the boundary layer flow of Casson hybrid nanofluid via a stretchable (or shrinkable) disk, taking into consideration the effects of radiative heat flux and velocity slippage. Casson liquid is often used to characterize non-Newtonian liquids that exhibit properties of a normal liquid but are influenced by the presence of two types of nanoparticles, Cu and TiO 2 . Similarity transformation is employed to derive similarity formula, which are computationally resolved utilizing the shooting technique with the assistance of Maple software. There are two solutions for both the stretchable and shrinkable states of a disk, however when λ = 0 , only one solution is seen. No solution is found for λ < λ c , whereas the obtained solutions are divided at λ = λ c . Lobatto-III bvp4c method in MATLAB software is applied to evaluate the stability of the occurrence of dual solutions. Moreover, the analysis demonstrates that the first solution is both stable and physically possible. The Casson, shrinking, and slippage parameters decrease the fluid velocity and surface frictional profile. Furthermore, an augmentation in nanoparticle volume fractions leads to an escalation in skin friction, whereas the Nusselt number decreases for λ > 0 and augments for λ > − 1 .