Exact Solutions for Non-Isothermal Flows of Second Grade Fluid between Parallel Plates

• Published in: Nanomaterials (Basel, Switzerland) Vol. 13; no. 8; p. 1409
• Main Author: Baranovskii, Evgenii S.
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 19.04.2023; MDPI
• Subjects: Analysis; Aqueous solutions; Boundary conditions; Boundary value problems; Energy conversion; Energy dissipation; Equality; Exact solutions; Fluids; Heat; heat and mass transfer; Heat transfer; Isothermal flow; nanofluids; Nanoparticles; no-slip condition; Non-Newtonian fluids; Parallel plates; Physical properties; Poiseuille flow; Polymers; Rheology; second grade fluids; Shear stress; Slip; Thermal energy; Velocity; Viscosity; Russia; exact solutions; Navier slip condition; nanofluids; Poiseuille flow; second grade fluids; threshold slip condition; heat and mass transfer; no-slip condition; non-Newtonian fluids
• ISSN: 2079-4991; 2079-4991
• DOI: 10.3390/nano13081409

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier’s slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries.