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

Area of Science:

• Fluid dynamics
• Heat transfer
• Non-Newtonian fluid mechanics

Background:

• Understanding non-isothermal fluid flow is crucial in many industrial processes.
• Second-grade fluids exhibit complex rheological behavior.
• Energy dissipation significantly impacts heat transfer in fluid systems.

Purpose of the Study:

• To derive exact solutions for unidirectional non-isothermal flow of a second-grade fluid in a plane channel.
• To analyze the influence of mechanical-to-thermal energy conversion on heat transfer.
• To investigate the effects of various boundary conditions (no-slip, threshold slip, mixed) on fluid flow.

Main Methods:

• Analytical derivation of exact solutions for the governing equations.
• Inclusion of fluid energy dissipation in the heat transfer equation.
• Application of diverse boundary conditions: no-slip, Navier's slip, and mixed conditions.

Main Results:

• New exact solutions for the specified flow problem were obtained.
• The dependence of flow behavior on different boundary conditions was analyzed.
• Explicit relationships were established to determine slip or no-slip regimes based on model parameters.

Conclusions:

• The study provides a comprehensive analysis of second-grade fluid flow under non-isothermal conditions.
• Boundary conditions play a critical role in determining flow characteristics and heat transfer.
• The derived relationships offer insights into controlling fluid behavior at channel walls.