The study of models related to non-Newtonian fluid flow behaviour has gained importance due to its significance in engineering applications, including extraction of oil and gas, aerodynamic heating, electrostatic precipitation, and so forth. Analysis of these classes of nonlinear models is often carried out utilizing either experimental or numerical methods. Recent advances in computational methods make it easier to find the exact solutions of linear models. However, it is still difficult to precisely solve the nonlinear models. This leads to the fact that limited literature is available on the fundamental solutions of non-Newtonian models. The availability of fundamental solutions helps in the verification of complex numerical codes and is beneficial to discuss in the stability analysis.

A symmetry transformation maps an equation into itself. The set of such transformations forms a Lie group and gives rise to Lie algebra which enables easier manipulation of the underlying differential equations to reduce and analyze them more easily. The Lie symmetry method is a powerful tool to solve or reduce ordinary differential equations, and a way to find exact solutions of partial differential equations by reducing the number of independent variables in the equations. Furthermore, Lie theory is a very reasonable differential algebraic approach in analyzing and solving engineering and applied science problems, which are modelled in terms of nonlinear and complicated ordinary and partial differential equations.

The focus of this Special Issue is to discuss analytical and numerical solutions to problems related primarily to the incompressible flow of non-Newtonian fluids in various physical geometries, such as internal or boundary layer flows. We welcome research papers on the applications of group theoretical methods to problems in non-Newtonian fluid mechanics, and review articles describing the latest research trends in the field. We hope that this Special Issue will give the scientific community an overall picture and up-to-date studies in the relevant field, which will eventually help both the industrial and engineering sectors. Submissions are welcome from experts and practitioners with mathematics, physics, or engineering backgrounds who utilize the Lie algebraic method as well as other allied approaches.

Potential topics include but are not limited to the following:

• Application to problems involving non-Newtonian flows
• Models to study non-Newtonian flow behaviour with heat transfer analysis
• Non-Newtonian nanofluids models
• Hybrid nanofluids characterization and modelling
• Thermophysical properties of hybrid nanofluids
• Magnetohydrodynamic flow
• Non-Newtonian fluid flow due to stretching or shrinking surface
• Non-Newtonian fluid flow phenomena in biological systems
• The use of the Lie and similarity method and then analytical approaches such as homotopy perturbation, homotopy analysis, perturbative series, etc.
• Numerical methods as well as implementations involving non-Newtonian fluid models
• Applications to nonlinear differential equations from mathematical physics that lead to enhancing its utility in fluid problems
• Non-classical, conditional or higher symmetry approaches
• Invariant approaches
• Conservation laws, Noether symmetry, and Hamiltonian approaches