Abstract
Experience shows that the Newtonian fluid model can be adequately employed for flow conditions of gases and small molecule liquids such as water. However, the behavior of a vast number of fluids cannot be considered under Newtonian fluid model. There are some non-Newtonian fluids with shear-independent viscosity, which nonetheless exhibit normal stress differences or other non-Newtonian behaviors. Many polymer solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, custard, toothpaste, starch suspensions, paint, blood, and shampoo. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, with the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different and can even be time dependent. Interestingly, the same fluid can behave as Newtonian or non-Newtonian under different flow conditions. The study of non-Newtonian fluids thus helps us to guide which model will be more appropriate under different sets of flow conditions. Besides the mathematical value for this study, the non-Newtonian fluids have attracted attention of a large number of researchers because of their industrial applications particularly in polymer industry. Unlike viscous fluids, the rheological properties of non-Newtonian fluids cannot be described by a single constitutive equation. Therefore a number of constitutive equations have been presented in the literature. Although many models have been proposed for non-Newtonian fluids, no accurate model is still available for large number of fluids under different flow conditions. Therefore, a lot of work is underway and needs to be undertaken to develop new models and use mathematical and numerical tools to understand the physics of non-Newtonian fluids and to address the real world problem in engineering and industry using the existing models.
The applications of non-Newtonian fluids are so enormous that Newtonian fluid is now being considered as exception rather than a rule. Mathematically, the governing equations for the existing non-Newtonian fluid models are highly nonlinear in nature and are almost impossible to solve analytically. The numerical solutions are generally provided. In this back drop, the complete volume of the special issue has been devoted to the problems arising in the transport and heat transfer phenomena of non-Newtonian fluids.
One of the most commonly used non-Newtonian fluids is the power-law fluid, or the Ostwald-de Waele relationship, which is a type of generalized Newtonian fluid for which the shear stress, τ, is given by τ = K(∂u/∂y) n , where K is the flow consistency index (SI units Pa·s n ), ∂u/∂y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s−1), and n is the flow behavior index (dimensionless). Further, the quantity τeff = Keff(∂u/∂y)n − 1 represents an apparent or effective viscosity as a function of the shear rate (SI unit Pa·s). This is also known as the Ostwald-de Waele power law; this mathematical relationship is useful because of its simplicity but only approximately describes the behavior of a real non-Newtonian fluid. For example, if n were less than one, the power law predicts that the effective viscosity would decrease with increasing shear rate indefinitely, requiring a fluid with infinite viscosity at rest and zero viscosity as the shear rate approaches infinity, but a real fluid has both a minimum and a maximum effective viscosity that depend on the physical chemistry at the molecular level.
Therefore, the power law is only a good description of fluid behavior across the range of shear rates to which the coefficients were fitted. There are a number of other models that better describe the entire flow behavior of shear-dependent fluids, but they do so at the expense of simplicity, so the power law is still used to describe fluid behavior, permit mathematical predictions, and correlate experimental data. Out of many more non-Newtonian fluids, the viscoelastic fluid (also known as second grade fluid) and micropolar fluid have drawn the attention of many scientists.
In this special issue, investigators were invited to contribute original research articles in certain topics, namely, boundary layer heat and mass transfer in non-Newtonian fluids; heat and mass transfer in internal flows of non-Newtonian fluids; unsteady non-Newtonian fluid flow; experimental data on non-Newtonian flow (internal and external); non-Newtonian fluid films.
Out of the many submitted papers, only six articles, dealing with power-law fluid and micropolar fluid, have been accepted. Because of time constraints, we had to close the submission deadline with the six articles for the special issue. The following articles have been published: “Modeling asymmetric flow of viscoelastic fluid in symmetric planar sudden expansion geometry based on user-defined function in FLUENT CFD package” by Z-Y. Zheng et al.; “Mixed convective heat transfer for MHD viscoelastic fluid flow over a porous wedge with thermal radiation” by M. M. Rashidi et al.; “Steady natural convection of non-Newtonian power-law fluid in a trapezoidal enclosure” by A. Sojoudi et al.; “Optimal solution of stagnation point flow of third grade fluid with Newtonian and Joules heating effects” by M. Nawaz et al.; “Non-Newtonian natural convection flow along a horizontal circular cylinder with uniform surface heat flux” by S. Bhowmick et al.; “Transient natural convection flow of thermo-micropolar fluid of micropolar thermal conductivity along a non-uniformly heated vertical surface” by M. Hossain et al.