Mathematical Analysis of Jeffrey Fluid Flow with Heat Transfer
Keywords:
Non-Newtonian Fluid, Boundary Layer Flow, Similarity Transformation, Viscoelastic FluidAbstract
The non-Newtonian fluid models play an important role to describe the complex rheological characteristics of industrial, biological and engineering fluids which cannot be quantitatively described by the classical Newtonian constitutive law. The Jeffrey fluid model, among others, has attracted great interest due to its ability to account for relaxation and retardation effects while still being easy to understand. The present work provides a mathematical analysis of the steady flow of Jeffrey fluid with heat transfer over a stretching surface. The equations are based on conservation of mass, momentum and energy and the Jeffrey constitutive relation. The different similarity transformations are used to turn nonlinear partial differential equations into coupled nonlinear ordinary differential equations. We investigate the effects of various dimensionless parameters such as the Jeffrey parameter, Deborah number, Reynolds number, and Prandtl number on the velocity and temperature distributions. We also discuss the presence of physically relevant solutions, qualitative stability and the effect of thermal transport on fluid behavior. We particularly discuss the momentum and thermal boundary layer and how heat transfer affects fluid motion at different rheological conditions. The mathematical formulation is applied to practical applications in polymer processing, lubrication systems, biomedical fluid transport, food industry and chemical industry, where viscoelastic fluids are frequently experienced. As well, the limitations of the classical Jeffrey fluid model are discussed and the areas of future research are discussed, such as fractional order formulation, magnetohydrodynamic effects, nanofluid transport, porous media and machine learning based parameter estimation.
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