Chemically-reacting fluids with variable transport properties

Abstract In this paper we study the flow and heat transfer in a chemically-reacting fluid, whose transport properties, i.e., viscosity, thermal conductivity and the diffusion coefficients, are assumed to be a function of the concentration. The equations for the shearing flow of such a fluid between two long horizontal parallel plates, which are at different temperatures, are made dimensionless and the boundary value problem is solved numerically; the velocity, concentration and temperature profiles are obtained for various dimensionless numbers.

[1]  Van C. Mow,et al.  Rheological Equations for Synovial Fluids , 1978 .

[2]  M. Massoudi,et al.  Flow of a non‐linear (density‐gradient‐dependent) viscous fluid with heat generation, viscous dissipation and radiation , 2008 .

[3]  Peter Haupt,et al.  Continuum Mechanics and Theory of Materials , 1999 .

[4]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[5]  Ingo Müller,et al.  On the entropy inequality , 1967 .

[6]  R. Larson The Structure and Rheology of Complex Fluids , 1998 .

[7]  Jaroslav Hron,et al.  On the Modeling of the Synovial Fluid , 2010 .

[8]  J.J. Shea,et al.  Rheology of Polymeric Systems , 1998, IEEE Electrical Insulation Magazine.

[9]  Kumbakonam R. Rajagopal,et al.  Mechanics of Mixtures , 1995 .

[10]  J. Lumley,et al.  Mechanics of non-Newtonian fluids , 1978 .

[11]  A. K. Uguz,et al.  Heat transfer and Couette flow of a chemically reacting non‐linear fluid , 2009 .

[12]  An approach to non-Newtonian fluid mechanics , 1984 .

[13]  Kumbakonam R. Rajagopal,et al.  On implicit constitutive theories for fluids , 2006, Journal of Fluid Mechanics.

[14]  R. Batra Elements of Continuum Mechanics , 2005 .

[15]  Mehrdad Massoudi,et al.  On the heat flux vector for flowing granular materials—part II: derivation and special cases , 2006 .

[16]  Mehrdad Massoudi,et al.  A note on the meaning of mixture viscosity using the classical continuum theories of mixtures , 2008 .

[17]  D. E. Rosner,et al.  Transport Processes in Chemically Reacting Flow Systems , 1986 .

[18]  Mehrdad Massoudi,et al.  On the heat flux vector for flowing granular materials—Part I: effective thermal conductivity and background , 2006 .

[19]  K. R. Rajagopal,et al.  Pulsatile Flow of a Chemically-Reacting Nonlinear Fluid , 2006, Comput. Math. Appl..

[20]  P. Glarborg,et al.  Chemically Reacting Flow : Theory and Practice , 2003 .

[21]  Mehrdad Massoudi,et al.  Flow of a generalized second grade fluid between heated plates , 1993 .

[22]  Mehrdad Massoudi,et al.  Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe , 1995 .

[23]  J. Rodrigues,et al.  On the stationary Boussinesq-Stefan problem with constitutive power-laws , 1998 .

[24]  Mehrdad Massoudi,et al.  A Mixture Theory formulation for hydraulic or pneumatic transport of solid particles , 2010 .

[25]  D. E. Carlson,et al.  An introduction to thermomechanics , 1983 .

[26]  R. Rivlin,et al.  Stress-Deformation Relations for Isotropic Materials , 1955 .

[27]  Satish Karra,et al.  On modeling the response of the synovial fluid: Unsteady flow of a shear-thinning, chemically-reacting fluid mixture , 2010, Comput. Math. Appl..

[28]  K. Rajagopal,et al.  On the Oberbeck–Boussinesq approximation for fluids with pressure dependent viscosities , 2009 .

[29]  J. E. Dunn,et al.  Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade , 1974 .

[30]  Jay D. Humphrey,et al.  A CONSTRAINED MIXTURE MODEL FOR GROWTH AND REMODELING OF SOFT TISSUES , 2002 .

[31]  S. Middleman,et al.  Fundamentals of polymer processing , 1977 .

[32]  John C. Slattery,et al.  Advanced transport phenomena , 1999 .