scholarly journals Influence of Viscous Dissipation on the Exiting Sheet Thickness in the Calendering of Newtonian Fluids

2020 ◽  
Vol 7 ◽  
Keyword(s):  
Mathematical Problem ◽  
Sheet Thickness ◽  
Newtonian Fluids ◽  
Temperature Fields ◽  
Balance Equations ◽  
Initial Thickness ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Velocity Pressure

In this work we treat theoretically the calendering process of Newtonian fluids with finite sheet initial thickness, taking into account that the viscosity of the fluid is a welldefined function of the temperature. We predict the influence of the temperature-dependent viscosity on the exiting sheet thickness in the calendering process. The mass, momentum and energy balance equations, based on the lubrication theory, were nondimensionalized and solved for the velocity, pressure and temperature fields by using perturbation and numerical techniques, where the exiting sheet thickness represents an eigenvalue of the mathematical problem. The numerical results show that the inclusion of temperature-dependent viscosity effect reduces about 20% the leave-off distance in comparison with the case of temperature-independent viscosity.

Effects of Temperature-Dependent Viscosity Variations and Boundary Conditions on Fully Developed Laminar Forced Convection in a Semicircular Duct

1998 ◽  
Vol 120 (3) ◽  
pp. 600-605 ◽  
Author(s):  
T. M. Harms ◽  
M. A. Jog ◽  
R. M. Manglik
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Numerical Solutions ◽  
Strong Dependence ◽  
Laminar Flows ◽  
Temperature Fields ◽  
Traditional Values ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

Fully developed laminar flows in a semicircular duct with temperature-dependent viscosity variations in the flow cross section are analyzed, where the viscosity-temperature behavior is described by the Arrhenius model. Both the T and H1 boundary conditions are considered, as they represent the most fundamental heating/cooling conditions encountered in practical compact heat exchanger applications. Numerical solutions for the flow velocity and the temperature fields have been obtained by finite difference technique. The friction factor and Nusselt number results display a strong dependence on the viscosity ratio (μw/μb), and this is correlated using the classical power-law relationship. However, results indicate that the power-law exponents are significantly different from traditional values for circular tube. They are found to be functions of the flow geometry, boundary condition, and direction of heat transfer (heating or cooling).

On MHD unsteady reactive Couette flow with heat transfer and variable properties

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Oluwole Makinde ◽  
Oswald Franks
Keyword(s):  
Couette Flow ◽  
Nonlinear Differential Equations ◽  
Exothermic Reaction ◽  
Temperature Fields ◽  
Integration Scheme ◽  
Variable Properties ◽  
Temperature Dependent ◽  
Arrhenius Kinetics ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

AbstractThis study is devoted to investigate the effect of magnetic field on a reactive unsteady generalized Couette flow with temperature dependent viscosity and thermal conductivity. It is assumed that conducting incompressible fluid is subjected to an exothermic reaction under Arrhenius kinetics, neglecting the consumption of the material. The model nonlinear differential equations governing the transient momentum and energy balance are obtained and tackled numerically using a semi-discretization finite difference technique coupled with Runge-Kutta Fehlberg integration scheme. Important properties of the velocity and temperature fields including thermal stability conditions are presented graphically and discussed quantitatively.

New Theory for Forced Convection Through Porous Media by Fluids With Temperature-Dependent Viscosity

2001 ◽  
Vol 123 (6) ◽  
pp. 1045-1051 ◽  
Author(s):  
Arunn Narasimhan ◽  
Jose´ L. Lage ◽  
Donald A. Nield
Keyword(s):  
Pressure Drop ◽  
Numerical Results ◽  
Balance Equations ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Flow Models ◽  
Nusselt Numbers ◽  
Conventional Procedure ◽  
Viscosity Variation ◽  
Dependent Viscosity

A theoretical analysis is performed to predict the effects of a fluid with temperature-dependent viscosity flowing through an isoflux-bounded porous medium channel. For validation purposes, the thermo-hydraulic behavior of this system is obtained also by solving numerically the differential balance equations. The conventional procedure for predicting the numerical pressure-drop along the channel by using the global Hazen-Dupuit-Darcy (HDD) model (also known as the Forchheimer-extended Darcy model), with a representative viscosity for the channel calculated at maximum or minimum fluid temperatures, is shown to fail drastically. Alternatively, new predictive theoretical global pressure-drop equations are obtained using the differential form of the HDD model, and validated against the numerical results. Heat transfer results from the new theory, in the form of Nusselt numbers, are compared with earlier results for Darcy flow models (with and without viscosity variation), and validated by using the numerical results. Limitations of the new theory are highlighted and discussed.

Temperature-Dependent Viscosity and Prandtl Number Effects on Natural Convection Methanol Boundary Layers about a Vertical Plate with Injection

2020 ◽  
pp. 218-223
Author(s):  
Roopadevi K.N. ◽  
A.T. Eswara
Keyword(s):  
Prandtl Number ◽  
Nonlinear Partial Differential Equations ◽  
Porous Plate ◽  
Temperature Fields ◽  
Effect Of Temperature ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Implicit Finite Difference Scheme ◽  
Natural Laminar Flow ◽  
Dependent Viscosity

<p>The present study deals with the effect of temperature-dependent viscosity and Prandtl number on the steady, natural, laminar flow of methanol past a vertical porous plate with injection. The coupled nonlinear partial differential equations governing the non-similar flow have been solved numerically using an implicit finite-difference scheme along with the quasilinearization technique. Numerical results indicate that temperature-dependent viscosity and Prandtl number, both have a major role on skin friction and heat transfer parameters as well as velocity and temperature fields.</p>

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