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).

Entrance, Viscous Dissipation and Temperature Dependent Viscosity Effects in Microchannel Flows With Convective Boundary Conditions

2006 ◽  
Author(s):  
C. Nonino ◽  
S. Del Giudice ◽  
S. Savino
Keyword(s):  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Circular Cross Section ◽  
Laminar Flows ◽  
Projection Algorithm ◽  
Convective Boundary Conditions ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Convective Boundary ◽  
Dependent Viscosity

The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of circular cross-section are studied with reference to convective boundary conditions. Viscosity is assumed to vary linearly with temperature, in order to allow a parametric investigation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for three different values of the Biot number. Examples of temperature profiles at different axial locations are also shown.

Temperature-Dependent Viscosity and Viscous Dissipation Effects in Simultaneously Developing Flows in Microchannels With Convective Boundary Conditions

2006 ◽  
Vol 129 (9) ◽  
pp. 1187-1194 ◽  
Author(s):  
C. Nonino ◽  
S. Del Giudice ◽  
S. Savino
Keyword(s):  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Laminar Flows ◽  
Projection Algorithm ◽  
Convective Boundary Conditions ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Convective Boundary ◽  
Radial Temperature ◽  
Dependent Viscosity

The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels are studied with reference to convective boundary conditions. Two different geometries, namely the circular tube and the parallel plate channel, are considered. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for two different values of the Biot number. Examples of radial temperature profiles at different axial locations and of axial distributions of centerline velocity and temperature are also shown.

Heat and Mass Transfer of Temperature-Dependent Viscosity Models in a Pipe: Effects of Thermal Radiation and Heat Generation

2020 ◽  
Vol 75 (3) ◽  
pp. 225-239 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Mubbashar Nazeer ◽  
Mubashara Saeed ◽  
Adila Saleem ◽  
Waqas Ali
Keyword(s):  
Thermal Radiation ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Physical Property ◽  
Solid Particles ◽  
Temperature Fields ◽  
Fluid Temperature ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Increasing Trends

AbstractIn this paper, a study of the flow of Eyring-Powell (EP) fluid in an infinite circular long pipe under the consideration of heat generation and thermal radiation is considered. It is assumed that the viscosity of the fluid is an exponential function of the temperature of the fluid. The flow of fluid depends on many variables, such as the physical property of each phase and shape of solid particles. To convert the given governing equations into dimensionless form, the dimensionless quantities have been used and the resultant boundary value problem is solved for the calculation of velocity and temperature fields. The analytical solutions of velocity and temperature are calculated with the help of the perturbation method. The effects of the fluidic parameters on velocity and temperature are discussed in detail. Finite difference method is employed to find the numerical solutions and compared with the analytical solution. The magnitude error in velocity and temperature is obtained in each case of the viscosity model and plotted against the radius of the pipe. Graphs are plotted to describe the influence of various parameter EP parameters, heat generation parameter and thermal radiation parameters against velocity and temperature profiles. The fluid temperature has decreasing and increasing trends with respect to radiation and heat generations parameters, respectively.

Buoyancy-driven convection in cylindrical geometries

1969 ◽  
Vol 36 (2) ◽  
pp. 239-258 ◽  
Author(s):  
S. F. Liang ◽  
A. Vidal ◽  
Andreas Acrivos
Keyword(s):  
Numerical Solutions ◽  
Perturbation Expansion ◽  
Boussinesq Equations ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cylindrical Cell ◽  
Prandtl Numbers ◽  
Buoyancy Driven Convection ◽  
Dependent Viscosity ◽  
Rayleigh Numbers

Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state régimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes.Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical régime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur.Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.

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.

Entrance, Viscous Dissipation and Temperature Dependent Viscosity Effects on the Laminar Forced Convection in Straight Microchannels With Uniform Wall Heat Flux

2008 ◽  
Author(s):  
C. Nonino ◽  
S. Savino ◽  
S. Del Giudice
Keyword(s):  
Heat Flux ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Laminar Flows ◽  
Uniform Heat Flux ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Wide Range ◽  
Dependent Viscosity ◽  
Laminar Forced Convection

A parametric investigation is carried out on the effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Reference is made to fluid heating conditions with a uniform heat flux imposed on the walls of the microchannels. Three different cross-sectional geometries are considered, chosen among those usually adopted for microchannels (rectangular, trapezoidal and hexagonal). Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Due to the high value of the ratio between the total length and the hydraulic diameter in microchannels, such an approach is very advantageous with respect to the one based on the steady-state solution of the elliptic form of the governing equations in a three-dimensional domain corresponding to the whole duct. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented. Numerical results confirm that, in the laminar forced convection in the entrance region of straight microchannels, the effects of viscous dissipation and temperature dependent viscosity cannot be neglected in a wide range of operative conditions.

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.

scholarly journals Rayleigh-Bénard Convection of Non-Newtonian Power-Law Fluids with Temperature-Dependent Viscosity

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kaddiri ◽  
Mohamed Naïmi ◽  
Abdelghani Raji ◽  
Mohammed Hasnaoui
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Bénard Convection ◽  
Benard Convection ◽  
Power Law Fluids ◽  
Dependent Viscosity ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Two-dimensional steady-state Rayleigh-Bénard convection of thermodependent power-law fluids confined in a square cavity, heated from the bottom and cooled on the top with uniform heat fluxes, has been conducted numerically using a finite difference technique. The effects of the governing parameters, which are the Pearson number (0≤m≤10), the flow behaviour index (0.6≤n≤1.4), and the Rayleigh number (0<Ra≤105), on the flow onset, flow structure, and heat transfer have been examined. The heatlines concept has been used to explain the heat transfer deterioration due to temperature-dependent viscosity effect that m expresses.

Sign in / Sign up

Export Citation Format

Share Document