scholarly journals Probe of Radiant Flow on Temperature-Dependent Viscosity Models of Differential Type MHD Fluid

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Azad Hussain ◽  
Sobia Akbar ◽  
Lubna Sarwar ◽  
Sohail Nadeem
Keyword(s):  
Numerical Solutions ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Porous Plate ◽  
Nonlinear Problems ◽  
Nonlinear Pdes ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Highly Nonlinear

This paper numerically investigates the combined effects of the radiation and MHD on the flow of a viscoelastic Walters’ B liquid fluid model past a porous plate with temperature-dependent variable viscosity. To study the effects of variable viscosity on the fluid model, the equations of continuity, momentum with magnetohydrodynamic term, and energy with radiation term have been expanded. To understand the phenomenon, Reynold’s model and Vogel’s model of variable viscosity are also incorporated. The dimensionless governing equations are two-dimensional coupled and highly nonlinear partial differential equations. The highly nonlinear PDEs are transferred into ODEs with the assistance of suitable transformations which are solved with the help of numerical techniques, namely, shooting technique coupled with Runge–Kutta method and BVP4c solution method for the numerical solutions of governing nonlinear problems. Viscosity is considered as a function of temperature. Skin friction coefficient and Nusselt number are investigated through tables and graphs in the present probe. The behavior of emerging parameters on the velocity and temperature profiles is studied with the help of graphs. For Reynold’s model, we have shrinking stream lines and increasing three-dimensional graphs. γ and Pr are reduced for both models.

scholarly journals A novel application of Lobatto IIIA solver for numerical treatment of mixed convection nanofluidic model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Iftikhar Ahmad ◽  
Tahir Nawaz Cheema ◽  
Muhammad Asif Zahoor Raja ◽  
Saeed Ehsan Awan ◽  
Norma Binti Alias ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Mixed Convection ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Temperature Dependent Viscosity ◽  
Numerical Computing

AbstractThe objective of the current investigation is to examine the influence of variable viscosity and transverse magnetic field on mixed convection fluid model through stretching sheet based on copper and silver nanoparticles by exploiting the strength of numerical computing via Lobatto IIIA solver. The nonlinear partial differential equations are changed into ordinary differential equations by means of similarity transformations procedure. A renewed finite difference based Lobatto IIIA method is incorporated to solve the fluidic system numerically. Vogel's model is considered to observe the influence of variable viscosity and applied oblique magnetic field with mixed convection along with temperature dependent viscosity. Graphical and numerical illustrations are presented to visualize the behavior of different sundry parameters of interest on velocity and temperature. Outcomes reflect that volumetric fraction of nanoparticles causes to increase the thermal conductivity of the fluid and the temperature enhances due to blade type copper nanoparticles. The convergence analysis on the accuracy to solve the problem is investigated viably though the residual errors with different tolerances to prove the worth of the solver. The temperature of the fluid accelerates due the blade type nanoparticles of copper and skin friction coefficient is reduced due to enhancement of Grashof Number.

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>

Elastic Effects on Rayleigh-Be´nard-Marangoni Convection in Liquids With Temperature-Dependent Viscosity

2009 ◽  
Author(s):  
G. N. Sekhar ◽  
G. Jayalatha
Keyword(s):  
Stress Relaxation ◽  
Variable Viscosity ◽  
Relaxation Parameter ◽  
Oscillatory Convection ◽  
Tight Coupling ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Viscoelastic Liquids ◽  
Retardation Parameter

A linear stability analysis of convection in viscoelastic liquids with temperature-dependent viscosity is studied using normal modes and Galerkin method. Stationary convection is shown to be the preferred mode of instability when the ratio of strain retardation parameter to stress relaxation parameter (elasticity ratio) is greater than unity. When the ratio is less than unity the possibility of oscillatory convection is shown to arise. Oscillatory convection is studied numerically for Rivlin-Ericksen, Walters B′, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. It is found that there is a tight coupling between the Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to Jeffreys description whereas the Rivlin-Ericksen and Walters B′ liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. The problem has applications in non-isothermal systems having viscoelastic liquids as working media.

Mathematical study for peristaltic flow of Williamson fluid in a curved channel

2015 ◽  
Vol 08 (01) ◽  
pp. 1550005 ◽  
Author(s):  
E. N. Maraj ◽  
Noreen Sher Akbar ◽  
S. Nadeem
Keyword(s):  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Curved Channel ◽  
Partial Differential ◽  
Williamson Fluid ◽  
Highly Nonlinear ◽  
Frame Transformation

In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

Flow of a Third Grade Fluid between Coaxial Cylinders with Variable Viscosity

2009 ◽  
Vol 64 (9-10) ◽  
pp. 588-596 ◽  
Author(s):  
Muhammad Y. Malik ◽  
Azad Hussain ◽  
Sohail Nadeem ◽  
Tasawar Hayat
Keyword(s):  
Variable Viscosity ◽  
Heat Transfer Analysis ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Coaxial Cylinders ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Dependent Viscosity

The influence of temperature dependent viscosity on the flow of a third grade fluid between two coaxial cylinders is carried out. The heat transfer analysis is further analyzed. Homotopy analysis method is employed in finding the series solutions. The effects of pertinent parameters have been explored by plotting graphs.

scholarly journals Effect of Porous Medium and Copper Heat Sink on Cooling of Heat-Generating Element

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2538 ◽  
Author(s):  
Marina Astanina ◽  
Mikhail Sheremet ◽  
U. S. Mahabaleshwar ◽  
Jitender Singh
Keyword(s):  
Energy Transport ◽  
Cooling System ◽  
Variable Viscosity ◽  
Optimal Number ◽  
Working Fluid ◽  
Heat Conducting ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Negative Effect ◽  
Dependent Viscosity

Cooling of heat-generating elements is a challenging problem in engineering. In this article, the transient free convection of a temperature-dependent viscosity liquid inside the porous cavity with copper radiator and the heat-generating element is studied using mathematical modeling techniques. The vertical and top walls of the chamber are kept at low constant temperature, while the bottom wall is kept adiabatic. The working fluid is a heat-conducting liquid with temperature-dependent viscosity. A mathematical model is developed based on dimensionless stream function, vorticity, and temperature variables. The governing properties are the variable viscosity, geometric parameters of the radiator, and size of thermally insulated strip on vertical surfaces of the cavity. The effect of these parameters on the energy transport and circulation patterns are analyzed numerically. Based on the numerical results obtained, recommendations are given on the optimal values of the governing parameters for the effective operation of the cooling system. It is shown that the optimal number of radiator fins for the cooling system configuration under consideration is 3. In addition, the thermal insulation of the vertical walls and the increased thickness of the radiator fins have a negative effect on the operation of the cooling system.

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.

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).

scholarly journals Temperature-Dependent Viscosity and Nanoparticle Effect on Wire Coating Using Third-Grade As a Polymer Liquid With Magnetic Field Flow Within Porous Die

2021 ◽  
Author(s):  
Zeeshan Khan ◽  
Prof. Dr. Ilyas Khan
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Numerical Technique ◽  
Wall Stress ◽  
Third Grade ◽  
Shear Forces ◽  
Temperature Dependent Viscosity ◽  
Wire Coating ◽  
Dependent Viscosity

Abstract The convective heat and mass propagation inside dies are used to determine the characteristics of coated wire products. As a result, comprehending the properties of polymerization mobility, heat mass transport, and wall stress concentration is crucial. The wire coating procedure necessitates an increase in thermal performance. As a result, this research aims to determine how floating nanoparticles affect the mass and heat transport mechanisms of third-grade fluid in the posttreatment for cable coating processes. For nanofluids, the Buongiorno model is used, including variable viscosity. The model equations are developed using continuity, momentum, energy, and nanoparticle volume fraction concentration. We propose a few nondimensional transformations that are relevant. The numerical technique Runge-Kutta fourth method is used to generate numerical solutions for nonlinear systems. Pictorial depictions are used to observe the influence of various factors in the nondimensional flow, radiative, and nanoparticle concentration fields. Furthermore, the numerical results are also verified analytically using Homotopy Analysis Method (HAM). The analytical findings of this investigation revealed that within the Reynolds modeling, the stress on the whole wire surface combined with shear forces at the surface predominates Vogel's model. The contribution of nanomaterials upon force on the entire surface of wire and shear forces at the surface appears positive. A non-Newtonian feature can increase the capping substance's velocity. This research could aid in the advancement of wire coating technologies.For the first instance, the significance of nanotechnology during wire coating evaluation is explored utilizing Brownian motion with generation/absorption slip processes. For time-dependent viscosity, two alternative models are useful.

Sign in / Sign up

Export Citation Format

Share Document