scholarly journals RK4 and HAM Solutions of Eyring–Powell Fluid Coating Material with Temperature-Dependent-Viscosity Impact of Porous Matrix on Wire Coating Filled in Coating Die: Cylindrical Co-Ordinates

Polymers ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3696
Author(s):  
Zeeshan Khan ◽  
Waris Khan ◽  
Ilyas Khan ◽  
Nawa Alshammari ◽  
Nawaf N. Hamadneh
Keyword(s):  
Variable Viscosity ◽  
Fluid Velocity ◽  
Porous Matrix ◽  
Transport Processes ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Flow Models ◽  
Boundary Layer Equations ◽  
Viscosity Parameter ◽  
Wire Coating

In this work, we studied the impacts of transmitting light, nonlinear thermal, and micropolar fluid mechanics on a wire surface coating utilizing non-Newtonian viscoelastic flow. Models with temperature-dependent variable viscosity were used. The boundary layer equations governing the flow and heat transport processes were solved using the Runge–Kutta fourth order method. A distinguished constituent of this study was the use of a porous matrix that acted as an insulator to reduce heat loss. In this paper we discuss the effects of numerous development parameters, including β0, Q, m, Ω, Kp, and Br (non-Newtonian parameter, heat-producing parameter, viscosity parameter, variable viscosity parameter, porosity parameter, and Brinkman number, respectively). Furthermore, the effects of two other parameters, D and M, are also discussed as they relate to velocity and temperature distributions. We observed that the velocity profiles decreased with increasing values of Kp. Fluid velocity increased as the values of M, Br, N, and D increased, while it decreased when the values of Kp, Q, and D increased. For increasing values of M, the temperature profile showed increasing behavior, while Br and Q showed decreasing behavior. Furthermore, the present work is validated by comparison with HAM and previously published work, with good results.

scholarly journals Effect of radiation with temperature dependent viscosity and thermal conductivity on unsteady a stretching sheet through porous media

2010 ◽  
Vol 15 (3) ◽  
pp. 257-270 ◽  
Author(s):  
M. M. M. Abdou
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Porous Media ◽  
Stretching Sheet ◽  
Variable Viscosity ◽  
Darcy Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Boundary Layer Equations ◽  
Dependent Viscosity

A numerical model is developed to study the effect of thermal radiation on unsteady boundary layer flow with temperature dependent viscosity and thermal conductivity due to a stretching sheet in porous media. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing equations reduced to similarity boundary layer equations using suitable transformations and then solved using the Runge–Kutta numerical integration, procedure in conjunction with shooting technique. A parametric study illustrating the influence of the radiation R, variable viscosity ε, Darcy number Da, porous media inertia coefficient γ, thermal conductivity κ and unsteady A parameters on skin friction and Nusselt number.

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.

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.

Theoretical Solutions for Combined Forced and Free Convection in Horizontal Tubes with Temperature-Dependent Viscosity

1976 ◽  
Vol 98 (3) ◽  
pp. 459-465 ◽  
Author(s):  
S. W. Hong ◽  
A. E. Bergles
Keyword(s):  
Circular Tube ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Flux Boundary Condition ◽  
Viscosity Parameter ◽  
Horizontal Tubes ◽  
Constant Viscosity ◽  
Heat Flux Boundary Condition ◽  
Dependent Viscosity ◽  
Good Agreement

A boundary layer solution is presented for fully developed laminar flow in a horizontal circular tube, assuming large Prandtl number and temperature-dependent viscosity and density. The solution is given by Nu = C1 Ra1/4, where C1 is a function of a nondimensional viscosity parameter and the heat flux boundary condition. The heat transfer predictions for large values of the viscosity parameter are 50 percent above the constant viscosity predictions. The present analysis is in good agreement with experimental data for water and ethylene glycol flowing in electrically heated tubes which approximate the boundary conditions assumed in the analysis.

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.

scholarly journals Heat Transfer Effect on Viscoelastic Fluid Used as a Coating Material for Wire with Variable Viscosity

Coatings ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 163 ◽  
Author(s):  
Zeeshan Khan ◽  
Haroon Ur Rasheed ◽  
Saeed Islam ◽  
Sahib Noor ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Heat Dissipation ◽  
Variable Viscosity ◽  
Numerical Technique ◽  
Mhd Flow ◽  
Temperature Dependent ◽  
Thermal Generation ◽  
Viscosity Models ◽  
Wire Coating ◽  
Source Sink ◽  
The Impact

This article examines a wire coating technique using a viscoelastic Eyring–Powell fluid in which magnetohydrodynamic (MHD) flow, thermal transfer, and Joule heating effects are studied. Temperature-dependent, variable-viscosity models are used. Flexible-viscosity models which are temperature dependent are also considered. The interface of the thermal boundary layer which describe the flux and thermal convection phenomena, are evaluated by using a dominant numerical technique known as the fourth-order Runge–Kutta method. In particular, this article takes into account the impact of a permeable matrix which behaves like a dielectric in order to avoid heat dissipation. The effect of thermal generation is also explained, since it controls power. The novel effects for the numerous parameters which affect the velocity and temperature profiles on the wire coating process are investigated through graphs explained in detail. These include non-Newtonian, hydromagnetic, permeability, and heat source/sink effects. For validation purposes, the numerical scheme is also compared with a semi-numerical technique HAM and BVPh2 software, and found a closed agreement with the numerical results.

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.

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