Numerical study of unsteady flow and heat transfer CNT-based MHD nanofluid with variable viscosity over a permeable shrinking surface

2019 ◽  
Vol 29 (12) ◽  
pp. 4607-4623 ◽  
Author(s):  
Zahid Ahmed ◽  
Sohail Nadeem ◽  
Salman Saleem ◽  
Rahmat Ellahi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Variable Viscosity ◽  
Numerical Study ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Content Type ◽  
Non Linear ◽  
Dependent Viscosity ◽  
Shrinking Surface

Purpose The purpose of this paper is to present a novel model on the unsteady MHD flow of heat transfer in carbon nanotubes with variable viscosity over a shrinking surface. Design/methodology/approach The temperature-dependent viscosity makes the proposed model non-linear and coupled. Consequently, the resulting non-linear partial differential equations are first reformed into set of ordinary differential equations through appropriate transformations and boundary layer approximation and are then solved numerically by the Keller box method. Findings Graphical and numerical results are executed keeping temperature-dependent viscosity of nanofluid. It is noted that, for diverse critical points, it is found that at one side of these critical values, multiple solutions exist; on the other side, no solution exists. A comparison is also computed for the special case of existing study. The temperature and pressure profiles are also plotted for various effective parameters. Originality/value The work is original.

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.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

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 Numerical Study for the Effects of Temperature Dependent Viscosity Flow of Non-Newtonian Fluid with Double Stratification

2020 ◽  
Vol 10 (2) ◽  
pp. 708 ◽  
Author(s):  
Hafiz Abdul Wahab ◽  
Hussan Zeb ◽  
Saira Bhatti ◽  
Muhammad Gulistan ◽  
Seifedine Kadry ◽  
...  
Keyword(s):  
Newtonian Fluid ◽  
Numerical Study ◽  
Mathematical Formulation ◽  
Nano Particles ◽  
Physical Parameters ◽  
Concentration Profiles ◽  
Temperature Dependent ◽  
Double Stratification ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

The main aim of the current study is to determine the effects of the temperature dependent viscosity and thermal conductivity on magnetohydrodynamics (MHD) flow of a non-Newtonian fluid over a nonlinear stretching sheet. The viscosity of the fluid depends on stratifications. Moreover, Powell–Eyring fluid is electrically conducted subject to a non-uniform applied magnetic field. Assume a small magnetic reynolds number and boundary layer approximation are applied in the mathematical formulation. Zero nano-particles mass flux condition to the sheet is considered. The governing model is transformed into the system of nonlinear Ordinary Differential Equation (ODE) system by using suitable transformations so-called similarity transformation. In order to calculate the solution of the problem, we use the higher order convergence method, so-called shooting method followed by Runge-Kutta Fehlberg (RK45) method. The impacts of different physical parameters on velocity, temperature and concentration profiles are analyzed and discussed. The parameters of engineering interest, i.e., skin fraction, Nusselt and Sherwood numbers are studied numerically as well. We concluded that the velocity profile decreases by increasing the values of S t , H and M. Also, we have analyzed the variation of temperature and concentration profiles for different physical parameters.

Crosswise stream of methanol–iron oxide (CH3OH–Fe3O4) with temperature-dependent viscosity and suction/injection effects

2019 ◽  
Vol 233 (5) ◽  
pp. 1013-1023 ◽  
Author(s):  
Rabil Tabassum ◽  
R Mehmood
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Treatment Plant ◽  
Exponential Model ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Coating Materials ◽  
Similarity Transformations ◽  
Dependent Viscosity ◽  
Energy Equations

Manufacturing of modern coating materials doped with magnetic nanoparticles has arisen as an exciting new area of materials processing fluid dynamics. Methanol is primarily used in chemical manufacturing, specialized vehicles fuel, energy carrier, as an antifreeze in pipelines, in wastewater treatment plant, and many more. In this article, a mathematical model is therefore developed to study crosswise flow of methanol-based ferromagnetic fluid through a permeable medium with suction/injection effects. Temperature-dependent viscosity is taken with Reynolds exponential model. The Tiwari–Das and Maxwell–Garnett nanofluid models are used, which alters the electrical conductivity, density, and thermal conductivity properties with nanoparticle volume fraction. The two-dimensional mass, momentum, and energy equations are normalized into nonlinear system comprising ordinary differential equations via appropriate similarity transformations. The solution of the emerging physical problem is attained by shooting scheme in MATLAB symbolic software. Validation of the results is presented through comparison with previously reported literature in the limiting sense. The influence of pertinent parameters on the flow and heat transfer characteristics is revealed through graphs. It is found that velocity profiles are suppressed with greater magnetic parameter and porosity parameters but temperature profile is enhanced. Velocity and temperature profiles for injection case are higher when compared with the suction phenomenon. Shear stress at the wall is decreased with volume fraction. Heat transfer gradient at the wall is significantly enhanced with volume fraction.

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