Analytical simulation of time dependent electromagneto-hydrodynamic flow of Williamson fluid due to oscillatory curved convectively heated Riga surface with variable thermal conductivity and diffusivity

Author(s):  
M. Naveed ◽  
Z. Abbas ◽  
M. Imran

The main objective of the present article is to provide an analytical simulation for time dependent boundary layer flow of non-Newtonian Williamson fluid due to stretchable curved oscillatory Riga surface. Also the characteristics of heat and mass transport are studied under the influence of variable thermal conductivity and diffusivity along with convective heat and mass boundary conditions. Additionally, energy equation is also characterized with the impact of heat production. Curvilinear coordinate scheme is followed to attain the boundary layer expressions for the flow model. The governing nonlinear partial differential equations are solved analytically via homotopy analysis method (HAM). Graphs are plotted to examine comprehensively the consequences of various concerned parameters like modified magnetic parameter and radius of curvature, Williamson fluid parameter, relation of the surface's oscillating frequency to its stretching rate constant, Prandtl number, variable conductivity and heat production parameters, Schmidt number and variable diffusivity parameter on concentration, temperature, pressure and velocity profile. Also the outcomes of afore said variables on surface drag force, rate of temperature and mass transmission (Nusselt and Sherwood numbers) are shown in tabular form. The liquid velocity amplitude is enhanced with modified magnetic parameter and shows opposite behavior for Williamson fluid parameter.

2002 ◽  
Vol 9 (3/4) ◽  
pp. 311-323 ◽  
Author(s):  
F. Dubuffet ◽  
D. A. Yuen ◽  
E. S. G. Rainey

Abstract. The thermal conductivity of mantle materials has two components, the lattice component klat from phonons and the radiative component krad due to photons. These two contributions of variable thermal conductivity have a nonlinear dependence in the temperature, thus endowing the temperature equation in mantle convection with a strongly nonlinear character. The temperature derivatives of these two mechanisms have different signs, with ∂klat /∂T negative and dkrad /dT positive. This offers the possibility for the radiative conductivity to control the chaotic boundary layer instabilities developed in the deep mantle. We have parameterized the weight factor between krad and klat with a dimensionless parameter f , where f = 1 corresponds to the reference conductivity model. We have carried out two-dimensional, time-dependent calculations for variable thermal conductivity but constant viscosity in an aspect-ratio 6 box for surface Rayleigh numbers between 106 and 5 × 106. The averaged Péclet < Pe > numbers of these flows lie between 200 and 2000. Along the boundary in f separating the chaotic and steady-state solutions, the < Pe > number decreases and the Nusselt number increases with internal heating, illustrating the feedback between internal heating and radiative thermal conductivity. For purely basal heating situation, the time-dependent chaotic flows become stabilized for values of f of between 1.5 and 2. The bottom thermal boundary layer thickens and the surface heat flow increases with larger amounts of radiative conductivity. For magnitudes of internal heating characteristic of a chondritic mantle, much larger values of f , exceeding 10, are required to quench the bottom boundary layer instabilities. By isolating the individual conductive mechanisms, we have ascertained that the lattice conductivity is partly responsible for inducing boundary layer instabilities, while the radiative conductivity and purely depth-dependent conductivity exert a stabilizing influence and help to control thermal chaos developed in the deep mantle. These results have been verified to exist also in three-dimensional geometry and would argue for the need to consider the potentially important role played by radiative thermal conductivity in controlling chaotic flows in time-dependent mantle convection, the mantle heat transfer, the number of hotspots and the attendant mixing of geochemical anomalies.


2020 ◽  
Vol 9 (1) ◽  
pp. 233-243 ◽  
Author(s):  
Nainaru Tarakaramu ◽  
P.V. Satya Narayana ◽  
Bhumarapu Venkateswarlu

AbstractThe present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu-water nanoparticles is more than that of Al2O3- water nanofluid. On the other hand, the axial velocity of the fluid in case of Al2O3- water nanofluid is more than that of TiO2nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.


2020 ◽  
Vol 9 (1) ◽  
pp. 338-351
Author(s):  
Usha Shankar ◽  
N. B. Naduvinamani ◽  
Hussain Basha

AbstractA two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with variable thermal conductivity and exterior squeezing with viscous dissipation effect is investigated, numerically. Present flow model is developed based on the considered flow geometry. Effect of Lorentz forces on flow behaviour is described in terms of magnetic field and which is accounted in momentum equation. Influence of variable thermal conductivity on heat transfer is considered in the energy equation. Present investigated problem gives the highly complicated nonlinear, unsteady governing flow equations and which are coupled in nature. Owing to the failure of analytical/direct techniques, the considered physical problem is solved by using Runge-Kutta scheme (RK-4) via similarity transformations approach. Graphs and tables are presented to describe the physical behaviour of various control parameters on flow phenomenon. Temperature boundary layer thickens for the amplifying value of Weissenberg parameter and permeable velocity parameter. Velocity profile decreased for the increasing squeezed flow index and permeable velocity parameter. Increasing magnetic number increases the velocity profile. Magnifying squeezed flow index magnifies the magnitude of Nusselt number. Also, RK-4 efficiently solves the highly complicated nonlinear complex equations that are arising in the fluid flow problems. The present results in this article are significantly matching with the published results in the literature.


Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 684
Author(s):  
Saeed Islam ◽  
Haroon Ur Rasheed ◽  
Kottakkaran Sooppy Nisar ◽  
Nawal A. Alshehri ◽  
Mohammed Zakarya

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.


2019 ◽  
Vol 103 ◽  
pp. 02001 ◽  
Author(s):  
Maatouk Khoukhi ◽  
Ahmed Hassan ◽  
Shaimaa Abdelbaqi

This paper illustrates the impact of embedding an insulation layer of variable thermal conductivity in a typical building wall on the cooling effect and energy performance. The evaluation was performed by applying a conjugate heat transfer model, which was tested in extremely hot conditions of Al Ain (UAE). The thermal performance of a building incorporating insulation layers of variable thermal conductivity (k-value) was compared to a non-variable thermal conductivity system by quantifying the additional heat transferred due to the k-relationship with time. The results show that, when the k-value is a function of operating temperature, its effects on the temperature profile through the wall assembly during daytime is significant compared with that obtained when a constant k-value for the polystyrene (EPS) insulation is adopted. A similar trend in the evolution of temperatures during the day and across the wall section was observed when EPS material with different moisture content was evaluated. For the polyurethane insulation, the inner surface temperature reached 44 °C when constant k-value was adopted, increasing to 48.5 °C when the k-value was allowed to vary under the same ambient conditions.


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