scholarly journals MHD Boundary Layer Flow of Carreau Fluid over a Convectively Heated Bidirectional Sheet with Non-Fourier Heat Flux and Variable Thermal Conductivity

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 618 ◽  
Author(s):  
Dianchen Lu ◽  
Mutaz Mohammad ◽  
Muhammad Ramzan ◽  
Muhammad Bilal ◽  
Fares Howari ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Flux ◽  
Numerical Solutions ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Close Correlation ◽  
Variable Thermal Conductivity ◽  
Carreau Fluid ◽  
Boundary Layer Problem

In the present exploration, instead of the more customary parabolic Fourier law, we have adopted the hyperbolic Cattaneo–Christov (C–C) heat flux model to jump over the major hurdle of “parabolic energy equation”. The more realistic three-dimensional Carreau fluid flow analysis is conducted in attendance of temperature-dependent thermal conductivity. The other salient impacts affecting the considered model are the homogeneous-heterogeneous (h-h) reactions and magnetohydrodynamic (MHD). The boundary conditions supporting the problem are convective heat and of h-h reactions. The considered boundary layer problem is addressed via similarity transformations to obtain the system of coupled differential equations. The numerical solutions are attained by undertaking the MATLAB built-in function bvp4c. To comprehend the consequences of assorted parameters on involved distributions, different graphs are plotted and are accompanied by requisite discussions in the light of their physical significance. To substantiate the presented results, a comparison to the already conducted problem is also given. It is envisaged that there is a close correlation between the two results. This shows that dependable results are being submitted. It is noticed that h-h reactions depict an opposite behavior versus concentration profile. Moreover, the temperature of the fluid augments for higher values of thermal conductivity parameters.

Homotopy Analysis Method for Variable Thermal Conductivity Heat Flux Gage with Edge Contact Resistance

2010 ◽  
Vol 65 (10) ◽  
pp. 771-776 ◽  
Author(s):  
Abdul Aziz ◽  
Farzad Khani ◽  
Mohammad Taghi Darvishi
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Contact Resistance ◽  
Homotopy Analysis Method ◽  
Heat Sink ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Radiation Emission ◽  
Homotopy Analysis

The homotopy analysis method (HAM) has been used to develop an analytical solution for the thermal performance of a circular-thin-foil heat flux gage with temperature dependent thermal conductivity and thermal contact resistance between the edge of the foil and the heat sink. Temperature distributions in the foil are presented illustrating the effect of incident heat flux, radiation emission from the foil, variable thermal conductivity, and contact resistance between the foil and the heat sink. The HAM results agree up to four places of decimal with the numerical solutions generated using the symbolic algebra package Maple. This close comparison vouches for the high accuracy and stability of the analytic solution.

scholarly journals Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet

2020 ◽  
Vol 9 (1) ◽  
pp. 233-243 ◽  
Author(s):  
Nainaru Tarakaramu ◽  
P.V. Satya Narayana ◽  
Bhumarapu Venkateswarlu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Variable Thermal Conductivity ◽  
Normal Velocity ◽  
Transfer Coefficients ◽  
Similarity Transformations ◽  
Frictional Coefficients ◽  
The Impact

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.

Generation of steady longitudinal vortices in hypersonic boundary layer

2013 ◽  
Vol 729 ◽  
pp. 702-731 ◽  
Author(s):  
A. I. Ruban ◽  
M. A. Kravtsova
Keyword(s):  
Boundary Layer ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Viscosity Coefficient ◽  
Momentum Equation ◽  
The Body ◽  
Nonlinear Behaviour ◽  
Hypersonic Boundary Layer ◽  
Stagnation Temperature ◽  
Characteristic Distance

AbstractIn this paper we study the three-dimensional perturbations produced in a hypersonic boundary layer by a small wall roughness. The flow analysis is performed under the assumption that the Reynolds number, $R{e}_{0} = {\rho }_{\infty } {V}_{\infty } L/ {\mu }_{0} $, and Mach number, ${M}_{\infty } = {V}_{\infty } / {a}_{\infty } $, are large, but the hypersonic interaction parameter, $\chi = { M}_{\infty }^{2} R{ e}_{0}^{- 1/ 2} $, is small. Here ${V}_{\infty } $, ${\rho }_{\infty } $ and ${a}_{\infty } $ are the flow velocity, gas density and speed of sound in the free stream, ${\mu }_{0} $ is the dynamic viscosity coefficient at the ‘stagnation temperature’, and $L$ is the characteristic distance the boundary layer develops along the body surface before encountering a roughness. We choose the longitudinal and spanwise dimensions of the roughness to be $O({\chi }^{3/ 4} )$ quantities. In this case the flow field around the roughness may be described in the framework of the hypersonic viscous–inviscid interaction theory, also known as the triple-deck model. Our main interest in this paper is the nonlinear behaviour of the perturbations. We study these by means of numerical solution of the triple-deck equations, for which purpose a modification of the ‘skewed shear’ technique suggested by Smith (United Technologies Research Center Tech. Rep. 83-46, 1983) has been used. The technique requires global iterations to adjust the viscous and inviscid parts of the flow. Convergence of such iterations is known to be a major problem in viscous–inviscid calculations. In order to achieve improved stability of the method, both the momentum equation for the viscous part of the flow, and the equations describing the interaction with the flow outside the boundary layer, are treated implicitly in this study. The calculations confirm the fact that in this sort of flow the perturbations are capable of propagating upstream in the boundary layer, resulting in a perturbation field which surrounds the roughness on all sides. We found that the perturbations decay rather fast with the distance from the roughness everywhere except in the wake behind the roughness. We found that if the height of the roughness is small, then the perturbations also decay in the wake, though much more slowly than outside the wake. However, if the roughness height exceeds some critical value, then two symmetric counter-rotating vortices form in the wake. They appear to support themselves and grow as the distance from the roughness increases.

Boundary layer at a swept stagnation line of semi-infinite extent

1970 ◽  
Vol 41 (4) ◽  
pp. 737-750 ◽  
Author(s):  
Paul A. Libby ◽  
Karl K. Chen
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Cross Flow ◽  
Differential Analysis ◽  
Eigenvalues And Eigenfunctions ◽  
Stagnation Line ◽  
Infinite Extent ◽  
Dimensional Boundary ◽  
Upstream Flow

A three-dimensional boundary layer developing along a semi-infinite swept stagnation line from a starting edge and evolving into that associated with such a line of infinite extent is calculated. A series solution useful for assessing the counteracting effects of cross-flow and mass transfer near the starting edge and for providing initial data for a subsequent streamwise, numerical solution is developed. The asymptotic behaviour far from the starting edge is examined and shown to involve only eigenfunction contributions associated with the far upstream flow. However, it is not presently possible to determine the relevant eigenvalues and eigenfunctions. Numerical solutions based on a difference-differential analysis yield the entire development of the boundary layer and indicate the streamwise length required for the case of the boundary layer at an infinite stagnation line to be obtained.

scholarly journals Midwinter Arctic leads form and dissipate low clouds

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Xia Li ◽  
Steven K. Krueger ◽  
Courtenay Strong ◽  
Gerald G. Mace ◽  
Sally Benson
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Sensible Heat Flux ◽  
Three Dimensional ◽  
The Arctic ◽  
Substantial Contribution ◽  
Boundary Layer Clouds ◽  
Low Clouds ◽  
Arctic Ice ◽  
High Lead

AbstractLeads are a key feature of the Arctic ice pack during the winter owing to their substantial contribution to the surface energy balance. According to the present understanding, enhanced heat and moisture fluxes from high lead concentrations tend to produce more boundary layer clouds. However, described here in our composite analyses of diverse surface- and satellite-based observations, we find that abundant boundary layer clouds are associated with low lead flux periods, while fewer boundary layer clouds are observed for high lead flux periods. Motivated by these counterintuitive results, we conducted three-dimensional cloud-resolving simulations to investigate the underlying physics. We find that newly frozen leads with large sensible heat flux but low latent heat flux tend to dissipate low clouds. This finding indicates that the observed high lead fractions likely consist of mostly newly frozen leads that reduce any pre-existing low-level cloudiness, which in turn decreases downwelling infrared flux and accelerates the freezing of sea ice.

Inverse Determination of Temperature-Dependent Thermal Conductivity Using Steady Surface Data on Arbitrary Objects

2000 ◽  
Vol 122 (3) ◽  
pp. 450-459 ◽  
Author(s):  
T. J. Martin ◽  
G. S. Dulikravich
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Steady State ◽  
Measurement Errors ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Computational Procedure ◽  
Heat Fluxes ◽  
Computational Method ◽  
Transfer Coefficients

An inverse computational method has been developed for the nonintrusive and nondestructive evaluation of the temperature-dependence of thermal conductivity. The methodology is based on an inverse computational procedure that can be used in conjunction with an experiment. Given steady-state heat flux measurements or convection heat transfer coefficients on the surface of the specimen, in addition to a finite number of steady-state surface temperature measurements, the algorithm can predict the variation of thermal conductivity over the entire range of measured temperatures. Thus, this method requires only one temperature probe and one heat flux probe. The thermal conductivity dependence on temperature (k-T curve) can be completely arbitrary, although a priori knowledge of the general form of the k-T curve substantially improves the accuracy of the algorithm. The influence of errors of measured surface temperatures and heat fluxes on the predicted thermal conductivity has been evaluated. It was found that measurement errors of temperature up to five percent standard deviation were not magnified by this inverse procedure, while the effect of errors in measured heat fluxes were even lower. The method is applicable to two-dimensional and three-dimensional solids of arbitrary shape and size. [S0022-1481(00)01703-5]

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