Nonlinear Dynamics of Cattaneo–Christov Heat Flux Model for Third-Grade Power-Law Fluid

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Bhuvnesh Sharma ◽  
Sunil Kumar ◽  
Carlo Cattani ◽  
Dumitru Baleanu
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Power Law ◽  
Shear Thinning ◽  
Third Grade ◽  
Power Law Fluid ◽  
Conservation Of Energy ◽  
Flux Model ◽  
The Impact ◽  
Heat Flux Model

Abstract A rigorous analysis of coupled nonlinear equations for third-grade viscoelastic power-law non-Newtonian fluid is presented. Initially, the governing partial differential equations for conservation of energy and momentum are transformed to nonlinear coupled ordinary differential equations using exact similarity transformations which are known as Cattaneo–Christov heat flux model for third-grade power-law fluid. The homotopy analysis method (HAM) is utilized to approximate the systematic solutions more precisely with shear-thickening, moderately shear-thinning, and most shear-thinning fluids. The solution depends on various parameters including Prandtl number, power index, and temperature variation coefficient. A systematic analysis of boundary-layer flow demonstrates the impact of these parameters on the velocity and temperature profiles.

scholarly journals Finite Element Analysis of Variable Viscosity Impact on MHD Flow and Heat Transfer of Nanofluid Using the Cattaneo–Christov Model

Coatings ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 395 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Finite Element ◽  
Differential Equations ◽  
Thermal Relaxation ◽  
Fluid Temperature ◽  
Flow And Heat Transfer ◽  
Flux Model ◽  
The Impact ◽  
Heat Flux Model

In this mathematical study, magnetohydrodynamic, time-independent nanofluid flow over a stretching sheet by using the Cattaneo–Christov heat flux model is inspected. The impact of the thermal, solutal boundary and gravitational body forces with the effect of double stratification on the mass flow and heat transfer phenomena is also observed. The temperature-dependent viscosity impact on heat transfer through a moving sheet with capricious heat generation in nanofluids have studied, and the viscosity of the fluid is presumed to deviate as the inverse function of temperature. With the appropriate transformations, the system of partial differential equations is transformed into a system of nonlinear ordinary differential equations. By applying the variational finite element method, the transformed system of equations is solved. The properties of the several parameters for buoyancy, velocity, temperature, stratification, and Brownian motion parameters have examined. The enhancement in the concentration and thermal boundary layer thickness of the nanofluid sheet due to the increment in the viscosity parameter, also increased the temperature and concentration of nanoparticles. Moreover, the fluid temperature declined with the increasing values of thermal relaxation parameter. This displays that the Cattaneo–Christov heat flux model provides a better assessment of temperature distribution. Moreover, confirmation of the code and precision of the numerical method has inveterate with the valuation of the presented results with previous studies.

Numerical simulation of Darcy-Forchheimer flow of third grade liquid with Cattaneo-Christov heat flux model

2017 ◽  
Vol 41 (12) ◽  
pp. 4352-4359 ◽  
Author(s):  
T. Hayat ◽  
M. Ijaz Khan ◽  
S. A. Shehzad ◽  
M. Imran Khan ◽  
A. Alsaedi
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Third Grade ◽  
Flux Model ◽  
Heat Flux Model ◽  
Forchheimer Flow

Analysis of radiative nonlinear heat transfer in a convective flow of dusty fluid by capitalizing a non-Fourier heat flux model

2021 ◽  
pp. 095440892110411
Author(s):  
G. Sowmya ◽  
B. Saleh ◽  
R. J. Punith Gowda ◽  
R. Naveen Kumar ◽  
R. S. Varun Kumar ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Slip ◽  
Slip Parameter ◽  
Dusty Fluid ◽  
Thermal Fields ◽  
Curvature Parameter ◽  
Flux Model ◽  
The Impact ◽  
Heat Flux Model

The study is concerned with the heat transfer in a slip flow of a dusty fluid with the impact of a magnetic field and nonlinear thermal radiation. Furthermore, for the heat transfer process the Cattaneo–Christov heat flux model is used. Suitable similarity transformations are used to transform the governing equations. Later, shooting method and the Runge-Kutta Fehlberg's fourth fifth order (RKF-45) process are utilized to solve these reduced system of nonlinear ordinary differential equations. Impact of numerous involved parameters on the flow, thermal fields of both dust and fluid phase, skin friction and rate of heat transfer are visually plotted through graphs and discussed quantitatively. The significant outcomes drawn from the current study are that, the rise in value of the velocity slip parameter decreases the velocity profile but improves the thermal profile of both the phases. The growing values of curvature parameter intensify the flow and the thermal fields of both phases. The cumulative values of magnetic parameter and dust particle mass concentration parameter declines the velocity and thermal gradients of both phases. The thermal relaxation time parameter decays the temperature profile. The heat transfer rate is strengthened with the growing values of the curvature parameter, the velocity slip parameter, and radiation parameter.

Impact of Cattaneo–Christov Heat Flux Model on Stagnation-Point Flow Toward a Stretching Sheet with Slip Effects

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Fayeza Al Sulti
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Fourier’S Law ◽  
Slip Effects ◽  
Flux Model ◽  
Fourier's Law ◽  
Heat Flux Model

Stagnation-point flow toward a stretching sheet with slip effects has been investigated. Unlike most classical works, Cattaneo–Christov heat flux model is utilized for the formulation of the energy equation instead of Fourier's law of heat conduction. A similarity transformation technique is adopted to reduce partial differential equations into a system of nonlinear ordinary differential equations. Numerical solutions are obtained by using shooting method to explore the features of various parameters for the velocity and temperature distributions. The obtained results are graphically presented and analyzed. It is found that fluid temperature has a converse relationship with the thermal relaxation time. A comparison of Cattaneo–Christov heat flux model and Fourier's law is also presented.

scholarly journals MHD Effects on Non-Newtonian Power-Law Fluid Past a Continuously Moving Porous Flat Plate with Heat Flux and Viscous Dissipation

2013 ◽  
Vol 18 (2) ◽  
pp. 425-445 ◽  
Author(s):  
N. Kishan ◽  
B. Shashidar Reddy
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Power Law ◽  
Porous Plate ◽  
Power Law Fluid ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Non Linear

The problem of a magneto-hydro dynamic flow and heat transfer to a non-Newtonian power-law fluid flow past a continuously moving flat porous plate in the presence of sucion/injection with heat flux by taking into consideration the viscous dissipation is analysed. The non-linear partial differential equations governing the flow and heat transfer are transformed into non-linear ordinary differential equations using appropriate transformations and then solved numerically by an implicit finite difference scheme. The solution is found to be dependent on various governing parameters including the magnetic field parameter M, power-law index n, suction/injection parameter ƒw, Prandtl number Pr and Eckert number Ec. A systematical study is carried out to illustrate the effects of these major parameters on the velocity profiles, temperature profile, skin friction coefficient and rate of heat transfer and the local Nusslet number.

Influence of Catteneo-Christov Heat Flux Model on Mixed Convection Flow of Third Grade Nanofluid over an Inclined Stretched Riga Plate

2018 ◽  
Vol 387 ◽  
pp. 121-134 ◽  
Author(s):  
Manoj Kumar Nayak ◽  
A.K. Abdul Hakeem ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Flux ◽  
Mixed Convection ◽  
Fluid Velocity ◽  
Third Grade ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Linear Temperature ◽  
Riga Plate ◽  
Flux Model ◽  
Heat Flux Model

Nature of the very idea of Cattaneo-Christov heat flux model and its influence on the mixed convection flow of third grade nanofluid subject to inclined stretched Riga plate has been studied. The study furthers the case for introducing temperature dependent viscosity modeled by Reynolds. A numerical solution of the transformed boundary layer equations has been accomplished by fourth order R-K and shooting methods. The study itself has pointed out that buoyancies (thermal as well as solutal) and viscosity parameters augment the fluid velocity while increase in Deborah number yields unperturbed diminishing trend of non-linear temperature profiles.

scholarly journals Nonlocal heat flux effects on temperature evolution of the solar atmosphere

2018 ◽  
Vol 615 ◽  
pp. A32
Author(s):  
S. S. A. Silva ◽  
J. C. Santos ◽  
J. Büchner ◽  
M. V. Alves
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Solar Corona ◽  
Heat Transport ◽  
Transition Region ◽  
Solar Atmosphere ◽  
Energy Transport ◽  
Flux Model ◽  
The Impact ◽  
Heat Flux Model

Context. Heat flux is one of the main energy transport mechanisms in the weakly collisional plasma of the solar corona. There, rare binary collisions let hot electrons travel over long distances and influence other regions along magnetic field lines. Thus, the fully collisional heat flux models might not describe transport well enough since they consider only the local contribution of electrons. The heat flux in weakly collisional plasmas at high temperatures with large mean free paths has to consider the nonlocality of the energy transport in the frame of nonlocal models in order to treat energy balance in the solar atmosphere properly. Aims. We investigate the impact of nonlocal heat flux on the thermal evolution and dynamics of the solar atmosphere by implementing a nonlocal heat flux model in a 3D magnetohydrodynamic simulation of the solar corona. Methods. We simulate the evolution of solar coronal plasma and magnetic fields considering both a local collision dominated and a nonlocal heat flux model. The initial magnetic field is obtained by a potential extrapolation of the observed line-of-sight magnetic field of AR11226. The system is perturbed by moving the plasma at the photosphere. We compared the simulated evolution of the solar atmosphere in its dependence on the heat flux model. Results. The main differences for the average temperature profiles were found in the upper chromosphere/transition region. In the nonlocal heat transport model case, thermal energy is transported more efficiently to the upper chromosphere and lower transition region and leads to an earlier heating of the lower atmosphere. As a consequence, the structure of the solar atmosphere is affected with the nonlocal simulations producing on average a smoother temperature profile and the transition region placed about 500 km higher. Using a nonlocal heat flux also leads to two times higher temperatures in some of the regions in the lower corona. Conclusions. The results of our 3D MHD simulations considering nonlocal heat transport supports the previous results of simpler 1D two-fluid simulations. They demonstrated that it is important to consider a nonlocal formulation for the heat flux when there is a strong energy deposit, like the one observed during flares, in the solar corona.

scholarly journals Analytical Solution of UCM Viscoelastic Liquid with Slip Condition and Heat Flux over Stretching Sheet: The Galerkin Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Zeeshan Khan ◽  
Haroon Ur Rasheed ◽  
Sahib Noor ◽  
Waris Khan ◽  
Qayyum Shah ◽  
...  
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Thermal Relaxation ◽  
Viscoelastic Liquid ◽  
Flux Model ◽  
The Galerkin Method ◽  
Limiting Case ◽  
Temperature And Velocity Fields ◽  
Elasticity Number ◽  
Heat Flux Model

This paper provides a substantial amount of study related to coupled fluid flow and heat conduction of an upper-convected-Maxwell viscoelastic liquid over a stretching plane with slip velocity. A new model, presented by Christov, for thermal convection is employed. The partial differential equations are converted to ordinary differential equations by using appropriate transformation variables. The transformed equations are solved analytically by using the Galerkin method. For the sake of soundness, a comparison is done with a numerical method, and good agreement is found. The impacts of various parameters like slip coefficient, elasticity number, the thermal relaxation time of heat flow, and the Prandtl number over the temperature and velocity fields are studied. Furthermore, the Cattaneo–Christov heat flux model is compared with Fourier’s law. Additionally, the present results are also verified by associating with the published work as a limiting case.

Heterogeneous and Homogeneous Reaction Analysis on MHD Oldroyd-B Fluid with Cattaneo-Christov Heat Flux Model and Convective Heating

2018 ◽  
Vol 387 ◽  
pp. 194-206 ◽  
Author(s):  
Sheniyappan Eswaramoorthi ◽  
Marimuthu Bhuvaneswari ◽  
S. Sivasankaran ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Flux ◽  
Fluid Velocity ◽  
Mhd Flow ◽  
Convective Heating ◽  
Fluid Temperature ◽  
Suction Parameter ◽  
Flux Model ◽  
Homogeneous Chemical ◽  
The Impact ◽  
Heat Flux Model

The impact of Cattaneo-Christov heat flux model for the MHD flow of an Oldroyd-B fluid on a stretching plate with convective heating and heterogeneous-homogeneous chemical reactions were analyzed. The governing PDE’s are converted into a nonlinear ODE’s with appropriate similarity variables and it is solved using homotopy analysis method (HAM). The graphical results of velocity, temperature and concentration profiles are presented(detailed). We found that the fluid velocity reduces with enhancing the injection/suction parameter. In addition, the fluid temperature boosted up when rising the Biot number and the solutal boundary layer thickness reduces both heterogeneous and homogeneous chemical reaction parameters.

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