Flow between Stretchable Rotating Disks in an Anisotropic Porous Medium with Cattaneo Christov Heat Flux

2019 ◽  
Vol 393 ◽  
pp. 138-148
Author(s):  
K. Gowthami ◽  
P. Hari Prasad ◽  
B. Mallikarjuna ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Thermal Relaxation ◽  
Relaxation Parameter ◽  
Transport Processes ◽  
Rotation Parameter ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Anisotropic Porous Medium ◽  
Physical Quantities

A study on fully developed fluid flow between 2two stretchable disks in a 1porous medium is presented. The porous medium is assumed to be an anisotropic porous medium and described using Darcy’s model. Moreover Cattaneo - Christov heat flux 1model is used for heat transport processes. Numerical method 1is used to compute the solutions of non-dimensionalized equations and obtained results are discussed with the aid of graphs and table values on physical quantities (fluid velocity, fluid temperature, skin frication coefficients and Nusselt numbers) for various values of physical parameters, Darcy’ number in different directions, stretchable disk parameters, rotation parameter and thermal relaxation parameter. Increasing stretchable disks parameter reports opposite behavior on physical quantities at different disks. Positive and negative values of rotation parameter impact on physical quantities are presented and discussed. As increase in thermal relaxation parameter fluid temperature transfers in different directions between disks and Nusselt number values are enhanced at both disks.

scholarly journals Micropolar mixed convective flow with Cattaneo-Christov heat flux: Non-fourier heat conduction analysis

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1345-1356 ◽  
Author(s):  
Abid Hussanan ◽  
Ilyas Khan ◽  
Waqar Khan ◽  
Zhi-Min Chen
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Mixed Convection ◽  
Thermal Relaxation ◽  
Relaxation Parameter ◽  
Rotation Parameter ◽  
Thermal Relaxation Time ◽  
Convection Flow ◽  
Fluid Temperature ◽  
The Impact

The purpose of this study is to investigate the impact of thermal relaxation time on the mixed convection flow of non-Newtonian micropolar fluid over a continuously stretching sheet of variable thickness in the presence of transverse magnetic field. An innovative and modified form of Fourier?s law, namely, Cattaneo-Christov heat flux is employed in the energy equation to study the characteristics of thermal relaxation time. The governing equations are transformed into ODE, using similarity transformations. Fourth order Runge-Kutta numerical method is used to solve these equations. The effects of relevant parameters such as a micro-rotation parameter, magnetic parameter, thermal relaxation parameter, Prandtl number, surface thickness parameter, and mixed convection parameter, on the physical quantities are graphically presented. Results illustrate that fluid temperature enhances with the rise of thermal relaxation parameter, but it reduces with an increase in micro-rotation parameter. The skin friction decreases with a rise in micro-rotation and micro-element parameters. However, variation in the rate of heat transfer is quite significant for small values of thermal relaxation parameter.

scholarly journals Mass transfer and Cattaneo-Christov heat flux for a chemically reacting nanofluid in a porous medium between two rotary disks

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 179-184
Author(s):  
Peter Habu ◽  
Noor Noor ◽  
Zailan Siri
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Thermal Radiation ◽  
Differential System ◽  
Thermal Relaxation ◽  
Fluid Temperature ◽  
Partial Differential System ◽  
Non Linear ◽  
Chemically Reacting ◽  
Increasing Functions

This paper examines the transport of a chemically reacting nanofluid in a porous medium between two rotary disks with Cattaneo-Christov?s heat flux. The non-linear ordinary differential system formed under Vonn Karman transformation of a non-linear partial differential system is solved via a shooting method with MATLAB bvp4c. The nanofluid thermodynamics profiles with variation in physical properties of thermal relaxation time, thermal radiation, porosity, and chemical reaction are observed. Axial, radial, and tangential velocities are found to be increasing functions of porous medium. A decrease in the fluid temperature is perceived as thermal radiation and thermal relaxation increase since more heat can be transported to neighboring surroundings. The concentration is enhanced with intensified Cattaneo-Christov?s thermal relaxation but it oscillates with reacting chemicals. The rotary disks bound the oscillating nanofluid from downward to up-ward directions and vice versa. The axial velocity represents the change in force due to porosity and radial stretching of the disks.

scholarly journals On the Cattaneo–Christov Heat Flux Model and OHAM Analysis for Three Different Types of Nanofluids

2020 ◽  
Vol 10 (3) ◽  
pp. 886 ◽  
Author(s):  
Umair Khan ◽  
Shafiq Ahmad ◽  
Arsalan Hayyat ◽  
Ilyas Khan ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Pure Water ◽  
Thermal Relaxation ◽  
Relaxation Parameter ◽  
Fluid Temperature ◽  
Optimal Homotopy Analysis Method ◽  
Similarity Transformations ◽  
Flux Model ◽  
Heat Flux Model

In this article, the boundary layer flow of a viscous nanofluid induced by an exponentially stretching surface embedded in a permeable medium with the Cattaneo–Christov heat flux model (CCHFM) is scrutinized. We took three distinct kinds of nanoparticles, such as alumina (Al2O3), titania (TiO2) and copper (Cu) with pure water as the base fluid. The features of the heat transfer mechanism, as well as the influence of the relaxation parameter on the present viscous nanofluid flow are discussed here thoroughly. The thermal stratification is taken in this phenomenon. First of all, the problem is simplified mathematically by utilizing feasible similarity transformations and then solved analytically through the OHAM (optimal homotopy analysis method) to get accurate analytical solutions. The change in temperature distribution and axial velocity for the selected values of the specific parameters has been graphically portrayed in figures. An important fact is observed when the thermal relaxation parameter (TRP) is increased progressively. Graphically, it is found that an intensification in this parameter results in the exhaustion of the fluid temperature together with an enhancement in the heat transfer rate. A comparative discussion is also done over the Fourier’s law and Cattaneo–Christov model of heat.

Implicit Homotopy Perturbation Method for MHD Non-Newtonian Nanofluid Flow with Cattaneo-Christov Heat Flux Due to Parallel Rotating Disks

2019 ◽  
Vol 8 (8) ◽  
pp. 1648-1653
Author(s):  
Mohamed Y. Abou-Zeid
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Tangential Velocity ◽  
Thermal Relaxation ◽  
Physical Parameters ◽  
Rotating Disks ◽  
Linear Ordinary Differential Equations ◽  
Homotopy Perturbation

This article deals with the influence of Cattaneo-Christov heat flux on MHD flow of biviscosity nanofluid between two rotating disks through a porous media. Von Karman transformations are used to transform system of partial differential equations to non-linear ordinary differential equations. This system are solved by using homotopy perturbation method. Numerical results for the behaviors of the radial, axial and tangential velocities, temperature and nanoparticles with the physical parameters of the problem are obtained. These results are depicted graphically and discussed in details. The obtained results show that the tangential velocity increases with the increase of both the stretching and rotation parameters. Moreover, it is found that the stretching and thermal relaxation parameters increase the temperature, while they increase or decrease the nanoparticles concentration. Comparison between the obtained results and those obtained by other researchers is made during this study.

scholarly journals Heat and Mass Transfer of Unsteady Hydromagnetic Free Convection Flow Through Porous Medium Past a Vertical Plate with Uniform Surface Heat Flux

2017 ◽  
Vol 47 (3) ◽  
pp. 25-58 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Aishah S. Yahya
Keyword(s):  
Mass Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Free Convection ◽  
Heat And Mass Transfer ◽  
Transport Model ◽  
Convection Flow ◽  
Physical Parameters ◽  
Free Convection Flow ◽  
Laplace Transform Technique

AbstractSimultaneous effects of thermal and concentration diffusions in unsteady magnetohydrodynamic free convection flow past a moving plate maintained at constant heat flux and embedded in a viscous fluid saturated porous medium is presented. The transport model employed includes the effects of thermal radiation, heat sink, Soret and chemical reaction. The fluid is considered as a gray absorbing-emitting but non-scattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. The dimensionless coupled linear partial differential equations are solved by using Laplace transform technique. Numerical results for the velocity, temperature, concentration as well as the skin friction coefficient and the rates of heat and mass transfer are shown graphically for different values of physical parameters involved.

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.

Spectral Quasi-Linearization Method for Entropy Generation Using the Cattaneo–Christov Heat Flux Model

2019 ◽  
Vol 17 (05) ◽  
pp. 1940002
Author(s):  
Hiranmoy Mondal ◽  
Precious Sibanda
Keyword(s):  
Heat Flux ◽  
Entropy Generation ◽  
Thermal Relaxation ◽  
Linearization Method ◽  
Physical Parameters ◽  
Bejan Number ◽  
Nonlinear Transport ◽  
Moving Plate ◽  
Flux Model ◽  
Heat Flux Model

In this paper, we studying the entropy generation in Sakiadis nanofluid flowing along a moving plate subject to magnetic field and a Cattaneo–Christov heat flux model that may predict the effects of thermal relaxation time on the boundary layer flow. The nonlinear transport equations are solved using a spectral quasi-linearization method. An analysis of the convergence of the method is presented, and the importance of various fluid and physical parameters concerning the behavior of the solutions is explored. Numerical analysis of the residual error and convergence properties of the method are also discussed. One of the benefits of the proposed method is that it is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process. It is shown that the method converges fast and gives accurate results. The results show that entropy generation increases with an increase in the Reynolds number. The Bejan number is strongly affected by variations in the magnetic parameter, Brinkman number and temperature difference parameter.

New models for heat flux splitting at the boundary of a porous medium: three energy equations for nanofluid flow under local thermal nonequilibrium conditions

2014 ◽  
Vol 92 (11) ◽  
pp. 1312-1319 ◽  
Author(s):  
M. Nazari ◽  
M.J. Maghrebi ◽  
T. Armaghani ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Solid Phase ◽  
Solid Matrix ◽  
Fluid Temperature ◽  
Transfer Coefficients ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium ◽  
Energy Equations

One of the challenging points in the simulation of a nanofluid flowing through a porous medium is modeling the surface heat flux in the presence of nanoparticles and internal solid matrix. The question is how much energy is absorbed by the solid phase, fluid phase, and particles at the surface of imposing heat flux? To reach a suitable answer, a local thermal nonequilibrium approach (including three energy equations) is presented in this paper and three heat flux models are proposed for the first time. The proposed models are compared and analyzed. The effects of interstitial heat transfer coefficients on the heat transfer in a porous channel are completely studied. The fluid temperature distributions and heat transfer rate obtained by homogenous and nonhomogenous approaches (for the proposed models) are completely studied and compared. The results show that the nonhomogeneous approach experiences larger Nusselt number than the homogeneous one for all the recommended heat flux models.

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