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.

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.

Unsteady Hydromagnetic Boundary Layer Flow of a Nanofluid over a Stretching Sheet: Using Cattaneo-Christov Heat Flux Model

2018 ◽  
Vol 388 ◽  
pp. 61-76 ◽  
Author(s):  
G. Vinod Kumar ◽  
S. Vijaya Kumar Varma ◽  
R.V.M.S.S. Kiran Kumar
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Stretching Sheet ◽  
Thermal Relaxation ◽  
Fluid Temperature ◽  
Shooting Technique ◽  
Buongiorno’S Model ◽  
Flux Model ◽  
Layer Flow ◽  
Heat Flux Model

The present investigation has put a focus on the hydromagnetic boundary layer unsteady flow of a nanofluid over a stretching sheet. A new heat flux model named Cattaneo-Christov is applied as the substitution of classical Fourier’s law. Buongiorno’s model is incorporated. The coupled non-linear transformed equations are solved numerically by using shooting technique with MATLAB bvp4c package. The obtained results are presented and discussed through graphs and tables in detail. Our results reveal that the unsteady parameter reduces all the three boundary layer thickness. The thermal relaxation parameter exhibits a non-conducting nature that makes the decline in fluid temperature.

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.

Direct Numerical Simulation of Turbulent Channel Flow With Heat Transfer for Low Prandtl and High Reynolds and Comparison With Algebraic Heat Flux Model

2015 ◽  
Author(s):  
Haomin Yuan ◽  
Elia Merzari
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Flux ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Liquid Metals ◽  
Turbulent Channel Flow ◽  
Flux Model ◽  
Heat Flux Model

The flow characteristic of fluid at low Prandtl number is of continued interest in the nuclear industry because liquid metals are to be used in the next-generation nuclear power reactors. In this work we performed direct numerical simulation (DNS) for turbulent channel flow with fluid of low Prandtl number. The Prandtl number was set to 0.025, which is representative of the behavior of liquid metals. Constant heat flux was imposed on the walls to study heat transfer behavior, with different boundary conditions for temperature fluctuation. The bulk Reynolds number was set as high as 50,000, with a corresponding friction Reynolds number of 1,200, which is closer to the situation in a reactor or a heat exchanger than used in normally available databases. Budgets for turbulent variables were computed and compared with predictions from several RANS turbulence models. In particular, the Algebraic Heat Flux Model (AHFM) has been the focus of this comparison with DNS data. The comparisons highlight some shortcomings of AHFM along with potential improvements.

Effect of Viscous Dissipation on Upper - Convected Maxwell Fluid with Cattaneo-Christov Heat Flux Model Using Spectral Relaxation Method

2018 ◽  
Vol 388 ◽  
pp. 146-157 ◽  
Author(s):  
K. Gangadhar ◽  
Chintalapudi Suresh Kumar ◽  
S. Mohammed Ibrahim ◽  
Giulio Lorenzini
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Relaxation Time ◽  
Thermal Relaxation ◽  
Relaxation Method ◽  
Maxwell Fluid ◽  
Spectral Relaxation Method ◽  
Flux Model ◽  
Spectral Relaxation ◽  
Heat Flux Model

The study observes the flow and heat transfer in upper-convected Maxwell fluid over a rapidly stretching surface with viscous dissipation. Cattaneo-Christov heat flux model has been used in the preparation of the energy equation. The model is used in guessing the impacts of thermal relaxation time over boundary layer. Similarity method has been used to keep normal the supervising boundary layer equations. Local similarity solutions have been obtained through spectral relaxation method. The fluid temperature has a relation with thermal relaxation time inversely and our calculations have shown the same.. In addition the fluid velocity is a receding activity of the fluid relaxation time. A comparative study of Fourier’s law and the Cattaneo-Christov’s law has been done and inserted in this.

Free convective heat transfer in Jeffrey fluid with suspended nanoparticles and Cattaneo–Christov heat flux

2020 ◽  
Vol 234 (3-4) ◽  
pp. 99-114
Author(s):  
B Vasu ◽  
Atul Kumar Ray ◽  
Rama SR Gorla
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Surface Temperature ◽  
Vertical Wall ◽  
Physical Parameters ◽  
Local Similarity ◽  
Species Concentration ◽  
Flux Model ◽  
Jeffrey Nanofluid ◽  
Heat Flux Model

Free convection flow of Jeffrey nanofluid past a vertical plate with sinusoidal variations of surface temperature and species concentration is presented. The study of heat transfer and nanofluid transport has been done by employing Cattaneo–Christov heat flux model and Buongiorno model, respectively. Equations governing the flow are non-dimensionalized using appropriate transformations. Furthermore, the method of local similarity and local non-similarity is used to reduce the equations into non-linear coupled system of equations which are then solved by homotopy analysis method. The obtained results are validated by comparing with the existing results available in the literature. The numerical results are found to be in good agreement. The effects of varying the physical parameters such as Deborah Number, Prandtl number, Schmidt number, thermophoresis parameter, Brownian motion parameter and buoyancy ratio parameter are obtained and presented graphically. The effect of sinusoidal variation of surface temperature and species concentration on the skin friction coefficient, Nusselt number and Sherwood number is also shown. Velocity for Jeffrey nanofluid is more than the Newtonian nanofluid while temperature and nanoparticle concentration for Jeffrey nanofluid is less than the Newtonian nanofluid. Raising value of thermal relaxation times leads to an increase in the heat transfer coefficient. It is observed that temperature of Cattaneo–Christov heat flux model is less than that in classical Fourier’s model away from the vertical wall. These types of boundary layer flow problems are found in vertical film solar energy collector, grain storage, transportation and power generation, thermal insulation, gas production, petroleum resources, geothermal reservoirs.

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