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 Micropolar Couple Stress Nanofluid Flow by Non-Fourier’s-Law Heat Flux Model past a Stretching Sheet

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Gosa Gadisa ◽  
Tagay Takele ◽  
Shibiru Jabessa
Keyword(s):  
Heat Flux ◽  
Numerical Method ◽  
Couple Stress ◽  
Stretching Sheet ◽  
Fourier’S Law ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Flux Model ◽  
Fourier's Law ◽  
Heat Flux Model

In this investigation, thermal radiation effect on MHD nonlinear convective micropolar couple stress nanofluid flow by non-Fourier’s-law heat flux model past a stretching sheet with the effects of diffusion-thermo, thermal-diffusion, and first-order chemical reaction rate is reported. The robust numerical method called the Galerkin finite element method is applied to solve the proposed fluid model. We applied grid-invariance test to approve the convergence of the series solution. The effect of the various pertinent variables on velocity, angular velocity, temperature, concentration, local skin friction, local wall couple stress, local Nusselt number, and local Sherwood number is analyzed in both graphical and tabular forms. The range of the major relevant parameters used for analysis of the present study was adopted from different existing literatures by taking into consideration the history of the parameters and is given by 0.07 ≤ Pr ≤ 7.0 , 0.0 ≤ λ , ε ≤ 1.0 , 0.0 ≤ R d , D f   , S r , K , ≤ 1.5 , 0.0 ≤ γ E ≤ 0.9 , 0.9 ≤ S c ≤ 1.5 , 0.5 ≤ M ≤ 1.5 , 0.0 ≤ β ≤ 1.0 , 0 . 2 ≤ N b ≤ 0 . 4 , 0 . 1 ≤ N t ≤ 0 . 3 . The result obtained in this study is compared with that in the available literatures to confirm the validity of the present numerical method. Our result shows that the heat and mass transfer in the flow region of micropolar couple stress fluid can be enhanced by boosting the radiation parameters.

scholarly journals Oblique Stagnation Point Flow of Nanofluids over Stretching/Shrinking Sheet with Cattaneo–Christov Heat Flux Model: Existence of Dual Solution

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1070 ◽  
Author(s):  
Xiangling Li ◽  
Arif Ullah Khan ◽  
Muhammad Riaz Khan ◽  
Sohail Nadeem ◽  
Sami Ullah Khan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Stagnation Point ◽  
Free Stream ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Branch Solution ◽  
Flux Model ◽  
Heat Flux Model

In the present work we consider a numerical solution for laminar, incompressible, and steady oblique stagnation point flow of Cu − water nanofluid over a stretching/shrinking sheet with mass suction S . We make use of the Cattaneo–Christov heat flux model to develop the equation of energy and investigate the qualities of surface heat transfer. The governing flow and energy equations are modified into the ordinary differential equations by similarity method for reasonable change. The subsequent ordinary differential equations are illuminated numerically through the function bvp4c in MATLAB. The impact of different flow parameters for example thermal relaxation parameter, suction parameter, stretching/shrinking parameter, free stream parameter, and nanoparticles volume fraction on the skin friction coefficient, local Nusselt number, and streamlines are contemplated and exposed through graphs. It turns out that the lower branch solution for the skin friction coefficient becomes singular in shrinking area, although the upper branch solution is smooth in both stretching and shrinking domain. For oblique stagnation-point flow the streamlines pattern are not symmetric, and reversed phenomenon are detected close to the shrinking surface. Also, we observed that the free stream parameter changes the direction of the oncoming flow and controls the obliqueness of the flow. The existing work mostly includes heat and mass transfer as a mechanism for improving the heat transfer rate, which is the main objective of the authors.

Unsteady Mhd Stagnation-point Flow of Fractional Oldroyd-b Fluid Over a Stretching Sheet with Modified Fractional Fourier's Law

2021 ◽  
Author(s):  
Yu Bai ◽  
Sa Wan ◽  
Yan Zhang
Keyword(s):  
Stagnation Point ◽  
Stretching Sheet ◽  
Thermal Relaxation ◽  
Momentum Equation ◽  
Stagnation Point Flow ◽  
Governing Equations ◽  
Fourier’S Law ◽  
Relaxation Parameters ◽  
Memory Characteristic ◽  
Fourier's Law

Abstract The aim of the article is to research the unsteady magnetohydrodynamic stagnation-point flow of fractional Oldroyd-B fluid over a stretched sheet. According to the distribution characteristics of pressure and magnetic field near the stagnation point, the momentum equation based on fractional Oldroyd-B constitutive model is derived. Moreover, the modified fractional Fourier's law considering thermal relaxation-retardation time is proposed, which applies in both the energy equation and the boundary condition of convective heat transfer. New finite difference scheme combined with L1 algorithm is established to solve the governing equations, whose convergence is confirmed by constructing the exact solution. The results indicate that the larger relaxation parameters of velocity block the flow, yet the retardation parameters of velocity show the opposite trend. It is particularly worth mentioning that all the temperature profiles first go up slightly to a maximal value and then descend markedly, which presents the thermal retardation characteristic of Oldroyd-B fluid. Additionally, under the effects of temperature's retardation and relaxation parameters, the intersection of the profiles far away from stretching sheet demonstrates the thermal memory characteristic.

Cattaneo-Christov (CC) heat flux model for nanomaterial stagnation point flow of Oldroyd-B fluid

2020 ◽  
Vol 187 ◽  
pp. 105247 ◽  
Author(s):  
T. Hayat ◽  
Sohail A. Khan ◽  
M. Ijaz Khan ◽  
Shaher Momani ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Flux ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Flux Model ◽  
Heat Flux Model

Stagnation-Point Flow over an Exponentially Shrinking/Stretching Sheet

2011 ◽  
Vol 66 (12) ◽  
pp. 705-711 ◽  
Author(s):  
Sin Wei Wong ◽  
Abu Omar Awang ◽  
Anuar Ishak
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Free Stream ◽  
Stagnation Point Flow ◽  
Stream Velocity ◽  
Heat Transfer Characteristics ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
Box Method

The steady two-dimensional stagnation-point flow of an incompressible viscous fluid over an exponentially shrinking/stretching sheet is studied. The shrinking/stretching velocity, the free stream velocity, and the surface temperature are assumed to vary in a power-law form with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations before being solved numerically by a finite difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique.

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