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

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.

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Roslinda Nazar ◽  
Mihaela Jaradat ◽  
Norihan Arifin ◽  
Ioan Pop

AbstractIn this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.


2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Fayeza Al Sulti

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Khairy Zaimi ◽  
Anuar Ishak

This paper considers the problem of a steady two-dimensional stagnation-point flow and heat transfer of an incompressible micropolar fluid over a nonlinearly stretching/shrinking sheet. A similarity transformation is employed to convert the partial differential equations into nonlinear ordinary ones which are then solved numerically using a shooting method. Numerical results obtained are presented graphically, showing the effects of the micropolar or material parameter and the stretching/shrinking parameter on the flow field and heat transfer characteristics. The dual solutions are found to exist in a limited range of the stretching/shrinking parameter for the shrinking case, while unique solutions are possible for all positive values of the stretching/shrinking parameter (stretching case). It is also observed that the skin friction coefficient and the magnitude of the local Nusselt number increase as the material parameter increases.


2014 ◽  
Vol 92 (12) ◽  
pp. 1703-1708 ◽  
Author(s):  
Kishore Kumar Ch. ◽  
Shankar Bandari

The present analysis deals with the study of two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow of a nanofluid towards a melting stretching sheet. Using similarity transformations, the governing differential equations were transformed into coupled, nonlinear ordinary differential equations, which were then solved numerically by using the Runge–Kutta fourth-order method along with the shooting technique for two types of nanoparticles namely copper (Cu) and silver (Ag) in the water-based fluid with Prandtl number Pr = 6.2, the skin friction coefficient, the local Nusselt number, the velocity and the temperature profiles are presented graphically and discussed.


2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
M. Suali ◽  
N. M. A. Nik Long ◽  
N. M. Ariffin

The unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction/injection is studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using a similarity transformation and solved numerically. Both stretching and shrinking cases are considered. Results for the skin friction coefficient, local Nusselt number, velocity, and temperature profiles are presented for different values of the governing parameters. It is found that the dual solutions exist for the shrinking case, whereas the solution is unique for the stretching case. Numerical results show that the range of dual solutions increases with mass suction and decreases with mass injection.


Sign in / Sign up

Export Citation Format

Share Document