Convective-Radiation Effects on Stagnation Point Flow of Nanofluids over a Stretching/Shrinking Surface with Viscous Dissipation

2014 ◽  
Vol 30 (3) ◽  
pp. 289-297 ◽  
Author(s):  
D. Pal ◽  
K. Vajravelu ◽  
G. Mandal
Keyword(s):  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Radiation Effects ◽  
Internal Heat ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Fifth Order ◽  
Shrinking Surface

ABSTRACTIn this paper, mixed convection stagnation point flow of nanofluids over a stretching/shrinking surface is studied numerically in the presence of thermal radiation and viscous dissipation. The governing boundary layer equations are transformed into a system of nonlinear ordinary differential equations, by using a similarity transformation, which are then solved numerically using a fifth-order Runge-Kutta-Fehlberg method with shooting technique. The effects of various physical parameters are analyzed and discussed. Computed results are presented in graphical and tabular forms. It is found that the Richardson number, thermal radiation and internal heat generation/absorption have interesting and significant effects on skin-friction and local Nusselt number for all the three types of nanofluids.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

scholarly journals Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Shooting Method ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Stagnation Point Flow ◽  
Stretching Surfaces

Abstract In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.

scholarly journals Thermal radiation effects on stagnation point flow past a stretching/shrinking sheet in a Maxwell fluid with slip condition

2017 ◽  
Vol 890 ◽  
pp. 012021 ◽  
Author(s):  
Nazila Ishak ◽  
Hasmawani Hashim ◽  
Muhammad Khairul Anuar Mohamed ◽  
Norhafizah Md Sarif ◽  
Norhayati Rosli ◽  
...  
Keyword(s):  
Thermal Radiation ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Maxwell Fluid ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Flow Past

Viscous Dissipation and Thermal Radiation effects in MHD flow of Jeffrey Nanofluid through Impermeable Surface with Heat Generation/Absorption

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Kalpna Sharma ◽  
Sumit Gupta
Keyword(s):  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Homotopy Analysis ◽  
Two Dimensional Flow ◽  
Jeffrey Nanofluid ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

AbstractThis paper investigates steady two dimensional flow of an incompressible magnetohydrodynamic (MHD) boundary layer flow and heat transfer of nanofluid over an impermeable surface in presence of thermal radiation and viscous dissipation. By using similarity transformation, the arising governing equations of momentum, energy and nanoparticle concentration are transformed into coupled nonlinear ordinary differential equations, which are than solved by homotopy analysis method (HAM). The effect of different physical parameters, namely, Prandtl number Pr, Eckert number

MHD stagnation point flow on a shrinking surface with hybrid nanoparticles and melting phenomenon effects

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ioan Pop ◽  
Iskandar Waini ◽  
Anuar Ishak
Keyword(s):  
Stagnation Point ◽  
Temporal Stability ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Heat Transfer Analysis ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Melting Phenomenon ◽  
Shrinking Surface

Purpose This study aims to explore the stagnation flow over a shrinking surface in a hybrid nanofluid consists of Al2O3 and Cu nanoparticles. Here, the flow is subjected to the magnetohydrodynamic (MHD) and the melting phenomenon effects. Design/methodology/approach The similarity variables are used to gain the similarity equations. These equations are solved via the bvp4c solver. The effects of several physical parameters on the flow and the thermal characteristics of the hybrid nanofluid are analysed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves. Findings Results show that two solutions are found for the limited range of the stretching/shrinking parameter λ, and then these solutions are terminated at λ=λc. The rise of the melting parameter Me from 0 to 2 contributes to enhance 109.63% of the local Nusselt number Rex-1/2Nux and 3.30% of the skin friction coefficient Rex1/2Cf. Contrarily, the values of Rex-1/2Nux and Rex1/2Cf decline by 25.04% and 5.58%, respectively, as the magnetic parameter Mg increases from 0 to 0.3. Additionally, Al2O3-Cu/water has the highest values of Rex1/2Cf and the lowest values of Rex-1/2Nux. Lastly, it is found that the first solution is physically stable as time evolves. Originality/value This paper considers the MHD stagnation point flow of a hybrid nanofluid over a shrinking surface with the melting phenomenon effects. Most importantly, it is shown that there exist dual solutions within a specific range of the physical parameters. Besides, the temporal stability of the solutions is also reported in this study. The finding can contribute to foresee the flow and thermal behaviours in industrial applications. Also, the suitable values of parameters can be determined to avoid misjudgement in flow and heat transfer analysis.

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