scholarly journals Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 788 ◽  
Author(s):  
Anuar Jamaludin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Source Sink

In this study we numerically examine the mixed convection stagnation-point flow of a nanofluid over a vertical stretching/shrinking sheet in the presence of suction, thermal radiation and a heat source/sink. Three distinct types of nanoparticles, copper (Cu), alumina (Al2O3) and titania (TiO2), were investigated with water as the base fluid. The governing partial differential equations were converted into ordinary differential equations with the aid of similarity transformations and solved numerically by utilizing the bvp4c programme in MATLAB. Dual (upper and lower branch) solutions were determined within a particular range of the mixed convection parameters in both the opposing and assisting flow regions and a stability analysis was carried out to identify which solutions were stable. Accordingly, solutions were gained for the reduced skin friction coefficients, the reduced local Nusselt number, along with the velocity and temperature profiles for several values of the parameters, which consists of the mixed convection parameter, the solid volume fraction of nanoparticles, the thermal radiation parameter, the heat source/sink parameter, the suction parameter and the stretching/shrinking parameter. Furthermore, the solutions were presented in graphs and discussed in detail.

scholarly journals Magnetohydrodynamic Mixed Convection Stagnation-Point Flow of a Power-Law Non-Newtonian Nanofluid towards a Stretching Surface with Radiation and Heat Source/Sink

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Macha Madhu ◽  
Naikoti Kishan
Keyword(s):  
Heat Source ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Power Law ◽  
Volume Fraction ◽  
Nonlinear Differential Equations ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Source Sink

Two-dimensional MHD mixed convection boundary layer flow of heat and mass transfer stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface in the presence of thermal radiation and heat source/sink is investigated numerically. The non-Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. The basic transport equations are made dimensionless first and the complete nonlinear differential equations with associated boundary conditions are solved numerically by finite element method (FEM). The numerical calculations for velocity, temperature, and nanoparticles volume fraction profiles for different values of the physical parameters to display the interesting aspects of the solutions are presented graphically and discussed. The skin friction coefficient, the local Nusslet number and the Sherwood number are exhibited and examined. Our results are compatible with the existing results for a special case.

Thermal Radiation Effects on the Mixed Convection Stagnation-Point Flow in a Jeffery Fluid

2011 ◽  
Vol 66 (10-11) ◽  
pp. 606-614 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
Saleem Obaidat
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Deborah Number ◽  
Stagnation Point Flow ◽  
Suction Parameter

This study describes the mixed convection stagnation point flow and heat transfer of a Jeffery fluid towards a stretching surface. Mathematical formulation is given in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux. Similarity transformations are employed to reduce the partial differential equations into the ordinary differential equations which are then solved by a homotopy analysis method (HAM). A comparative study is made with the known numerical solutions in a limiting sense and an excellent agreement is noted. The characteristics of involved parameters on the dimensionless velocity and temperature are also examined. It is noticed that the velocity increases with an increase in Deborah number. Further, the temperature is a decreasing function of mixed convection parameter. We further found that for fixed values of other parameters, the local Nusselt number increases by increasing suction parameter and Deborah number.

scholarly journals Stagnation-point flow past a shrinking sheet in a nanofluid

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Roslinda Nazar ◽  
Mihaela Jaradat ◽  
Norihan Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Nonlinear System ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

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.

scholarly journals Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

scholarly journals Homann Stagnation Point Flow and Heat Transfer of Hybrid Nanofluids Over a Permeable Radially Stretching/Shrinking Sheet

2021 ◽  
Vol 85 (1) ◽  
pp. 101-112
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Mohd Hisyam Ariff ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Nanoparticle Volume Fraction ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids ◽  
Water Base

The steady two-dimensional Homan stagnation point flow and heat transfer of water base hybrid nanofluids (Al2O3 & Cu) over a permeable radially stretching/shrinking sheet have been studied. The similarity variables are introduced to transform the partial differential equations of the model into the ordinary differential equations. Numerical findings and dual solutions have been carried out by implementing the bvp4c code through MATLAB software. The most prominent effect is illustrated in the boundary layer thickness where the velocity profile increases upon the increment of the suction intensity but decreases in the temperature profile. Besides, the reduced Nusselt number also decreases as enlarging the value of copper and alumina nanoparticle volume fraction. The analysis of the first and second solutions are presented graphically with critical values as well as the detail discussions on the effects of the other involving parameters.

scholarly journals Numerical Solution of Stagnation Point Flow and Heat Transfer over a Nonlinear Stretching/Shrinking Sheet in Hybrid Nanofluid: Stability Analysis

2020 ◽  
Vol 76 (2) ◽  
pp. 85-98
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Norihan Md Arifin ◽  
Haliza Rosali
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Pure Water ◽  
Nonlinear Parameter ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Local Skin

The steady, laminar, stagnation point flow of hybrid nanofluid past a nonlinearly stretching and shrinking sheet is studied. Hybrid nanofluid is regarded by disseminated two distinct nano-sized particles, silver (Ag) and copper oxide (CuO) in pure water. Similarity technique was used for the transformation of partial differential equations (PDEs) into an ordinary differential equations (ODEs). Obtained ODEs were solved using Matlab’s built in function (bvp4c). The results of important governing parameters which are nonlinear parameter, stretching/shrinking parameter and nanoparticle volume fraction are evaluated and discussed in graphical and tabular form for the velocity and temperature profiles, along with local skin friction, local Nusselt number. Nonunique solutions (first and second branch) are visible for some limit of shrinking parameter. It is noticed that nonlinear parameter hastens flow separations. Hence, a stability analysis is executed to identify which solutions are stable and physically feasible.

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