scholarly journals Analytical Investigation of Magnetic Field on Unsteady Boundary Layer Stagnation Point Flow of Water-Based Graphene Oxide-Water and Graphene Oxide-Ethylene Glycol Nanofluid over a Stretching Surface

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ali Rehman ◽  
Zabidin Salleh
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Graphene Oxide ◽  
Ethylene Glycol ◽  
Stagnation Point ◽  
Analytical Method ◽  
Stagnation Point Flow ◽  
Optimal Homotopy Analysis Method ◽  
Approximate Analytical Method ◽  
Water Based

This study explains the effect of magnetic field of the stagnation point flow of a water-based nanofluid graphene oxide-water (GO-W) and graphene oxide-ethylene glycol (GO-EG). Heat transfer analyses are discussed by converting the given partial differential equation into a nonlinear ordinary differential equation using the similarity transformation and solved using an approximate analytical method, namely, the optimal homotopy analysis method (OHAM), to obtain an approximate analytical solution of the nonlinear problem that analyzes the problem. The BVPh 2.0 package function of Mathematica is used to obtain the numerical results. The results of important parameters such as the magnetic field parameter, unsteady parameter, stretching parameter, Prandtl number, Eckert number, and kinematic parameter for both velocity and temperature profiles are plotted and discussed. The convergence control parameter of the approximate analytical method is obtained up to the 25th iteration using the BVPh 2.0 package. The skin friction coefficient and Nusselt number are explained in tabular form.

scholarly journals Impact of the Marangoni and thermal radiation convection on the graphene-oxide-water-based and ethylene-glycol-based nanofluids

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985677 ◽  
Author(s):  
Taza Gul ◽  
Waqas Noman ◽  
Muhammad Sohail ◽  
Muhammad Altaf Khan
Keyword(s):  
Graphene Oxide ◽  
Ethylene Glycol ◽  
Thermal Radiation ◽  
Thermal Efficiency ◽  
Solid Particles ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Water Based ◽  
Homotopy Analysis ◽  
The Impact

The low thermal efficiency of the base liquids is the main issue among the researchers and to resolve this issue, scientists use the small-sized (1–100 nm) metal solid particles in the base liquids to increase the thermal efficiency of the base solvents. In the recent article, a theoretical study has been carried out for the thermal application functioning of graphene-oxide-water-based and graphene-oxide-ethylene-glycol-based nanofluids under the impact of the Marangoni convection. The nanofluid flow is also subjected to thermal radiation and magnetic field. The problem has been solved through optimal homotopy analysis method. The impacts of the embedded parameters over the velocity and temperature pitches have been analysed. Due to strong thermophysical properties of graphene-oxide-ethylene-glycol-based nanofluid, it is observed that the heat transfer rate of this sort of nanofluid is more efficient as compared to the graphene-oxide-water-based nanofluids. All the obtained outputs have been presented graphically and numerically.

Three dimensional MHD stagnation point flow of Al-Cu alloy suspended water based nanofluid with second order slip and convective heating

2017 ◽  
Vol 27 (12) ◽  
pp. 2879-2901
Author(s):  
N. Nithyadevi ◽  
P. Gayathri ◽  
A. Chamkha
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Convective Heating ◽  
Slip Effect ◽  
Content Type ◽  
Water Based

Purpose The paper aims to examine the boundary layers of a three-dimensional stagnation point flow of Al-Cu nanoparticle-suspended water-based nanofluid in an electrically conducting medium. The effect of magnetic field on second-order slip effect and convective heating is also taken into account. Design/methodology/approach The thermophysical properties of alloy nanoparticles such as density, specific heat capacity and thermal conductivity are computed using appropriate formula. The non-linear parabolic partial differential equations are transformed to ordinary differential equations and solved by shooting technique. Findings The influence of compositional variation of alloy nanoparticle, nanoparticle concentration, magnetic effect, slip parameters and Biot number are presented for various flow characteristics. Interesting results on skin friction and Nusselt number are obtained for different composition of aluminium and copper. Originality/value A novel result of the analysis reveals that impact of magnetic field near the boundary is suppressed by the slip effect.

Numerical analysis of time-dependent stagnation point flow of Oldroyd-B fluid subject to modified Fourier’s law

2021 ◽  
pp. 2150187
Author(s):  
Foukeea Qasim ◽  
Tian-Chuan Sun ◽  
S. Z. Abbas ◽  
W. A. Khan ◽  
M. Y. Malik
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equation ◽  
Thermal Relaxation ◽  
Stagnation Point Flow ◽  
Time Dependent ◽  
Parameter Values

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study’s findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically.

scholarly journals MHD stagnation-point flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid with induced magnetic field

2019 ◽  
Vol 30 (3) ◽  
pp. 1345-1364 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Norihan Md Arifin ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Induced Magnetic Field ◽  
Content Type

Purpose The purpose of this paper is to investigate the steady magnetohydrodynamics (MHD) boundary layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking sheet with the effect of induced magnetic field. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via the similarity transformations before they are solved numerically using the “bvp4c” function in MATLAB. Findings It is found that there exist non-unique solutions, namely, dual solutions for a certain range of the stretching/shrinking parameters. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in the heat transfer field such as electronic cooling, engine cooling, generator cooling, welding, nuclear system cooling, lubrication, thermal storage, solar heating, cooling and heating in buildings, biomedical, drug reduction, heat pipe, space aircrafts and ships with better efficiency than that of nanofluids applicability. The results obtained are very useful for researchers to determine which solution is physically stable, whereby, mathematically more than one solution exist. Originality/value The present results are new and original for the problem of MHD stagnation-point flow over a stretching/shrinking sheet in a hybrid nanofluid, with the effect of induced magnetic field.

Effects of Second-Order Slip and Magnetic Field on Mixed Convection Stagnation-Point Flow of a Maxwellian Fluid: Multiple Solutions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
M. M. Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Reverse Flow ◽  
Second Order ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Variable Surface

In this paper, we investigate the effects of second-order slip and magnetic field on the nonlinear mixed convection stagnation-point flow toward a vertical permeable stretching/shrinking sheet in an upper convected Maxwell (UCM) fluid with variable surface temperature. Numerical results are obtained using the bvp4c function from matlab for the reduced skin-friction coefficient, the rate of heat transfer, the velocity, and the temperature profiles. The results indicate that multiple (dual) solutions exist for a buoyancy opposing flow for certain values of the parameter space irrespective to the types of surfaces whether it is stretched or shrinked. It is found that an applied magnetic field compensates the suction velocity for the existence of the dual solutions. Depending on the parametric conditions; elastic parameter, magnetic field parameter, first- and second-order slip parameters significantly controls the flow and heat transfer characteristics. The illustrated streamlines show that for upper branch solutions, the effects of stretching and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag away from the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions when the mixed convection effect is less significant.

scholarly journals Unsteady electromagnetic radiative nanofluid stagnation-point flow from a stretching sheet with chemically reactive nanoparticles, Stefan blowing effect and entropy generation

2018 ◽  
Vol 232 (2-3) ◽  
pp. 69-82 ◽  
Author(s):  
Puneet Rana ◽  
Nisha Shukla ◽  
O Anwar Bég ◽  
A Kadir ◽  
Bani Singh
Keyword(s):  
Magnetic Field ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Dimensional System ◽  
Electrical Field ◽  
Electric Parameter ◽  
Entropy Generation Number

This article investigates the combined influence of nonlinear radiation, Stefan blowing and chemical reactions on unsteady electro-magneto-hydrodynamic stagnation-point flow of a nanofluid from a horizontal stretching sheet. Both electrical and magnetic body forces are considered. In addition, the effects of velocity slip, thermal slip and mass slip are considered at the boundaries. An analytical method named as homotopy analysis method is applied to solve the non-dimensional system of nonlinear partial differential equations which are obtained by applying similarity transformations on governing equations. The effects of emerging parameters such as Stefan blowing parameter, electric parameter and magnetic parameter on the important physical quantities are presented graphically. In addition, an entropy generation analysis is provided in this article for thermal optimization. The flow is observed to be accelerated both with increasing magnetic field and electrical field. Entropy generation number is markedly enhanced with greater magnetic field, electrical field and Reynolds number, whereas it is reduced with increasing chemical reaction parameter.

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