scholarly journals Free Convective Flow of Water/Ethylene Glycol Based Micropolar Nanofluid Over a Shrinking Sheet

2021 ◽  
Vol 11 (5) ◽  
pp. 12596-12605
Keyword(s):  
Ethylene Glycol ◽  
Shrinking Sheet ◽  
Heat Equations ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Micropolar Nanofluid ◽  
Non Linear ◽  
Linear Differential ◽  
The Impact ◽  
Linear Pdes

In this article, the free convective micropolar nanofluid was investigated over a shrinking sheet in the presence of a heat source by tacking into the water/ethylene glycol-based nanofluid account. The physical problem is first modeled. Under the assumptions of Boussinesq's approximation, the governing equations are reduced into non-linear PDEs. The combined non-linear PDEs representing momentum and non-homogeneous heat equations were reduced to a series of regular non-linear differential equations with appropriate similarity transformations. By applying the Runge-Kutta procedure followed by the Shooting technique, the transformed equations are then solved. Via the diagrams, the impact of related parameters characterizing the flow was presented and then addressed. It is observed that volumetric fraction has a substantial influence on the velocity profile and also induces a decrease in the boundary layer because water-based nanofluid has high thermal conductivity relative to Ferro nanofluid based on ethylene glycol.

scholarly journals Analysis of Chemical Reaction on MHD Micropolar Fluid Flow over a Shrinking Sheet near Stagnation Point with Nanoparticles and External Heat

2021 ◽  
Vol 39 (1) ◽  
pp. 262-268
Author(s):  
Krishnandan Verma ◽  
Debozani Borgohain ◽  
Bishwaram Sharma
Keyword(s):  
Stagnation Point ◽  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Numerical Data ◽  
Mhd Flow ◽  
Heat Transfer Process ◽  
External Heat ◽  
Shrinking Sheet ◽  
Similarity Transformations ◽  
Micropolar Nanofluid

The present study investigates numerically MHD flow near the stagnation point of micropolar fluid through a shrinking sheet containing nanoparticles under the influence of chemical reaction and external heat. The study is an attempt to investigate the flow behaviour of micropolar nanofluid because of its importance in heat transfer process in industries as well as cooling systems. The governing equations are converted to nonlinear ordinary differential equations by implementing similarity transformations. Numerical results are investigated in the form of figures and tables by using MATLAB built in solver bvp4c for various dimensionless parameters. The impacts of external heat parameter on temperature and chemical reaction factor on concentration of the nanofluid are illustrated in the form of graphs. It is observed that the temperature of the nanofluid and nanoparticle volume distributions increase when Biot number attain larger values. Rise in Thermophoretic parameter increases the nanoparticles concentration in the boundary layer. Numerical data are presented for Nusselt number and Sherwood number.

Characteristics of Magnetohydrodynamics Nanofluid Flow in the Presence of Porous Medium Towards a Stretching Sheet with a Convective Boundary Condition

2020 ◽  
Vol 9 (4) ◽  
pp. 346-353
Author(s):  
M. Satya Prasad ◽  
N. V. Swamy Naidu ◽  
R. Srinivasa Raju
Keyword(s):  
Porous Medium ◽  
Variable Viscosity ◽  
Convective Boundary Condition ◽  
Dimensionless Temperature ◽  
Nanoparticle Concentration ◽  
Convective Boundary ◽  
Nano Fluid ◽  
Non Linear ◽  
Linear Differential ◽  
The Impact

With the effects of variable viscosity and convective boundary conditions, the contemporary studies work ambitions to investigate the together effects of the magnetic field and porous medium on non-Newtonian nano fluid flow to a stretching layer. In this latest work, to examine the impact of thermophoresis and Brownian motion, the nanofluid model is utilized. To lessen the basic governing coupled non-linear PDE’s for velocity (momentum), temperature (energy), and nanoparticle concentration to an assortment of ordinary non-linear differential equations, the necessary transformations are used. Utilizing the fourth-fifth order Runge-Kutta-Fehlberg strategy, the resulting reshaped conditions are tackled mathematically. The effects on the dimensionless temperature, velocity, nanoparticle concentration profiles of various engineering parameters are discussed and graphically analyzed. The numerically computed values of skin-friction, coefficients of heat transfer rate and mass transfer are tabulated. The numerical findings got are contrasted and the outcomes recently detailed as unique instances of the current examination and viewed as in reasonable consistence.

scholarly journals Boundary layer flow of magneto-micropolar nanofluid flow with Hall and ion-slip effects using variable thermal diffusivity

2017 ◽  
Vol 65 (3) ◽  
pp. 383-390 ◽  
Author(s):  
M. Bilal ◽  
S. Hussain ◽  
M. Sagheer
Keyword(s):  
Thermal Diffusivity ◽  
Differential Equations ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Micropolar Nanofluid ◽  
Ion Slip ◽  
Layer Flow ◽  
Linear Differential

AbstractIn the present article, magneto-micropolar nanofluid flow with suction or injection in a porous medium over a stretching sheet for the heat and mass transfer is analyzed numerically. Both Hall and ion-slip effects are considered along with variable thermal diffusivity. The governing partial differential equations are transformed to ordinary differential equations using usual similarity transformations. These coupled non-linear differential equations are solved using the shooting method. Effects of prominent parameter on velocities, temperature and concentration are discussed graphically. Numerical values of skin-friction coefficient, local Nusselt number and local Sherwood number are also tabulated and discussed.

scholarly journals Numerical Solution of Boundary Layer MHD Flow with Viscous Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
S. R. Mishra ◽  
S. Jena
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Graphical Representation ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Shrinking Sheet ◽  
Shooting Technique ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Runge Kutta Method

The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.

Melting heat transfer in boundary layer stagnation-point flow of a nanofluid towards a stretching–shrinking sheet

2014 ◽  
Vol 92 (12) ◽  
pp. 1703-1708 ◽  
Author(s):  
Kishore Kumar Ch. ◽  
Shankar Bandari
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Fourth Order Method

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.

Double Diffusion Effects on Magnetohydrodynamic Non-Newtonian Fluid Nanoparticles

2017 ◽  
Vol 14 (1) ◽  
pp. 694-703 ◽  
Author(s):  
Noreen Sher Akbar ◽  
C. M Khalique ◽  
Z. H Khan
Keyword(s):  
Fluid Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Double Diffusion ◽  
Skin Friction Coefficient ◽  
Shooting Technique ◽  
Flow Equations ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Micropolar Nanofluid

In the present article, the double-diffusive natural convection of a micropolar nanofluid over a linearly stretching sheet is discussed. The flow equations are transformed into ordinary differential equations using similarity transformations. The numerical solutions are computed using shooting technique and compared with the literature for the special case of pure fluid flow and found to be in good agreement. Graphical results are presented to illustrate the effects of various fluid flow parameters on velocity, heat transfer, nanoparticle volume fraction, salt concentration, Nusselt number, Sherwood number and skin friction coefficient for both assisting and opposing flows.

scholarly journals Thermo-Diffusion and Multislip Effects on MHD Mixed Convection Unsteady Flow of Micropolar Nanofluid over a Shrinking/Stretching Sheet with Radiation in the Presence of Heat Source

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 49 ◽  
Author(s):  
Sohaib Abdal ◽  
Bagh Ali ◽  
Saba Younas ◽  
Liaqat Ali ◽  
Amna Mariam
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Mixed Convection ◽  
Unsteady Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Linear Ordinary Differential Equations ◽  
Micropolar Nanofluid ◽  
Non Linear ◽  
Fourth Order Method

The main purpose of this study is to investigate the multislip effects on the magneto-hydrodynamic (MHD) mixed convection unsteady flow of micropolar nano-fluids over a stretching/shrinking sheet along with radiation in the presence of a heat source. The consequences of multislip and buoyancy conditions have been integrated. By using the suitable similarity variables are used to solve the governing non-linear partial differential equations into a system of coupled non-linear ordinary differential equations. The transformed equations are solved numerically by using Runge–Kutta fourth-order method with shooting technique. The impacts of the several parameters on the velocity, temperature, micro-rotation, and concentration profiles as well as on the skin friction coefficient, Sherwood number, and Nusselt number are discussed with the help of graphs and tables.

Influence of nonlinear thermal radiation on rotating flow of Casson nanofluid

2018 ◽  
Vol 7 (2) ◽  
pp. 91-101 ◽  
Author(s):  
M. Archana ◽  
B. J. Gireesha ◽  
B. C. Prasannakumara ◽  
R.S.R. Gorla
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Nonlinear Thermal Radiation ◽  
Shooting Technique ◽  
Casson Nanofluid ◽  
Similarity Transformations ◽  
Heating Effects ◽  
Temperature Component ◽  
Fifth Order ◽  
The Impact

Abstract The heat and mass transfer of rotating Casson nanofluid flow is incorporated in the present study. Influence of magnetic field, nonlinear thermal radiation, viscous dissipation and Joule heating effects are taken into the account. A set of nonlinear ordinary differential equations are obtained from the governing partial differential equations with the aid of suitable similarity transformations. The resultant equations are solved for the numerical solution using Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique. The impact of several existing physical parameter on velocity, temperature and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that, velocity component decreases and temperature component increases for rotating parameter.

scholarly journals Analysis of Ethylene Glycol (EG)-based ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) Hybrid Nanofluids for Optimal Car Radiator Coolant

2020 ◽  
pp. 34-50
Author(s):  
J. A. Okello ◽  
W. N. Mutuku ◽  
A. O. Oyem
Keyword(s):  
Differential Equations ◽  
Ethylene Glycol ◽  
Waste Heat ◽  
Cooling System ◽  
Integration Scheme ◽  
Shooting Technique ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Hybrid Nanofluids

Coolants are vital in any automotive since they manage the heat in the internal combustion of the engines by preventing corrosion in the cooling system as well as assist in eradicating the engine’s waste heat. This paper examines three different types of ethylene glycol-based hybrid nanofluids ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) to establish their cooling capabilities for industrial cooling applications. The vertical flow of these hybrid nanofluids combination through a semi-infinite convectively heated flat plate mimicking the flow of coolant in car radiator is modeled. The governing non-linear partial differential equations of fluid flow are transformed into a system of coupled non-linear ordinary differential equations using a suitable similarity transformation variables and the numerical solution executed using the shooting technique together with the fourth-order Runge-Kutta-Fehlberg integration scheme. The numerical simulation is executed using MATLAB and results are displayed graphically. The effects of pertinent parameters on velocity, temperature, skin friction, and local Nusselt number are investigated. From the study (Cu-Al2O3  hybrid nanocoolant leads to a rapid decrease in temperature at the boundary layer.

scholarly journals Modified MHD Radiative Mixed Convective Nanofluid Flow Model with Consideration of the Impact of Freezing Temperature and Molecular Diameter

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 833 ◽  
Author(s):  
Umar Khan ◽  
Adnan Abbasi ◽  
Naveed Ahmed ◽  
Saima Noor ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Energy Equation ◽  
Flow Characteristics ◽  
Freezing Temperature ◽  
Point Of View ◽  
Effective Density ◽  
Nanofluid Flow ◽  
Shooting Technique ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
The Impact

Magnetohydrodynamics (MHD) deals with the analysis of electrically conducting fluids. The study of nanofluids by considering the influence of MHD phenomena is a topic of great interest from an industrial and technological point of view. Thus, the modified MHD mixed convective, nonlinear, radiative and dissipative problem was modelled over an arc-shaped geometry for Al2O3 + H2O nanofluid at 310 K and the freezing temperature of 273.15 K. Firstly, the model was reduced into a coupled set of ordinary differential equations using similarity transformations. The impact of the freezing temperature and the molecular diameter were incorporated in the energy equation. Then, the Runge–Kutta scheme, along with the shooting technique, was adopted for the mathematical computations and code was written in Mathematica 10.0. Further, a comprehensive discussion of the flow characteristics is provided. The results for the dynamic viscosity, heat capacity and effective density of the nanoparticles were examined for various nanoparticle diameters and volume fractions.

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