scholarly journals Impact of Activation Energy in Darcy-Forchheimer Flow of Cross Nanofluid over a Radial Stretching Surface with Viscous Dissipation and Joule Heating

2021 ◽  
Vol 39 (5) ◽  
pp. 1557-1566
Author(s):  
Cherlacola Srinivas Reddy ◽  
Besthapu Prabhakar
Keyword(s):  
Activation Energy ◽  
Temperature Field ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Graphical Representation ◽  
Energy Parameter ◽  
System Of Nonlinear Equations ◽  
The Impact ◽  
Forchheimer Flow

This framework analyzes the impact of activation energy (AE) and binary chemical reaction (BCR) in Darcy-Forchheimer flow of cross fluid with nanoparticles due to radially stretched surface. Moreover slip, joule heating and viscous dissipation aspects have been considered. Ordinary differential equations acquired from the modelled governing partial differential equations with the assistance of suitable transformations. Further the system of nonlinear equations is computed numerically by Runge-Kutta-Fehlberg method cum shooting technique. Graphical representation has been given to analyze the velocity, temperature and concentration fields with the effect of various pertinent parameters. It is evident that inertia coefficient declines the velocity. Velocity decays for larger Weissenberg number while opposite trend observed in temperature field. Temperature field rises for augmented values of Eckert number. Concentration increases with increase of energy parameter.

Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

Impact of Joule heating and viscous dissipation on magnetohydrodynamics boundary layer flow of viscous nanofluid subject to the stretched surface

2021 ◽  
pp. 095440892110641
Author(s):  
M. Riaz Khan ◽  
Awatef Abidi ◽  
Jamel Madiouli ◽  
Kamel Guedri ◽  
A.M. Al-Bugami ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Base Fluid ◽  
Fluid Temperature ◽  
Suction Parameter ◽  
Nanoparticles Concentration ◽  
The Impact

The two-dimensional magnetohydrodynamics incompressible flow of nanofluid about a stretching surface is investigated with the existence of viscous dissipation and Joule heating. Moreover, the impact of the convective condition and mass suction is applied with the viscous nanofluid containing copper nanoparticles and the base fluid water. The similarity variables have been employed to transform the coupled nonlinear partial differential equations into the ordinary differential equations and the numerical scheme bp4c is implemented for the further analysis of the solution. The diverse results of temperature, skin friction coefficient, velocity, and the Nusselt number according to numerous parameters have been shown graphically. It appears that the Nusselt number and the skin friction reduces, which is caused by the enhancement of both Hartman number and nanoparticles concentration. Moreover, the fluid temperature surges with the growth of Biot number, and Eckert number whereas the growth of nanoparticles concentration and suction parameter diminishes the velocity and temperature profile. The inclusion of a significant quantity of nanoparticles in the base fluid increases the density of the corresponding nanofluids and accordingly the temperature of the coupled nanoparticles in the base fluids can be modified. Hence, nanofluids build an outstanding performance in electronic components appliances and other electrical devices. The existing research is further effective in refrigerators for stabilizing their rate of cooling.

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
K. Ganesh Kumar ◽  
N.G. Rudraswamy ◽  
B.J. Gireesha ◽  
M.R. Krishnamurthy
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Nonlinear Thermal Radiation ◽  
Nonlinear Ordinary Differential Equations ◽  
Three Dimensional Flow

AbstractPresent exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge–Kutta–Fehlberg fourth–fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences

2020 ◽  
pp. 095440622096484
Author(s):  
Muhammad Nazim Tufail ◽  
Musharafa Saleem ◽  
Qasim Ali Chaudhry
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Casson Fluid ◽  
Graphical Analysis ◽  
Thermal Transfer ◽  
Fluid Parameter ◽  
Two Parameters ◽  
Unsteady Effects ◽  
Physical Quantities

The model encountered an unsteady laminar and two-dimensional convective flow of Casson fluid passing through an inclined permeable vertical stretching sheet. The momentum, thermal and concentrated boundary layers (BLs) are used to analyze the unsteady effects of magnetohydrodynamics (MHD) (neglecting induced magnetic field), viscous dissipation, Joule heating and chemical reactions. The governed partial differential equations (PDEs) of the model are reduced to the ordinary differential equations (ODEs). The ξ and χ are selected as the two parameters of the scaling transformations. By using bvp4c with MATLAB, the ODEs are solved numerically and represent their results through the graphs and tables. After the non-dimensionalizing of the equations system, we get the emerging dimensionless parameters. The concentration process was enhanced by the Casson fluid parameter but it reduced the fluid flow and thermal transfer that can be found through the graphical results. The effect of Buoyancy is highlighted as it reduced the velocity profile function, but it is a growing function of the thermal and concentrated profiles. The physical quantities are integrated through the table and graphical analysis. In the center of the wall, the number Shx versus Sc decreases, but at the end it increases.

scholarly journals Impact of Nonlinear Thermal Radiation and the Viscous Dissipation Effect on the Unsteady Three-Dimensional Rotating Flow of Single-Wall Carbon Nanotubes with Aqueous Suspensions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 207 ◽  
Author(s):  
Muhammad Jawad ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Jihen Majdoubi ◽  
I. Tlili ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Carbon Nanotubes ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Temperature Profile ◽  
Viscous Dissipation ◽  
Single Wall Carbon Nanotubes ◽  
Nonlinear Thermal Radiation ◽  
Aqueous Suspensions ◽  
The Impact

The aim of this article is to study time dependent rotating single-wall electrically conducting carbon nanotubes with aqueous suspensions under the influence of nonlinear thermal radiation in a permeable medium. The impact of viscous dissipation is taken into account. The basic governing equations, which are in the form of partial differential equations (PDEs), are transformed to a set of ordinary differential equations (ODEs) suitable for transformations. The homotopy analysis method (HAM) is applied for the solution. The effect of numerous parameters on the temperature and velocity fields is explanation by graphs. Furthermore, the action of significant parameters on the mass transportation and the rates of fiction factor are determined and discussed by plots in detail. The boundary layer thickness was reduced by a greater rotation rate parameter in our established simulations. Moreover, velocity and temperature profiles decreased with increases of the unsteadiness parameter. The action of radiation phenomena acts as a source of energy to the fluid system. For a greater rotation parameter value, the thickness of the thermal boundary layer decreases. The unsteadiness parameter rises with velocity and the temperature profile decreases. Higher value of augments the strength of frictional force within a liquid motion. For greater and ; the heat transfer rate rises. Temperature profile reduces by rising values of .

scholarly journals Effects of Binary Chemical Reaction and Activation Energy on MHD Boundary Layer Heat and Mass Transfer Flow with Viscous Dissipation and Heat Generation/Absorption

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Kh. Abdul Maleque
Keyword(s):  
Activation Energy ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Porous Plate ◽  
Local Similarity

We study an unsteady MHD free convection heat and mass transfer boundary layer incompressible fluid flow past a vertical porous plate in the presence of viscous dissipation, heat generation/absorption, chemical reaction, and Arrhenius activation energy. The plate is moving with uniform velocity. The chemical reaction rate in the function of temperature is also considered. The governing partial differential equations are reduced to ordinary differential equations by introducing local similarity transformation (Maleque (2010)) and then are solved numerically by shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically as well as the tabular form for difference values of the various parameters.

scholarly journals Thermal Analysis of 3D Electromagnetic Radiative Nanofluid Flow with Suction/Blowing: Darcy–Forchheimer Scheme

Micromachines ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1395
Author(s):  
Hammad Alotaibi ◽  
Mohamed R. Eid
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Melt Spinning ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Brownian Diffusion ◽  
Force Coefficient ◽  
Catalytic Reactors ◽  
Nanofluid Flow ◽  
The Impact

This paper discusses the Darcy–Forchheimer three dimensional (3D) flow of a permeable nanofluid through a convectively heated porous extending surface under the influences of the magnetic field and nonlinear radiation. The higher-order chemical reactions with activation energy and heat source (sink) impacts are considered. We integrate the nanofluid model by using Brownian diffusion and thermophoresis. To convert PDEs (partial differential equations) into non-linear ODEs (ordinary differential equations), an effective, self-similar transformation is used. With the fourth–fifth order Runge–Kutta–Fehlberg (RKF45) approach using the shooting technique, the consequent differential system set is numerically solved. The influence of dimensionless parameters on velocity, temperature, and nanoparticle volume fraction profiles is revealed via graphs. Results of nanofluid flow and heat as well as the convective heat transport coefficient, drag force coefficient, and Nusselt and Sherwood numbers under the impact of the studied parameters are discussed and presented through graphs and tables. Numerical simulations show that the increment in activation energy and the order of the chemical reaction boosts the concentration, and the reverse happens with thermal radiation. Applications of such attractive nanofluids include plastic and rubber sheet production, oil production, metalworking processes such as hot rolling, water in reservoirs, melt spinning as a metal forming technique, elastic polymer substances, heat exchangers, emollient production, paints, catalytic reactors, and glass fiber production.

scholarly journals A Numerical Approach for an Unsteady Tangent Hyperbolic Nanofluid Flow past a Wedge in the Presence of Suction/Injection

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
U. Shahzad ◽  
M. Mushtaq ◽  
S. Farid ◽  
K. Jabeen ◽  
R.M.A. Muntazir
Keyword(s):  
Differential Equations ◽  
Graphical Representation ◽  
Numerical Technique ◽  
Darcy Number ◽  
Numerical Approach ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Flow Past ◽  
Layer Flow ◽  
The Impact

The analysis of unsteady tangent hyperbolic nanofluid flow past a wedge with injection-suction, because of its beneficial uses, has gained a lot of attention. The present study is mainly concerned with tangent hyperbolic nanofluid (non-Newtonian nanofluid). First, we have converted the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) with the help of appropriate similarity transformations. Boundary conditions are also transformed by utilizing suitable similarity transformation. Now, for the obtained ODEs, we have used the numerical technique bvp 4 c and investigated the velocity, temperature, and concentration profiles. The accuracy of the flow model is validated by applying MAPLE d-solve command having good agreement while comparing the numerical results obtained by bvp4c for both suction and injection cases. The effects of distinct dimensionless parameters on the various profiles are being analyzed. The novel features such as thermophoresis and Brownian motion are also discussed to investigate the characteristics of heat and mass transfer. Graphical representation of the impact of varying parameters and the solution method for the abovementioned model is thoroughly discussed. It was observed that suction or injection can play a key role in controlling boundary layer flow and brings stability in the flow. It was also noticed that by increasing the Darcy number, velocity profile increases in both injection-suction cases.

scholarly journals Heat Transport Phenomena for the Darcy–Forchheimer Flow of Casson Fluid over Stretching Sheets with Electro-Osmosis Forces and Newtonian Heating

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2525
Author(s):  
Xianqin Zhang ◽  
Dezhi Yang ◽  
Muhammad Israr Ur Rehman ◽  
Aamir Hamid
Keyword(s):  
Differential Equations ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Similarity Transformations ◽  
Governing System ◽  
Electro Osmosis ◽  
The Impact ◽  
Osmotic Effects ◽  
Forchheimer Flow ◽  
Good Agreement

In this study, an investigation has been carried out to analyze the impact of electro-osmotic effects on the Darcy–Forchheimer flow of Casson nanofluid past a stretching sheet. The energy equation was modelled with the inclusion of electro-osmotic effects with viscous and Joule dissipations. The governing system of partial differential equations were transformed by using the suitable similarity transformations to a system of ordinary differential equations and then numerically solved by using the Runge–Kutta–Fehlberg method with a shooting scheme. The effects of various parameters of interest on dimensionless velocity and temperature distributions, as well as skin friction and heat transfer coefficient, have been adequately delineated via graphs and tables. A comparison with previous published results was performed, and good agreement was found. The results suggested that the electric and Forchheimer parameters have the tendency to enhance the fluid velocity as well as momentum boundary layer thickness. Enhancements in temperature distribution were observed for growing values of Eckert number. It was also observed that higher values of electric field parameter diminished the wall shear stress and local Nusselt number.

scholarly journals Insights into the Generalized Fourier's and Fick's Laws for Simulating Mixed Bioconvective Flows of Radiative-Reactive Walters-B Fluids Conveying Tiny Particles subject to Lorentz Force

2021 ◽  
Author(s):  
A. Wakif ◽  
I. L. Animasaun ◽  
Umair Khan ◽  
Ahmed Mohammed Alshehri
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Computational Cost ◽  
Energy Parameter ◽  
Linearization Method ◽  
Surface Drag ◽  
Force Coefficient ◽  
Buongiorno’S Model ◽  
Similarity Transformations ◽  
Nanoparticles Concentration

Abstract The current improvement in nanoscience and nanotechnology areas has attracted researchers' attention to biofuel, bioengineering, and biomedical and mechanical engineering applications. However, there is no report on the extension of Buongiorno's model incorporating the Cattaneo-Christov theory and the generalized Fick's law to reflect the significant impacts of Brownian motion, thermophoresis diffusion, thermal radiation, and activation energy. The governing partial differential equations (PDEs) suitable to model the case as mentioned above were converted into a unified set of ordinary differential equations (ODEs) by applying appropriate similarity transformations and solved numerically by using the Spectral Local Linearization Method (SLLM) and MATLAB in-built package. The SLLM numerical method provides robustness results with a higher level of exactness and low‐computational cost. It is worthy to conclude that the nanoparticles concentration distribution can be heightened considerably either by diminishing the Prandtl number and concentration relaxation parameter or increasing the values of nanoparticles concentration Biot number and activation energy parameter. An attractive reduction in the surface drag force coefficient is achievable via the intensifying values of the non-Newtonian parameter.

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