Dynamics of Activation Energy and Nonlinear Mixed Convection in Darcy-Forchheimer Radiated Flow of Carreau Nanofluid near Stagnation Point Region

2020 ◽  
pp. 1-20
Author(s):  
Muhammad Ijaz Khan ◽  
Faris Alzahrani
Keyword(s):  
Activation Energy ◽  
Ohmic Heating ◽  
Colloidal Suspensions ◽  
Continuous Phase ◽  
Nonlinear Flow ◽  
Brownian Diffusion ◽  
Bejan Number ◽  
Surface Drag ◽  
Similarity Transformations ◽  
The Impact

Abstract Nanofluid comprising nanometer sized materials, called nanoparticles. These liquids are built colloidal suspensions of nanomaterials in a continuous phase liquid. The nanomaterials utilized in nanoliquids are typically made of carbon nanotubes, oxides and metals. In this research communication, the impact of Brownian diffusion and thermophoresis is addressed in flow of non-Newtonian fluid with CC model towards shrinking/stretching surface. The energy equation is developed subject to dissipation, radiative flux (nonlinear) and Ohmic heating. Activation energy is further considered for chemical reaction. The nonlinear flow expressions are transformed into ordinary differential equations with the help of similarity transformations. The obtained systems of ODE's are numerically solved through Shooting method (bvp4c). The concentration, temperature and velocity profiles are determined graphically. Mass transfer, surface drag force and heat transfer rate are showed by tables. In last, entropy and Bejan number are discussed through graphs in which entropy showed increasing behavior for magnetic, radiation, Brinkman and diffusivity parameter but Bejan number showed opposite behavior for them.

Binary chemical reaction with activation energy in dissipative flow of non-Newtonian nanomaterial

2020 ◽  
Vol 19 (03) ◽  
pp. 2040006 ◽  
Author(s):  
M. Ijaz Khan ◽  
Faris Alzahrani
Keyword(s):  
Activation Energy ◽  
Mass Transfer ◽  
Chemical Reaction ◽  
Ohmic Heating ◽  
Skin Friction Coefficient ◽  
Entropy Rate ◽  
Brownian Diffusion ◽  
Jeffrey Fluid ◽  
Bejan Number ◽  
Engineering Sciences

This paper deals with the entropy optimization and heat transport of magneto-nanomaterial flow of non-Newtonian (Jeffrey fluid) towards a curved stretched surface. MHD fluid is accounted. The modeling of energy expression is developed subject to Brownian diffusion, Joule (Ohmic) heating, thermophoresis and viscous dissipation. Total entropy rate is discussed with the help of fluid friction irreversibility, mass transfer irreversibility, Joule heating irreversibility and heat transfer irreversibility. Binary chemical reaction with the smallest amount of activation energy is further considered. The governing equations of Jeffrey fluid with effects of hydrodynamic, thermal radiation, heat and mass transfer were solved through built-in-shooting method. The flow variables on the entropy rate, velocity field, concentration, Bejan number, skin friction coefficient and temperature are physically discussed through various graphs. The outcomes reveal that the entropy rate increases with an enhancement in curvature parameter. Such obtained outcomes help in mechanical and industrial engineering sciences. Moreover, the velocity and temperature decays versus ratio of relaxation to retardation times are also noticed.

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 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.

Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy

2021 ◽  
Vol 10 (1) ◽  
pp. 75-82
Author(s):  
Gadamsetty Revathi ◽  
Jayachandra Babu Macherla ◽  
Chakravarthula Sivakrishnam Raju ◽  
Rohit Sharma ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Activation Energy ◽  
Biot Number ◽  
Schmidt Number ◽  
Surface Drag ◽  
Dissipative Flow ◽  
Curvature Parameter ◽  
The Impact ◽  
Local Sherwood Number ◽  
Acceptable Agreement

This paper theoretically clarifies the impact of pertinent parameters, including viscous dissipation on the flow of Carreau fluid through a permeable arched elongating sheet. Flow describing equations are metamorphosed as ODEs and executed using the combination of shooting and Runge-Kutta strategies. Consequences are elucidated using tables and graphs. We discovered that (a) an appreciable decline in the concentration against temperature difference and reaction rate parameters (b) curvature parameter and porosity parameters registered opposite behaviour to each other on velocity profile (c) there is a reduction in the heat transfer rate with larger Eckert number and curvature parameters (d) Biot number ameliorates the temperature and local Nusselt number (e) Schmidt number and activation energy parameters are showing different behaviours on local Sherwood number. And also, magnetic field and porosity parameters minimize the velocity and surface drag force and Biot number ameliorates the temperature. Further, present results are validated with the earlier outcomes and perceived an acceptable agreement.

Entropy generation in radiative flow of Ree-Eyring fluid due to due rotating disks

2019 ◽  
Vol 29 (6) ◽  
pp. 2057-2079 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Sohail Ahmad Khan ◽  
Tasawar Hayat ◽  
Muhammad Faisal Javed ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Transfer ◽  
Entropy Generation ◽  
Magnetic Parameter ◽  
Nonlinear Flow ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Rotating Disks ◽  
Content Type ◽  
The Impact

Purpose This study aims to examine the flow characteristics of Ree–Eyring fluid between two rotating disks. The characteristics of heat transfer are discussed in presence of viscous dissipation, heat source/sink and nonlinear radiative heat flux. Design/methodology/approach Nonlinear flow expressions lead to ordinary ones through adequate similarity transformations. The ordinary differential system has been tackled through optimal homotopic method. The impact of different flow variables on the velocity field, entropy generation rate and temperature fields is graphically discussed. The surface drag force and heat transfer rate are numerically examined via various pertinent parameters. Findings By minimization of values of stretching parameter and Brinkman number, the entropy generation rate can be controlled. The entropy generation rate enhances for higher values of magnetic parameter, while the Bejan number is decreased via magnetic parameter. Originality/value No such work is yet published in the literature.

scholarly journals Entropy Generation in MHD Radiative Flow of CNTs Casson Nanofluid in Rotating Channels with Heat Source/Sink

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Poom Kumam ◽  
Zahir Shah ◽  
Abdullah Dawar ◽  
Haroon Ur Rasheed ◽  
Saeed Islam
Keyword(s):  
Heat Source ◽  
Entropy Generation ◽  
Second Law Of Thermodynamics ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Bejan Number ◽  
Surface Drag ◽  
Casson Nanofluid ◽  
Source Sink ◽  
The Impact

We presented the applications of entropy generation for SWCNTs and MWCNTs based on kerosene oil for Casson nanofluid flow by rotating channels. Kerosene oil has advanced thermal conductivity and exclusive features and has a lot of practical uses due to its unique behavior. That is why we have used kerosene oil as a based fluid. For the entropy generation second law of thermodynamics is applied and implemented for the nanofluid transport mechanism. In the presence of magnetic field, the effects of thermal radiations and heat source/sink on the temperature profiles are studied. The fluid flow is supposed in steady state. With the help of suitable similitude parameters, the leading equations have been transformed to a set of differential equations. The solution of the modeled problem has been carried out with the homotopic approach. The physical properties of carbon nanotubes are shown through tables. The effects of the imbedded physical parameters on the velocities, temperature, entropy generation rate, and Bejan number profiles are investigated and presented through graphs. Moreover, the impact of significant parameters on surface drag force and heat transfer rate is tabulated.

Numerical modelling of activation energy and hydromagnetic non-Newtonian fluid particle deposition flow in a rotating disc

2021 ◽  
pp. 095440892110459
Author(s):  
B. Hari Babu ◽  
P. Srinivasa Rao ◽  
M. Gnaneswara Reddy ◽  
S.V.K. Varma
Keyword(s):  
Activation Energy ◽  
Chemical Reaction ◽  
Particle Deposition ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Momentum Equation ◽  
Thermal Mass ◽  
Rotating Disc ◽  
Similarity Transformations ◽  
The Impact

This mathematical model explains the three-dimensional flow of Casson liquid through a stretchable rotating disk. In momentum equation magnetic effect and in mass equation Arrhenius chemical reaction and activation energy effects are incorporated. The equation which represents the described flow pattern is reduced to ordinary differential equations (ODEs) by using apposite similarity transformations and then they are tackled with the RKF45 method with shooting proficiency. The impact of pertinent parameters on thermal, mass and velocity curves are deliberated graphically. Further statistical values of skin friction, Nusselt number and Sherwood number are portrayed in table format. The result outcome reveals that, increase in the values of a magnetic parameter reduces velocity gradient. The concentration profile declines for augmented values of chemical reaction rate parameter, but a contrasting trend is seen in the concentration gradient for increased values of activation energy. Further, upsurge in thermophoretic and Brownian motion parameter reduces the mass transfer.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Slip flow of Jeffrey nanofluid with activation energy and entropy generation applications

2021 ◽  
Vol 13 (3) ◽  
pp. 168781402110065
Author(s):  
Hu Ge-JiLe ◽  
Sumaira Qayyum ◽  
Faisal Shah ◽  
M Ijaz Khan ◽  
Sami Ullah Khan
Keyword(s):  
Activation Energy ◽  
Entropy Generation ◽  
Slip Flow ◽  
Graphical Analysis ◽  
Thermal Engineering ◽  
Bejan Number ◽  
Nano Technology ◽  
Flow Equations ◽  
Jeffrey Nanofluid ◽  
Buongiorno Model

The growing development in the thermal engineering and nano-technology, much attention has been paid on the thermal properties of nanoparticles which convey many applications in industrial, technological and medical era of sciences. The noteworthy applications of nano-materials included heat transfer enhancement, thermal energy, solar systems, cooling of electronics, controlling the heat mechanisms etc. Beside this, entropy generation is an optimized scheme which reflects significances in thermodynamics systems to control the higher energy efficiency. On this end, present work presents the slip flow of Jeffrey nanofluid over a stretching sheet with applications of activation energy and viscous dissipation. The entropy generation features along with Bejan number significance is also addressed in present analysis. Buongiorno model of nanofluid is used to discuss the heat and mass transfer. The formulated flow equations are attained into non-dimensional form. An appropriate ND MATHEMATICA built-in scheme is used to find the solution. The solution confirmation is verified by performing the error analysis. For developed flow model and impacted parameters, a comprehensive graphical analysis is performed. It is observed that slip phenomenon is used to decays the velocity profile. Temperature and concentration are in direct relation with Brownian motion parameter and activation energy respectively. Entropy and Bejan number have same results for greater diffusion parameter.

Dissipative effects on a chemically and thermally radiative heat fluid flow past a shrinking porous sheet

2020 ◽  
pp. 1-14
Author(s):  
A. Shahid ◽  
M. Ali Abbas ◽  
H.L. Huang ◽  
S.R. Mishra ◽  
M.M. Bhatti
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Linearization Method ◽  
Surface Drag ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Dissipative Effects ◽  
Successive Linearization Method

The present study analyses the dissipative influence into an unsteady electrically conducting fluid flow embedded in a pervious medium over a shrinkable sheet. The behavior of thermal radiation and chemical reactions are also contemplated. The governing partial differential equations are reformed to ordinary differential equations by operating similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the Successive linearization method (SLM) via Matlab software. The velocity, temperature, and concentration magnitudes for distant values of the governing parametric quantities are conferred, and their conduct is debated via graphical curves. The surface drag coefficient increases, whereas the local Nusselt number and Sherwood number decreases for enhancing unsteadiness parameter across suction parameter. Moreover, the magnetic and suction parameters accelerate velocity magnitudes while by raising porosity parameter, velocity decelerates. Larger numeric of thermal radiation parameter and Eckert number accelerates the temperature profile while by enhancing Prandtl number it decelerates. Schmidt number and chemical reaction parameters slowdowns the concentration distribution, and the chemical reaction parameter influences on the point of chemical reaction that benefits the interface mass transfer. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities.

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