Stagnation point flow of Jeffrey nanofluid with activation energy and convective heat and mass conditions

2021 ◽  
pp. 095440892110442
Author(s):  
K. Muhammad ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Activation Energy ◽  
Relaxation Time ◽  
Differential Equations ◽  
Prandtl Number ◽  
Convective Heat ◽  
Deborah Number ◽  
Fluid Temperature ◽  
Retardation Time ◽  
Transport Parameters ◽  
Jeffrey Nanofluid

This research reports stagnation flow of Jeffrey nanofluid toward a permeable stretching cylinder. Brownian motion, thermophoresis, thermal radiation and viscous dissipation are explored. Convective heat-mass conditions are implemented. Moreover, activation energy is taken into account. Transformations (variables) are utilized in order to convert PDEs (Partial DIfferential Equations). (continuity, momentum, energy and concentration equation) into ODEs (Ordinary Differential Equations). Resulting systems are solved by the optimal homotopy analysis method. Behaviors of involved flow, heat and mass transport parameters for velocity, concentration and temperature are examined. Surface friction and Sherwood number and Nusselt numbers are also examined. Velocity of the fluid can be minimized by higher estimations of parameter due to ratio of relaxation and retardation time, suction and injection parameters. Decay in fluid temperature is observed for higher Prandtl number and Deborah number for relaxation time parameter. Skin friction coefficient is controlled via higher values of parameter due to ratio of relaxation and retardation time. Intensification in heat transfer rate (Nusselt number) is seen via higher values of parameter due to ratio of relaxation and retardation time, radiation parameter, Prandtl number and Deborah number for relaxation time and curvature parameter.

scholarly journals MHD three dimensional flow of Oldroyd-B nanofluid over a bidirectional stretching sheet: DTM-Padé Solution

2019 ◽  
Vol 8 (1) ◽  
pp. 744-754 ◽  
Author(s):  
Sumit Gupta ◽  
Sandeep Gupta
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Prandtl Number ◽  
Comparative Study ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Deborah Number ◽  
Motion Parameter ◽  
Physical Parameters ◽  
Brownian Motion Parameter

Abstract Current article is devoted with the study of MHD 3D flow of Oldroyd B type nanofluid induced by bi-directional stretching sheet. Expertise similarity transformation is confined to reduce the governing partial differential equations into ordinary nonlinear differential equations. These dimensionless equations are then solved by the Differential Transform Method combined with the Padé approximation (DTM-Padé). Dealings of the arising physical parameters namely the Deborah numbers β1 and β2, Prandtl number Pr, Brownian motion parameter Nb and thermophoresis parameter Nt on the fluid velocity, temperature and concentration profile are depicted through graphs. Also a comparative study between DTM and numerical method are presented by graph and other semi-analytical techniques through tables. It is envisage that the velocity profile declines with rising magnetic factor, temperature profile increases with magnetic parameter, Deborah number of first kind and Brownian motion parameter while decreases with Deborah number of second kind and Prandtl number. A comparative study also visualizes comparative study in details.

Effects of Chemical Reaction, Activation Energy and Thermal Energy on Magnetohydrodynamics Maxwell Fluid Flow in Rotating Frame

2021 ◽  
Vol 10 (1) ◽  
pp. 67-74
Author(s):  
Hunegnaw Dessie
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Heat Radiation ◽  
Rotating Frame ◽  
Rotational Parameter ◽  
The Impact

The purpose of this research is to see how chemical processes, activation energy, and heat radiation affect MHD flow of Maxwell fluid in a rotating frame. Using applicable similarity transformations, the partial differential equations that regulate the flow are reduced to extremely nonlinear ordinary differential equations. Graphs and tables are used to study the impact of monitoring parameters on velocity, temperature, concentration profiles, reduced Nusselt number, reduced Sherwood numbers, and skin friction coefficients. Outstanding agreement is obtained when the present findings of the study is compared with the previous related research works. In the study, it is noted that an increase of the thermal radiation parameters contributes to an increase of the flow temperature region. When a fluid is subjected to a greater rotation parameter, the thermal boundary layer thickens and the heat transfer rate decrease. Moreover, a decline of mass transfer rate is observed for a rise of Prandl number, rotational parameter or Deborah number.

scholarly journals Effects of Joule Heating and Viscous Dissipation on Magnetohydrodynamic Boundary Layer Flow of Jeffrey Nanofluid over a Vertically Stretching Cylinder

Coatings ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 353
Author(s):  
Haroon Ur Rasheed ◽  
Abdou AL-Zubaidi ◽  
Saeed Islam ◽  
Salman Saleem ◽  
Zeeshan Khan ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Formulation ◽  
Skin Friction Coefficient ◽  
Deborah Number ◽  
Radiation Absorption ◽  
Partial Differential ◽  
System Parameters ◽  
Jeffrey Nanofluid

This article investigates unsteady magnetohydrodynamic (MHD) mixed convective and thermally radiative Jeffrey nanofluid flow in view of a vertical stretchable cylinder with radiation absorption and heat; the reservoir was addressed. The mathematical formulation of Jeffrey nanofluid is established based on the theory of boundary layer approximations pioneered by Prandtl. The governing model expressions in partial differential equations (PDEs) form was transformed into dimensionless form via similarity transformation technique. The set of nonlinear nondimensional partial differential equations are solved with the help of the homotopic analysis method. For the purpose of accuracy, the optimizing system parameters, convergence, and stability analysis of the analytical algorithm (CSA) were performed graphically. The velocity, temperature, and concentration flow are studied and shown graphically with the effect of system parameters such as Grashof number, Hartman number, Prandtl number, thermal radiation, Schmidt number, Eckert number, Deborah number, Brownian parameter, heat source parameter, thermophoresis parameter, and stretching parameter. Moreover, the consequence of system parameters on skin friction coefficient, Nusselt number, and Sherwood number is also examined graphically and discussed.

scholarly journals Boundary layer flow over a moving plate in MHD Jeffrey nanofluid: A revised model

2018 ◽  
Vol 189 ◽  
pp. 02005
Author(s):  
S M Zokri ◽  
N S Arifin ◽  
A R M Kasim ◽  
N F Mohammad ◽  
M Z Salleh
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Temperature Profile ◽  
Graphical Representation ◽  
Numerical Approach ◽  
Deborah Number ◽  
Physical Parameters ◽  
Moving Plate ◽  
Perfect Agreement ◽  
Jeffrey Nanofluid

The flow and heat transfer of magnetohydrodynamic (MHD) Jeffrey nanofluid induced by a moving plate is examined numerically. The formulation is established by using the revised model of passively controlled boundary layer instead of actively, which is more realistic physically. The similarity transformation variables are used to transform the partial differential equations into a set of ordinary differential equations before solving it via numerical approach called as the Runge-Kutta Fehlberg method. Graphical representation of the physical parameters over the temperature profile is deliberated. Temperature profile is slowed down due to the parameters of Deborah number and plate velocity while the reverse trend is observed for thermophoresis diffusion parameter. The Brownian motion has shown an insignificant outcome on the temperature profile. A comparison with the earlier publication has been conducted and a perfect agreement between the data is detected.

Significance of Activation Energy and Effective Prandtl Number in Accelerated Flow of Jeffrey Nanoparticles With Gyrotactic Microorganisms

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Sami Ullah Khan ◽  
Iskander Tlili
Keyword(s):  
Activation Energy ◽  
Prandtl Number ◽  
Thermal Radiation ◽  
Flow Problem ◽  
Skin Friction Coefficient ◽  
Deborah Number ◽  
Flow Parameters ◽  
Gyrotactic Microorganism ◽  
The Impact ◽  
Buoyancy Ratio

Abstract This research addresses the interesting rheological features of Jeffrey nanofluid containing gyrotactic microorganism over an accelerated configuration. The additional consequences of activation energy and thermal radiation are also encountered in the current flow problem. The characteristics of nanofluid is utilized by using Buongiorno’s nanofluid model, while the phenomenon of bioconvection is evaluated by Kuznestov and Nield model. Unlike traditional attempts, the analysis for thermal radiation is performed by using “one parametric approach” by expressing the Prandtl number and thermal radiation parameter in combined form, namely, effective Prandtl number. The governing equations reflecting the flow problem are analytically treated with the help of homotopic algorithm. The impact of flow parameters is graphically elaborated with relevant physical significance. Further, the numerical expressions for effective local Nusselt number, local Sherwood number, and motile density number with variation of flow parameters in articulated tabular form. It is observed that magnitude of skin friction coefficient oscillates periodically with time and magnitude of oscillation increases with increment of Deborah number and mixed convection constant. It is further emphasized that the temperature distribution is enhanced with buoyancy ratio constant and bioconvection Rayleigh number. The microorganism distribution increases with buoyancy ratio constant but reverse trend has been examined for Peclet number. The observations from the reported problem can be more effective for the development of bifurcation processes, biofuels, enzymes, etc.

Entropy Generation Analysis of Radiated Magnetohydrodynamic Flow of Carbon Nanotubes Nanofluids with Variable Conductivity and Diffusivity Subjected to Chemical Reaction

2021 ◽  
Vol 10 (4) ◽  
pp. 491-505
Author(s):  
Gopinath Mandal ◽  
Dulal Pal
Keyword(s):  
Magnetic Field ◽  
Activation Energy ◽  
Carbon Nanotubes ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Entropy Generation ◽  
Concentration Profile ◽  
Fluid Temperature

The purpose of this article is to analyze the entropy generation and heat and mass transfer of carbon nano-tubes (CNTs) nanofluid by considering the applied magnetic field under the influence of thermal radiation, variable thermal conductivity, variable mass diffusivity, and binary chemical reaction with activation energy over a linearly stretching cylinder. Convective boundary conditions on heat and mass transfer are considered. An isothermal model of homogeneous-heterogeneous reactions is used to regulate the solute concentration profile. It is assumed that the water-based nanofluid is composed of single and multi-walled carbon nanotubes. Employing a suitable set of similarity transformations, the system of partial differential equations is transformed into the system of nonlinear ordinary differential equations before being solved numerically. Through the implementation of the second law of thermodynamics, the total entropy generation is calculated. In addition, entropy generation for fluid friction, mass transfer, and heat transfer is discussed. This study is specially investigated for the impact of the chemical reaction, and activation energy with entropy generation subject to distinct flow parameters. It is found that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with higher radiation parameters and thermal Biot number. Entropy and Bejan number are found to be an increasing function of solid volume fraction, magnetic field, and curvature parameters. Binary chemical reaction and activation energy on concentration profile have opposite effects.

scholarly journals Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 917-928 ◽  
Author(s):  
Zeeshan Khan ◽  
Haroon Ur Rasheed ◽  
Tawfeeq Abdullah Alkanhal ◽  
Murad Ullah ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Physical Parameters ◽  
Fluid Temperature

Abstract The effect of magnetic field on the flow of the UCMF (Upper-Convected-Maxwell Fluid) with the property of a heat source/sink immersed in a porous medium is explored. A shrinking phenomenon along with the permeability of the wall are considered. The governing equations for the motion and transfer of heat of the UC MF along with boundary conditions are converted into a set of coupled nonlinear mathematical equations. Appropriate similarity transformations are used to convert the set of nonlinear partial differential equations into nonlinear ordinary differential equations. The modeled ordinary differential equations have been solved by the Homotopy Analysis Method (HAM). The convergence of the series solution is established. For the sake of comparison, numerical (ND-Solve method) solutions are also obtained. Special attention is given to how the non-dimensional physical parameters of interest affect the flow of the UCMF. It is observed that with the increasing Deborah number the velocity decreases and the temperature inside the fluid increases. The results show that the velocity and temperature distribution increases with a porous medium. It is also observed that the magnetic parameter has a decelerating effect on velocity while the temperature profiles increases in the entire domain. Due to the increase in Prandtl number the temperature profile increases. It is also observed that the heat source enhance the thermal conductivity and increases the fluid temperature while the heat sink provides a decrease in the fluid temperature.

scholarly journals Falkner–Skan Equation with Heat Transfer: A New Stochastic Numerical Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Imran Khan ◽  
Hakeem Ullah ◽  
Hussain AlSalman ◽  
Mehreen Fiza ◽  
Saeed Islam ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Thermal Boundary Layer ◽  
Feedforward Neural Networks ◽  
Numerical Approach ◽  
Deborah Number ◽  
Squeezing Flow ◽  
And Performance

In this study, a new computing model is developed using the strength of feedforward neural networks with the Levenberg–Marquardt method- (NN-BLMM-) based backpropagation technique. It is used to find a solution for the nonlinear system obtained from the governing equations of Falkner–Skan with heat transfer (FSE-HT). Moreover, the partial differential equations (PDEs) for the unsteady squeezing flow of heat and mass transfer of the viscous fluid are converted into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated in different scenarios by a variation of various embedding parameters, Deborah number ( β ) and Prandtl number (Pr). The training (TR), testing (TS), and validation (VD) of the NN-BLMM model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics such as the mean square error (MSE), error histogram (EH), and regression (RG) plots are utilized for measuring the effectiveness and performance of the NN-BLMM infrastructure model. The experiments showed that comparisons between the results of the proposed model and the reference results match in terms of convergence up to E-05 to E-10. This proves the validity of the NN-BLMM model. Furthermore, the results demonstrated that there is an increase in the velocity profile and a decrease in the thickness of the thermal boundary layer by increasing the Deborah number. Also, the thickness of the thermal boundary layer is decreased by increasing the Prandtl number.

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.

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