Impact of Velocity Slip and Temperature Jump of Nanofluid in the Flow over a Stretching Sheet with Variable Thickness

2016 ◽  
Vol 71 (5) ◽  
pp. 413-425 ◽  
Author(s):  
Chengjie Guo ◽  
Liancun Zheng ◽  
Chaoli Zhang ◽  
Xuehui Chen ◽  
Xinxin Zhang
Keyword(s):  
Brownian Motion ◽  
Variable Thickness ◽  
Stretching Sheet ◽  
Temperature Jump ◽  
Industrial Process ◽  
Lewis Number ◽  
Velocity Slip ◽  
Solid Boundary ◽  
Physical Parameters ◽  
Homotopy Analysis

AbstractIn this study, the generalised velocity slip and the generalised temperature jump of nanofluid in the flow over a stretching sheet with variable thickness are investigated. Because of the non-adherence of the fluid to a solid boundary, the velocity slip and the temperature jump between fluid and moving sheet may happen in industrial process, so taking velocity slip and temperature jump into account is indispensable. It is worth mentioning that the analysis of the velocity v, which has not been seen in the previous references related to the variable thickness sheet, is presented. The thermophoresis and the Brownian motion, which are the two very important physical parameters, are fully studied. The governing equations are simplified into ordinary differential equations by the proper transformations. The homotopy analysis method (HAM) is applied to solve the reduced equations for general conditions. In addition, the effects of involved parameters such as velocity slip parameter, temperature jump parameter, Prandtl number, magnetic field parameter, permeable parameter, Lewis number, thermophoresis parameter, and Brownian motion parameter are investigated and analysed graphically.

scholarly journals Bioconvection heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2347-2356 ◽  
Author(s):  
Bingyu Shen ◽  
Liancun Zheng ◽  
Chaoli Zhang ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Stretching Sheet ◽  
Temperature Jump ◽  
Lewis Number ◽  
Velocity Slip ◽  
Analysis Method ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Effects Of Radiation

This paper presents an investigation for bioconvection heat transfer of a nanofluid containing gyrotactic microorganisms over a stretching sheet, in which the effects of radiation, velocity slip, and temperature jump are taken into account. The non-linear governing equations are reduced into four ordinary differential equations by similarity transformations and solved by homotopy analysis method, which is verified with numerical results in good agree. Results indicate that the density of motile microorganisms and gyrotactic microorganisms increase with bioconvection Rayleigh number, while decrease with increasing in bioconvection Peclet number and bioconvection Lewis number. It is also found that the Nusselt number, Sherwood number, and gyrotactic microorganisms density depend strongly on the buoyancy, nanofluids, and bioconvection parameters.

scholarly journals Role of Brownian Motion and Thermophoresis Effects on Hydromagnetic Flow of Nanofluid Over a Nonlinearly Stretching Sheet with Slip Effects and Solar Radiation

2019 ◽  
Vol 24 (3) ◽  
pp. 489-508
Author(s):  
S.P. Anjali Devi ◽  
S. Mekala
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Hydromagnetic Flow ◽  
Nonlinearly Stretching Sheet

Abstract Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

scholarly journals Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Umar ◽  
Rizwan Akhtar ◽  
Zulqurnain Sabir ◽  
Hafiz Abdul Wahab ◽  
Zhu Zhiyu ◽  
...  
Keyword(s):  
Activation Energy ◽  
Nonlinear System ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Lewis Number ◽  
Velocity Slip ◽  
Dynamical Analysis ◽  
Physical Parameters ◽  
Similarity Transformations ◽  
Computational Paradigm

In this manuscript, a computational paradigm of technique shooting is exploited for investigation of the three-dimensional Eyring-Powell fluid with activation energy over a stretching sheet with slip arising in the field of fluid dynamics. The problem is modeled and resulting nonlinear system of PDEs is transformed into nonlinear system of ODEs using well-known similarity transformations. The strength of shooting based computing approach is employed to analyze the dynamics of the system. The proposed technique is well-designed for different scenarios of the system based on three-dimensional non-Newtonian fluid with activation energy over a stretching sheet. Slip condition is also incorporated to enhance the physical and dynamical analysis of the system. The proposed results are compared with the bvp4C method for the correctness of the solver. Graphical and numerical illustrations are used to envisage the behavior of different proficient physical parameters of interest including magnetic parameter, stretching rate parameter, velocity slip parameter, Biot number on velocity, and Lewis number on temperature and concentration.

Heat transfer in nano fluid from a stretching (shrinking), porous and heated sheet of variable thickness

2021 ◽  
pp. 095440622199070
Author(s):  
Azhar Ali ◽  
Dil Nawaz Khan Marwat ◽  
Aftab Alam
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Variable Thickness ◽  
Lewis Number ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Nano Fluid ◽  
Special Cases ◽  
Classical Models ◽  
New Variables

Heat transfer in Nano fluid from a stretching (shrinking) and porous sheet of variable thickness is investigated in this paper. A set of unseen transformations is generated and the new variables are consequently used for the solution of partial differential equations under consideration. The classical models of heat transfer in Nano fluids from rigid/porous and stretching/shrinking sheets with Brownian motion and thermophoresis effects will be the special case of current study. The set of generalized similarity variables is introduced into the systems of boundary layer equations and boundary conditions and a system of coupled and non-linear ODE’s is formed. The final ODE’s are characterized by several dimensionless parameters and their effects are examined on field quantities. The governing parameters are: suction (injection), stretching (shrinking) parameters, Brownian motion number ( Nb), Thermophoresis number ( Nt) and Lewis number ( Le). The numerical observations are shown in different graphs and tables, whereas, effects of physical parameters are seen on the rate of heat transfer [Formula: see text] and mass transfer [Formula: see text], defined at the surface of the sheet. Moreover, the new results are presented in the respective sections. The remarkable aspects of the present simulations are scrutinized, however, special cases of current simulations give the previous problems, which are highlighted in the consequent sections.

scholarly journals Influence of interfacial electrokinetic on MHD radiative nanofluid flow in a permeable microchannel with Brownian motion and thermophoresis effects

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 726-737
Author(s):  
Abdul Samad Khan ◽  
Yufeng Nie ◽  
Zahir Shah ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Body Force ◽  
Lewis Number ◽  
Physical Parameters ◽  
Analysis Method ◽  
Flat Plates ◽  
Preceding Work ◽  
Magnetohydrodynamic Effect ◽  
Homotopy Analysis

AbstractIn this study, the behavior of a microchannel flow is examined. The fluid is considered to be a nanofluid, which moves between two parallel flat plates in the presence of an electrical double layer. The Buongiorno nanofluid is considered with body force. In this study, the unphysical supposition presented in the preceding work to the discontinuity of the flow fled where the electrostatic potential in the central of the canal must be equal to zero is removed. The incorrect supposition that the pressure constant is preserved, which is considered a known form, is corrected. The current fresh model equation is modified by using dimensionless parameters to convert partial differential equations into ordinary differential equations. The transformed nonlinear equations are solved by the homotopy analysis method. The physical parameters, magnetic parameters, Eckert number, Lewis number, Brownian motion parameters, thermophoresis parameters, and Prandtl number are analyzed. The influence of both the viscous and Joule dissipation in the presence of magnetohydrodynamic effect is examined.

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.

scholarly journals A Non-Newtonian Magnetohydrodynamics (MHD) Nanofluid Flow and Heat Transfer with Nonlinear Slip and Temperature Jump

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1199 ◽  
Author(s):  
Jing Zhu ◽  
Yaxin Xu ◽  
Xiang Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Jump ◽  
Thin Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Slip Condition ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Flow And Heat Transfer

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches 10 − 6 from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

scholarly journals Hydromagnetic boundary layer flow of a dusty fluid in a porous medium over a stretching sheet with slip effect

2017 ◽  
Vol 13 (3) ◽  
Author(s):  
Noorzehan Fazahiyah Md Shab ◽  
Anati Ali
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Particle Interaction ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Dusty Fluid ◽  
Linear Ordinary Differential Equations ◽  
Layer Flow

This paper investigated the problem of hydromagnetic boundary layer flow and heat transfer of a dusty fluid over a stretching sheet through a porous medium. The velocity slip was considered instead of the no-slip condition at the boundary. The governing partial equations were reduced into a set of non-linear ordinary differential equations by using the suitable similarity transformation. The transformed equations were numerically integrated using bvp4c in Matlab. The effects of various physical parameters on the velocity and temperature profiles of both phases, such as fluid-particle interaction parameter, magnetic parameter, mass concentration parameter, porosity parameter and Prandtl number were obtained and analyzed through several plots. Useful discussions were carried out with the help of plotted graphs and tables. Under the limiting cases, the obtained numerical results were compared and found to be in good agreement with previously published results.

scholarly journals The new analytical study for boundary-layer slip flow and heat transfer of nanofluid over a stretching sheet

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 289-301 ◽  
Author(s):  
Fazle Mabood ◽  
Waqar Khan ◽  
Muhammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Prandtl Number ◽  
Stretching Sheet ◽  
Lewis Number ◽  
Partial Slip ◽  
Surface Shear Stress ◽  
Slip Parameter ◽  
Slip Factor

In this article, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary layer decreases and thermal boundary layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.

scholarly journals Assisting and Opposing Stagnation Point Pseudoplastic Nano Liquid Flow towards a Flexible Riga Sheet: A Computational Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aysha Rehman ◽  
Azad Hussain ◽  
Sohail Nadeem
Keyword(s):  
Brownian Motion ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Lewis Number ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Diverse Range ◽  
Flow Equations ◽  
Buongiorno Model

Nanofluids are used as coolants in heat transport devices like heat exchangers, radiators, and electronic cooling systems (like a flat plate) because of their improved thermal properties. The preeminent perspective of this study is to highlight the influence of combined convection on heat transfer and pseudoplastic non-Newtonian nanofluid flow towards an extendable Riga surface. Buongiorno model is incorporated in the present study to tackle a diverse range of Reynolds numbers and to analyze the behavior of the pseudoplastic nanofluid flow. Nanofluid features are scrutinized through Brownian motion and thermophoresis diffusion. By the use of the boundary layer principle, the compact form of flow equations is transformed into component forms. The modeled system is numerically simulated. The effects of various physical parameters on skin friction, mass transfer, and thermal energy are numerically computed. Fluctuations of velocity increased when modified Hartmann number and mixed convection parameter are boosted, where it collapses for Weissenberg number and width parameter. It can be revealed that the temperature curve gets down if modified Hartmann number, mixed convection, and buoyancy ratio parameters upgrade. Concentration patterns diminish when there is an incline in width parameter and Lewis number; on the other hand, it went upward for Brownian motion parameter, modified Hartmann, and Prandtl number.

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