Computational analysis of non-Newtonian boundary layer flow of nanofluid past a semi-infinite vertical plate with partial slip

2018 ◽  
Vol 7 (1) ◽  
pp. 29-43 ◽  
Author(s):  
C.H. Amanulla ◽  
N. Nagendra ◽  
M. Suryanarayana Reddy
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Vertical Plate ◽  
Lewis Number ◽  
Velocity Slip ◽  
Partial Slip ◽  
Thermal Slip ◽  
Slip Factor ◽  
Infinite Vertical Plate

Abstract An analysis of this paper is examined, two-dimensional, laminar with heat and mass transfer of natural convective nanofluid flow past a semi-infinite vertical plate surface with velocity and thermal slip effects are studied theoretically. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The influences of the emerging parameters i.e. Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Buoyancy ratio parameter (N), Lewis number (Le), Prandtl number (Pr), Velocity slip factor (Sf) and Thermal slip factor (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. The major sources of nanoparticle migration in Nanofluids are Thermophoresis and Brownian motion. A suitable agreement with existing published literature is made and an excellent agreement is observed for the limiting case and also validation of solutions with a Nakamura tridiagonal method has been included. It is observed that nanoparticle concentrations on surface decreases with an increase in slip parameter. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

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 Numerical analysis of heat and mass transfer along a stretching wedge surface

2017 ◽  
Vol 14 (2) ◽  
pp. 135-144
Author(s):  
M. Ali ◽  
M. A. Alim ◽  
R. Nasrin ◽  
M. S. Alam
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Pressure Gradient ◽  
Ordinary Differential Equations ◽  
Velocity Ratio ◽  
Lewis Number ◽  
Nanoparticle Concentration ◽  
Wedge Surface ◽  
Mhd Boundary Layer ◽  
Moving Wedge

In this work, the effects of dimensionless parameters on the velocity field, thermal field and nanoparticle concentration have been analyzed. In this respect, the magnetohydrodynamic (MHD) boundary layer nanofluid flow along a moving wedge is considered. Therefore, a similarity solution has been derived like Falkner – Skan solution and identified the point of inflexion. So the governing partial differential equations transform into ordinary differential equations by using the similarity transformation. These ordinary differential equations are numerically solved using fourth order Runge–Kutta method along with shooting technique. The present results have been shown graphically and in tabular form. From the graph, the results indicate that the velocity increases with increasing values of pressure gradient, magnetic induction and velocity ratio. The temperature decreases for velocity ratio, Brownian motion and Prandtl number but opposite result arises for increasing values of thermophoresis. The nanoparticle concentration decreases with an increase in pressure gradient, Brownian motion and Lewis number, but increases for thermophoresis. Besides, the solution of nanoparticle concentration exists in the case of Brownian motion is less than 0.2, thermophoresis is less than 0.14 and lewis number is greater than 1.0. Finally, for validity and accuracy the present results have been compared with previous work and found to be in good agreement. 

MHD Flow of Carreau Liquid with Partial Slip and Newtonian Heating

2018 ◽  
Vol 7 (4.10) ◽  
pp. 637
Author(s):  
S. Eswaramoorthi ◽  
K. Loganathan ◽  
S. Sivasankaran ◽  
M. Bhuvaneswari ◽  
S. Rajan
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Partial Slip ◽  
Newtonian Heating ◽  
Linear Ordinary Differential Equations

This work deliberates the MHD flow of Carreau liquid past a stretching plate with thermal radiation, viscous dissipation and Joule heating. Additionally, partial velocity slip and Newtonian heating effects are included in our study. The similarity transformations are used to convert the governing dimensional partial differential equations into dimensionless ordinary differential equations. Homotopy analysis method (HAM) is employed to find the convergent series solutions of the governed non-linear ordinary differential equations. It is found that the magnetic field parameter slowdown the liquid motion and rises the liquid temperature. In addition, heat generation parameter enhances the thermal boundary layer thickness and chemical reaction parameter suppresses the solutal boundary layer thickness.  

scholarly journals Analytical Solution of MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet with Partial Slip

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Samir Kumar Nandy
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Temperature Fields ◽  
Partial Slip ◽  
Thermal Slip ◽  
Slip Parameter ◽  
Flow And Heat Transfer

This paper investigates the hydromagnetic boundary layer flow and heat transfer of a non-Newtonian Casson fluid in the neighborhood of a stagnation point over a stretching surface in the presence of velocity and thermal slips at the boundary. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformations. The analytic solutions are developed by a homotopy analysis method (HAM). The results pertaining to the present study indicate that the flow and temperature fields are significantly influenced by Casson parameter (), the magnetic parameter , the velocity slip parameter , and the thermal slip parameter . An increase in the velocity slip parameter causes decrease in the flow velocity, while an increase in the value of the thermal slip parameter causes increase in the temperature of the fluid. It is also observed that the velocity at a point decreases with increase in .

scholarly journals Boundary Layer Analysis in Nanofluid Flow Past a Permeable Moving Wedge in Presence of Magnetic Field by Using Falkner – Skan Model

2018 ◽  
Vol 23 (4) ◽  
pp. 1005-1013 ◽  
Author(s):  
M. Ali ◽  
M.A. Alim
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Pressure Gradient ◽  
Ordinary Differential Equations ◽  
Velocity Ratio ◽  
Lewis Number ◽  
Motion Parameter ◽  
Gradient Parameter ◽  
Brownian Motion Parameter

Abstract In the present work, the effect of various dimensionless parameters on the momentum, thermal and concentration boundary layer are analyzed. In this respect we have considered the MHD boundary layer flow of heat and transfer over a porous wedge surface in a nanofluid. The governing partial differential equations are converted into ordinary differential equations by using the similarity transformation. These ordinary differential equations are numerically solved using fourth order Runge–Kutta method along with shooting technique. The present results have been shown in a graphical and also in tabular form. The results indicate that the momentum boundary layer thickness reduces with increasing values of the pressure gradient parameter β for different situations and also for the magnetic parameter M but increases for the velocity ratio parameter λ and permeability parameter K*. The heat transfer rate increases for the pressure gradient parameter β, velocity ratio parameter λ, Brownian motion parameter Nb and Prandtl number Pr but opposite result is found for the increasing values of the thermoporesis parameter Nt. The nanoparticle concentration rate increases with an increase in the pressure gradient parameter β, velocity ratio parameter λ, Brownian motion parameter Nb and Lewis number Le, but decreases for the thermoporesis parameter Nt. Finally, the numerical results has compared with previously published studies and found to be in good agreement. So the validity of our results is ensured.

Pathwise convergent higher order numerical schemes for random ordinary differential equations

2007 ◽  
Vol 463 (2087) ◽  
pp. 2929-2944 ◽  
Author(s):  
Peter E Kloeden ◽  
Arnulf Jentzen
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Time Variable ◽  
Numerical Schemes ◽  
Hölder Continuous ◽  
Usual Order

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) with a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus, but since the driving stochastic process is usually only Hölder continuous in time, the vector field is not differentiable in the time variable, so traditional numerical schemes for ODEs do not achieve their usual order of convergence when applied to RODEs. Nevertheless deterministic calculus can still be used to derive higher order numerical schemes for RODEs via integral versions of implicit Taylor-like expansions. The theory is developed systematically here and applied to illustrative examples involving Brownian motion and fractional Brownian motion as the driving processes.

scholarly journals Mathematical analysis of non-Newtonian nanofluid transport phenomena past a truncated cone with Newtonian heating

2018 ◽  
Vol 15 (1) ◽  
pp. 17-35 ◽  
Author(s):  
Nagendra Nallagundla ◽  
C. H. Amanulla ◽  
M. Suryanarayana Reddy
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Biot Number ◽  
Lewis Number ◽  
Casson Fluid ◽  
External Boundary ◽  
Partial Differential ◽  
Truncated Cone ◽  
Highly Nonlinear

In the present study, we analyze the heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid past a truncated cone surface with Biot Number effect is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer Biot Number effect. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via. Appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. Casson fluid parameter (?), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Buoyancy ratio parameter (N ), Prandtl number (Pr) and Biot number (Bi) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length.  Validation of solutions with a Nakamura tri-diagonal method has been included. The study is relevant to enrobing processes for electric-conductive nano-materials of potential use in aerospace and other industries.

scholarly journals Insights into the Stability of Mixed Convective Darcy–Forchheimer Flows of Cross Liquids from a Vertical Plate with Consideration of the Significant Impact of Velocity and Thermal Slip Conditions

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 31 ◽  
Author(s):  
Umair Khan ◽  
Aurang Zaib ◽  
Ilyas Khan ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Vertical Plate ◽  
Thermal Slip ◽  
Slip Conditions ◽  
Drag Forces ◽  
Similarity Transformations ◽  
Mixed Convective Flow ◽  
The Stability ◽  
The Impact

This paper reflects the effects of velocity and thermal slip conditions on the stagnation-point mixed convective flow of Cross liquid moving over a vertical plate entrenched in a Darcy–Forchheimer porous medium. A Cross liquid is a type of non-Newtonian liquid whose viscosity depends on the shear rate. The leading partial differential equations (PDEs) are altered to nonlinear ordinary differential equations (ODEs) via feasible similarity transformations. These transmuted equations are computed numerically through the bvp4c solver. The authority of sundry parameters on the temperature and velocity distributions is examined graphically. In addition, the characteristics of heat transfer are analyzed in the presence of the impact of drag forces. The outcomes reveal that the permeability parameter decelerates the drag forces and declines the rate of heat transfer in both forms of solutions. Moreover, it is found that the drag forces decline with the growing value of the Weissenberg parameter in the upper branch solutions, while a reverse trend is revealed in the lower branch solutions. However, the rate of heat transfer shows a diminishing behavior with an increasing value of the Weissenberg parameter.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

scholarly journals Radiative Boundary Layer Flow of Casson Fluid Over an Exponentially Permeable Slippery Riga Plate with Viscous Dissipation

2020 ◽  
Vol 21 (1) ◽  
pp. 41-51
Author(s):  
Nur Syamila Yusof ◽  
Siti Khuzaimah Soid ◽  
Mohd Rijal Illias ◽  
Ahmad Sukri Abd Aziz ◽  
Nor Ain Azeany Mohd Nasir
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Numerical Results ◽  
Thermal Slip ◽  
Slip Parameter ◽  
Riga Plate

This study is aimed to analyze the steady of stagnation point flow and radiative heat transfer of a non-Newtonian fluid which is Casson fluid passing over an exponentially permeable slippery Riga plate in presence of thermal radiation, magnetic field, velocity slip, thermal slip, and viscous dissipation effects. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation then solved numerically by boundary value problem solver (BVP4C) in MATLAB software package. The numerical results are evaluated with previous researches to reach an agreement with the parameters of the current study. This study is discussing the behavior of the velocity and temperature profiles as well as skin friction coefficient and local Nusselt number for various physical parameters such as magnetic field, radiation, suction, thermal slip, velocity slip, Prandtl number, Eckert number and modified Hartmann number. Numerical results are shown graphically for each parameter with different values. It is found that the momentum boundary layer thickness increases with increasing the values of Casson parameter. The temperature decreases when the velocity slip parameter and thermal slip parameter are increased.

Sign in / Sign up

Export Citation Format

Share Document