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.

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. 

scholarly journals Sensitivity Analysis on Thermal Conductivity Characteristics of a Water-Based Bionanofluid Flow Past a Wedge Surface

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Sze Qi Chan ◽  
Fazlina Aman ◽  
Syahira Mansur
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Lewis Number ◽  
Motion Parameter ◽  
Nonlinear Ordinary Differential Equations ◽  
Shooting Technique ◽  
Wedge Surface ◽  
Water Based ◽  
Local Sherwood Number ◽  
Brownian Motion Parameter

Thermobioconvection boundary layer flow in a suspension of water-based bionanofluid holding both nanoparticles and motile microorganisms past a wedge surface was studied. The governing nonlinear partial differential equations on reference of the Buongiorno model were transformed into a set of coupled nonlinear ordinary differential equations. Shooting technique was then used to solve the transformed nonlinear ordinary differential equations numerically. The solutions were found to be contingent on several values of the governing parameters. As highlighted, the velocity profile as well as the skin friction coefficient was affected by the pressure gradient parameter, the function of the wedge angle parameter. On the other hand, the temperature, nanoparticle concentration, and density of motile microorganism’s distributions together with its corresponding local Nusselt number, local Sherwood number, and local density of the motile microorganisms change with the thermophoresis and Brownian motion parameter and so Lewis number, Schmidt number, and bioconvection Péclet number. An experimental scheme together with sensitivity analysis on the basis of Response Surface Methodology (RSM) was applied to examine the dependency of the response parameters of interest to the input parameters’ change. Obviously, local Nusselt number was more sensitive towards the Brownian motion parameter when the Brownian motion parameter was at 0.2 and 0.3. However local Sherwood number was more sensitive towards the Lewis number for all values of Brownian motion parameter. Compatibility found by comparing results between RSM and shooting technique gave confidence for the model’s accuracy. The findings would provide initial guidelines for future device fabrication. Finally, the numerical results obtained were thoroughly inspected and verified with the existing values reported by some researchers.

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.

MHD Pulsating Flow of Casson Nanofluid in a Vertical Porous Space with Thermal Radiation and Joule Heating

2020 ◽  
Vol 36 (4) ◽  
pp. 535-549
Author(s):  
Challa Kalyan Kumar ◽  
Suripeddi Srinivas ◽  
Anala Subramanyam Reddy
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Motion Parameter ◽  
Porous Space ◽  
Perturbation Scheme ◽  
Casson Nanofluid ◽  
Nanoparticles Concentration ◽  
The Impact ◽  
Brownian Motion Parameter

ABSTRACTIn this investigation, the magnetohydrodynamic pulsatile flow of Casson nanofluid through a vertical channel embedded in porous medium with thermal radiation and heat generation/absorption has been analyzed using Buongiorno model. The influence of viscous and Joules dissipations are taken into account. The governing coupled partial differential equations are reduced to ordinary differential equations using perturbation scheme and then solved numerically by using Runge-Kutta fourth order technique along with shooting method. The impact of various emerging parameters on velocity, temperature, nanoparticles concentration, Nusselt number and Sherwood number distributions are analyzed in detail. Analysis indicates that the temperature distribution increases for a given increase in Brownian motion parameter and thermophoresis parameter, while it decreases with an increase in Hartmann number. Further, the nanoparticles concentration distribution decreases with an increase in the chemical reaction parameter and the Lewis number, while it increases for a given increase in the Brownian motion parameter.

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 Numerical Analysis of Boundary Layer Flow Adjacent to a Thin Needle in Nanofluid with the Presence of Heat Source and Chemical Reaction

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 543 ◽  
Author(s):  
Siti Nur Alwani Salleh ◽  
Norfifah Bachok ◽  
Norihan Md Arifin ◽  
Fadzilah Md Ali
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Boundary Layer Flow ◽  
Velocity Ratio ◽  
Dual Solutions ◽  
Reaction Parameters ◽  
Layer Flow

The steady boundary layer flow of a nanofluid past a thin needle under the influences of heat generation and chemical reaction is analyzed in the present work. The mathematical model has been formulated by using Buongiornos’s nanofluid model which incorporates the effect of the Brownian motion and thermophoretic diffusion. The governing coupled partial differential equations are transformed into a set of nonlinear ordinary differential equations by using appropriate similarity transformations. These equations are then computed numerically through MATLAB software using the implemented package called bvp4c. The influences of various parameters such as Brownian motion, thermophoresis, velocity ratio, needle thickness, heat generation and chemical reaction parameters on the flow, heat and mass characteristics are investigated. The physical characteristics which include the skin friction, heat and mass transfers, velocity, temperature and concentration are further elaborated with the variation of governing parameters and presented through graphs. It is observed that the multiple (dual) solutions are likely to exist when the needle moves against the direction of the fluid flow. It is also noticed that the reduction in needle thickness contributes to the enlargement of the region of the dual solutions. The determination of the stable solution has been done using a stability analysis. The results indicate that the upper branch solutions are linearly stable, while the lower branch solutions are linearly unstable. The study also revealed that the rate of heat transfer is a decreasing function of heat generation parameter, while the rate of mass transfer is an increasing function of heat generation and chemical reaction parameters.

Biomedical study of effects nanoparticles on unsteady blood (non-Newtonian) flow through a catheterized stenotic vessel

2019 ◽  
Vol 97 (5) ◽  
pp. 487-497
Author(s):  
Akbar Zaman ◽  
M. Sajid ◽  
Nabeela Kousar
Keyword(s):  
Brownian Motion ◽  
Cross Section ◽  
Lewis Number ◽  
Elastic Parameter ◽  
Weissenberg Number ◽  
Motion Parameter ◽  
Cross Model ◽  
Explicit Finite Difference ◽  
Stenotic Vessel ◽  
Brownian Motion Parameter

The purpose of this article is to theoretically discuss the unsteady hemo-dynamics of blood through a catheterized overlapping stenotic vessel with nanoparticles. The nature of the blood is characterized by the constitutive Cross model equation. This study is conducted under the assumption of mild stenotic conditions and the equations of momentum and temperature are simplified after making this assumption. Explicit finite difference method is employed to obtain the numerical results of the governing equations. Results for different values of emerging parameters, such as Weissenberg number, Lewis number, thermophoresis parameter, and Brownian motion parameter are shown at different locations of an arterial cross section. These results demonstrate a pictorial way to comprehend the theoretical biomedical problem. These results reveal that Lewis number (Le) and visco-elastic parameter Weissenberg number (We) both are decreasing functions of velocity profiles at each arterial cross section. Furthermore, it is also noted that the thermophoresis parameter (Nt) quantitatively decreases the flow of blood inside the vessel while the Brownian motion parameter (Nb) shows the opposite effects on blood flow; it increases the magnitude of velocity.

scholarly journals Magneto-Burgers Nanofluid Stratified Flow with Swimming Motile Microorganisms and Dual Variables Conductivity Configured by a Stretching Cylinder/Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Hassan Waqas ◽  
Umair Manzoor ◽  
Zahir Shah ◽  
Muhammad Arif ◽  
Meshal Shutaywi
Keyword(s):  
Thermal Conductivity ◽  
Activation Energy ◽  
Brownian Motion ◽  
Peclet Number ◽  
Current Model ◽  
Lewis Number ◽  
Motion Parameter ◽  
Stretching Cylinder ◽  
Péclet Number ◽  
Brownian Motion Parameter

Background. The study of nanofluid gains interest of researchers because of its uses in treatment of cancer, wound treatment, fuel reserves, and elevating the particles in the bloodstream to a tumour. This artefact investigates the magnetohydrodynamic flow of Burgers nanofluid with the interaction of nonlinear thermal radiation, activation energy, and motile microorganisms across a stretching cylinder. Method. The developed partial differential equations (PDEs) are transformed into a structure of ODEs with the help of similarity transformation. The extracted problem is rectified numerically by using the bvp4c program in computational software MATLAB. The novelty of analysis lies in the fact that the impacts of bioconvection with magnetic effects on Burgers nanofluid are taken into account. Moreover, the behaviours of thermal conductivity and diffusivity are discussed in detail. The impacts of activation energy and motile microorganism are also explored. No work has been published yet in the literature survey according to the authors’ knowledge. The current observation is the extension of Khan et al.’s work [51]. Results. The consequences of the relevant parameters, namely, thermophoresis parameter, Brownian motion parameter, the reaction parameter, temperature difference parameter, activation energy, bioconvection Lewis number and Peclet number against the velocity of Burgers nanofluid, temperature profile for nanoliquid, the concentration of nanoparticles, and microorganisms field, have been explored in depth. The reports had major impacts in the development of medications for the treatment of arterial diseases including atherosclerosis without any need for surgery, which may reduce spending on cardiovascular and postsurgical problems in patients. Conclusions. The current investigation depicts that fluid velocity increases for uplifting values of mixed convection parameter. Furthermore, it is analyzed that flow of fluid is risen by varying the amount of Burgers fluid parameter. The temperature distribution is escalated by escalating the values of temperature ratio parameter and thermal conductivity parameter. The concentration field turns down for elevated values of Lewis number and Brownian motion parameter, while conflicting circumstances are observed for the thermophoresis parameter and solutal Biot number. Larger values of Peclet number reduce the microorganism’s field. Physically the current model is more significant in the field of applied mathematics. Furthermore, the current model is more helpful to improve the thermal conductivity of base fluids and heat transfer rate.

scholarly journals Thin Film Flow of Couple Stress Magneto-Hydrodynamics Nanofluid with Convective Heat over an Inclined Exponentially Rotating Stretched Surface

Coatings ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 338 ◽  
Author(s):  
Asifa Tassaddiq ◽  
Ibni Amin ◽  
Meshal Shutaywi ◽  
Zahir Shah ◽  
Farhad Ali ◽  
...  
Keyword(s):  
Thin Film ◽  
Brownian Motion ◽  
Differential Equations ◽  
Prandtl Number ◽  
Ordinary Differential Equations ◽  
Couple Stress ◽  
Magnetic Parameter ◽  
Film Flow ◽  
Thin Film Flow ◽  
Brownian Motion Parameter

In this article a couple stress magneto-hydrodynamic (MHD) nanofluid thin film flow over an exponential stretching sheet with joule heating and viscous dissipation is considered. Similarity transformations were used to obtain a non-linear coupled system of ordinary differential equations (ODEs) from a system of constitutive partial differential equations (PDEs). The system of ordinary differential equations of couple stress magneto-hydrodynamic (MHD) nanofluid flow was solved using the well-known Homotopy Analysis Method (HAM). Nusselt and Sherwood numbers were demonstrated in dimensionless forms. At zero Prandtl number the velocity profile was analytically described. Furthermore, the impact of different parameters over different state variables are presented with the help of graphs. Dimensionless numbers like magnetic parameter M, Brownian motion parameter Nb, Prandtl number Pr, thermophoretic parameter Nt, Schmidt number Sc, and rotation parameter S were analyzed over the velocity, temperature, and concentration profiles. It was observed that the magnetic parameter M increases the axial, radial, drainage, and induced profiles. It was also apparent that Nu reduces with greater values of Pr. On increasing values of the Brownian motion parameter the concentration profile declines, while the thermophoresis parameter increases.

scholarly journals Numerical study of nano-biofilm stagnation flow from a nonlinear stretching/shrinking surface with variable nanofluid and bioconvection transport properties

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdulaziz Alsenafi ◽  
O. Anwar Bég ◽  
M. Ferdows ◽  
Tasveer A. Bég ◽  
A. Kadir
Keyword(s):  
Thermal Conductivity ◽  
Brownian Motion ◽  
Skin Friction ◽  
Volume Fraction ◽  
Lewis Number ◽  
Motion Parameter ◽  
Nano Particle ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Brownian Motion Parameter

AbstractA mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno’s two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter $$({c}_{2})$$ ( c 2 ) , thermal conductivity parameter (c4), nano-particle mass diffusivity (c6), micro-organism species diffusivity (c8), thermophoresis parameter $$(Nt)$$ ( N t ) , Brownian motion parameter $$(Nb)$$ ( N b ) , Lewis number $$(Le)$$ ( L e ) , bioconvection Schmidt number $$(Sc)$$ ( S c ) , bioconvection constant (σ) and bioconvection Péclet number $$(Pe)$$ ( P e ) . Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter ($${\mathrm{c}}_{2})$$ c 2 ) whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter ($${\mathrm{c}}_{4})$$ c 4 ) whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter ($${c}_{6}$$ c 6 ) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent ($$m),$$ m ) , skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter ($${\mathrm{c}}_{8}$$ c 8 ) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes.

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