Viscous Dissipation and Joule Heating Effects on MHD Bioconvection Flow of a Nanofluid Containing Gyrotactic Microorganisms Over a Vertical Isothermal Cone

2020 ◽  
Vol 9 (3) ◽  
pp. 242-255
Author(s):  
Hossam A. Nabwey ◽  
S. M. M. El-Kabeir ◽  
A. M. Rashad ◽  
M. M. M. Abdou
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Sherwood Number ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Gyrotactic Microorganisms ◽  
Local Skin Friction ◽  
Local Sherwood Number

The main objective of the present study is to explore the flow of a nanofluid containing gyrotactic microorganisms over a vertical isothermal cone surface in the presence of viscous dissipation and Joule heating. The combined effects of a transverse magnetic field and Navier slip in the flow are considered. Using appropriate transforms the set of partial differential equations governing the flow are converted to a set of ordinary differential equations. Influence of the parameters governing the flow is shown for velocity, temperature, concentration and motilemicroorganisms as well as local skin Friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number. An increasing in the value of Eckert number rises the velocity of the fluid and reduce the temperature, concentration and density of motile microorganisms profiles, while buoyancy ratio Nr and magnetic field parameters increase local skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number decrease as a result of the presence of Lorentz force which resist the motion of the flow. On the other hand, the motile microorganisms boundary layer thickness decreases with an increasing on the bioconvection Lewis number.

Non-similar characteristics of mixed convective slip flow over a wedge with temperature-dependent thermo-physical properties

2019 ◽  
Vol 33 (36) ◽  
pp. 1950455
Author(s):  
Nepal Chandra Roy ◽  
Sudharonjon Roy ◽  
Naved Azum ◽  
Anish Khan ◽  
Abdullah M. Asiri ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Sherwood Number ◽  
Local Nusselt Number ◽  
Slip Flow ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Local Skin Friction ◽  
Local Sherwood Number

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Khairy Zaimi ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Stagnation Point ◽  
Sherwood Number ◽  
Local Nusselt Number ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Gyrotactic Microorganisms ◽  
Local Sherwood Number

The stagnation-point flow and heat transfer toward a stretching/shrinking sheet in a nanofluid containing gyrotactic microorganisms with suction are investigated. Using a similarity transformation, the nonlinear system of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a shooting method. The skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms profiles are analyzed subject to several parameters of interest, namely suction parameter, thermophoresis parameter, Brownian motion parameter, Lewis number, Schmidt number, bioconvection Péclet number, and the stretching/shrinking parameter. It is found that dual solutions exist for a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms increase with suction effect. It is also observed that suction widens the range of the stretching/shrinking parameter for which the solution exists.

Axisymmetric Stagnation-Point Flow of Nanofluid Over a Stretching Surface

2014 ◽  
Vol 6 (2) ◽  
pp. 220-232 ◽  
Author(s):  
M. Nawaz ◽  
T. Hayat
Keyword(s):  
Nusselt Number ◽  
Sherwood Number ◽  
Base Fluid ◽  
Convective Heat Transfer Coefficient ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Homotopy Analysis ◽  
Local Skin Friction ◽  
Layer Flow ◽  
Local Sherwood Number

AbstractThis paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet. Nanofluid model exhibiting Brownian motion and thermophoresis is used. Series solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method (HAM). Comparative study between the HAM solutions and previously published numerical results shows an excellent agreement. Velocity, temperature and mass fraction are displayed for various values of parameters. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are computed. It is observed that the presence of nanoparticles enhances the thermal conductivity of base fluid. It is found that the convective heat transfer coefficient (Nusselt number) is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.

scholarly journals Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

A numerical investigation of transient MHD free convective flow of a nanofluid over a moving semi-infinite vertical cylinder

2017 ◽  
Vol 34 (5) ◽  
pp. 1393-1412 ◽  
Author(s):  
V. Rajesh ◽  
A.J. Chamkha ◽  
Ch. Sridevi ◽  
A.F. Al-Mudhaf
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Volume Fraction ◽  
Vertical Cylinder ◽  
Skin Friction Coefficient ◽  
Free Convective Flow ◽  
Local Skin ◽  
Content Type ◽  
Local Skin Friction

Purpose The purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite vertical cylinder with heat transfer Design/methodology/approach The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. The fluid is a water-based nanofluid containing nanoparticles of copper. The Brinkman model for dynamic viscosity and Maxwell–Garnett model for thermal conductivity are used. The governing boundary layer equations are written according to The Tiwari–Das nanofluid model. A robust, well-tested, implicit finite difference method of Crank–Nicolson type, which is unconditionally stable and convergent, is used to find the numerical solutions of the problem. The velocity and temperature profiles are studied for significant physical parameters such as the magnetic parameter, nanoparticles volume fraction and the thermal Grashof number Gr. The local skin-friction coefficient and the Nusselt number are also analysed and presented graphically. Findings The present computations have shown that an increase in the values of either magnetic parameter M or nanoparticle volume fraction decreases the local skin-friction coefficient, whereas the opposite effect is observed for thermal Grashof number Gr. The local Nusselt number increases with a rise in Gr and ϕ values. But an increase in M reduces the local Nusselt number. Originality/value This paper is relatively original and presents numerical investigation of transient two-dimensional laminar boundary layer free convective flow of a nanofluid over a moving semi-infinite vertical cylinder in the presence of an applied magnetic field. The present study is of immediate application to all those processes which are highly affected by heat enhancement concept and a magnetic field. Further the present study is relevant to nanofluid materials processing, chemical engineering coating operations exploiting nanomaterials and others.

scholarly journals Boundary-layer flow and heat transfer of cross fluid over a stretching sheet

2019 ◽  
Vol 23 (1) ◽  
pp. 307-318 ◽  
Author(s):  
Masood Khan ◽  
Mehwish Manzur ◽  
Masood Rahman
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Weissenberg Number ◽  
Local Skin ◽  
Flow And Heat Transfer ◽  
Local Skin Friction

The current study is a pioneering work in presenting the boundary-layer equations for the 2-D flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of PDE is turned down into highly non-linear ODE by applying suitable similarity transformations. The stretching sheet solutions are presented via. a numerical technique namely the shooting method and graphs are constructed. The impact of the emerging parameters namely the power-law index, n, the local Weissenberg number, We, and the Prandtl number on the velocity and temperature fields are investigated through graphs. The numerical values of the local skin friction coefficient and the local Nusselt number are also presented in tabular form. Additionally, the graphs are sketched for the local skin friction coefficient and the local Nusselt number. It is observed that with growing values of the local Weissenberg number the velocity profiles exhibited a decreasing trend while opposite behavior is seen for the temperature field. Further, comparisons are made with previously available literature for some limiting cases and an excellent agreement is achieved.

Natural Convective Boundary Layer Flow of Nanofluids Above an Isothermal Horizontal Plate

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Kaustav Pradhan ◽  
Subho Samanta ◽  
Abhijit Guha
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Nanoparticle Volume Fraction ◽  
Convective Boundary ◽  
Local Skin ◽  
Local Skin Friction ◽  
Layer Flow

The natural convective boundary layer flow of a nanofluid over an isothermal horizontal plate is studied analytically. The model used for the nanofluid accounts for the effects of Brownian motion and thermophoresis. The analysis shows that the velocity, temperature, and nanoparticle volume fraction profiles in the respective boundary layers depend not only on the Prandtl number (Pr) and Lewis number (Le) but also on three additional dimensionless parameters: the Brownian motion parameter Nb, the buoyancy ratio parameter Nr and the thermophoresis parameter Nt. The velocity, temperature, and nanoparticle volume fraction profiles for the nanofluid are found to have a weak dependence on the values of Nb, Nr, and Nt. The effect of the above-mentioned parameters on the local skin-friction coefficient and Nusselt number has been studied extensively. It has been observed that as Nr increases, the local skin-friction coefficient decreases whereas local Nusselt number remains almost constant. As Nb or Nt increases, the local skin-friction coefficient increases whereas the local Nusselt number decreases.

Theoretical Investigation of an Unsteady MHD Free Convection Heat and Mass Transfer Flow of a Non-Newtonian Fluid Flow Past a Permeable Moving Vertical Plate in the Presence of Thermal Diffusion and Heat Sink

2015 ◽  
Vol 16 ◽  
pp. 90-109 ◽  
Author(s):  
V. Ravikumar ◽  
M.C. Raju ◽  
G.S.S. Raju
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Sherwood Number ◽  
Skin Friction Coefficient ◽  
Stream Velocity ◽  
Local Skin ◽  
Soret Number

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing Rivlin-Ericksen flow fluid along a semi-infinite vertical permeable moving plate has been investigated. A uniform transverse magnetic field is applied in the direction of the flow. The presence of thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration distributions within the boundary layer are presented. Skin-friction coefficient, Nusselt number and Sherwood number are also discussed with the help of the graphs. Local skin-friction coefficient increases with an increase in the permeability parameter, and Soret number whereas reverse effects is seen in the case of dimensionless viscoelasticity parameter of the Rivlin-Ericksen fluid. Nusselt number decreases in the presence of heat absorption. The presence of Soret number Sherwood number increases.

Measurement of the Wall Shear Stress With Sublayer Thin Plate of Thermochromic Liquid Crystal

2015 ◽  
Author(s):  
Takashi Kodama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Liquid Crystal ◽  
Friction Coefficient ◽  
Wall Shear Stress ◽  
Skin Friction ◽  
Channel Flow ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Local Skin Friction ◽  
Wall Shear

New optical method for measurement of the local wall shear stress has been developed by using thermo-chromic liquid crystal temperature measurement based on hue [1], [2] of the camera view. The flow field is the fully developed turbulent channel flow. Thin film made of thermo-chromic liquid crystal is placed on the wall. A rectangular shaped obstacle is glued on the film. The obstacle is within a region of buffer layer with height from the wall. Temperature of the film and the obstacle are slightly raised by a heater below the wall. The air flow makes non-uniform temperature distribution and non-uniform color distribution appears on the surface of the film. Relations between hue and local skin friction coefficient were examined in a turbulent air channel flow. It is indicated that a certain hue of a point is varying linearly against the corresponding local skin friction coefficient.

scholarly journals Computation of electroconductive gyrotactic bioconvection under nonuniform magnetic field: Simulation of smart bio-nanopolymer coatings for solar energy

2020 ◽  
Vol 34 (05) ◽  
pp. 2050028 ◽  
Author(s):  
Madhu Aneja ◽  
Sapna Sharma ◽  
Sireetorn Kuharat ◽  
O. Anwar Beg
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Differential Equations ◽  
Sherwood Number ◽  
Nonuniform Magnetic Field ◽  
Ohmic Dissipation ◽  
Local Skin ◽  
Brownian Motion And Thermophoresis ◽  
Micro Organisms

The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms (moves under the effects of gravity) over a nonlinear inclined stretching sheet in the presence of a nonuniform magnetic field has been investigated. This regime is encountered in the bio-nanomaterial electroconductive polymeric processing systems currently being considered for third-generation organic solar coatings, anti-fouling marine coatings, etc. Oberbeck–Boussinesq approximation along with ohmic dissipation (Joule heating) is considered in the problem. The governing equations of the flow are nonlinear partial differential equations and are converted into ordinary differential equations via similarity transformations. These equations are then solved by the Finite Element Method. The effect of various important parameters on nondimensional velocity, temperature distribution, nanoparticle concentration, the density of motile micro-organisms is analyzed graphically in detail. It is observed from the obtained results that the flow velocity decreases with rising angle of inclination [Formula: see text] while temperature, nanoparticle’s concentration and density of motile micro-organisms increase. The local skin friction coefficient, Nusselt number, Sherwood number, motile micro-organism’s density number are calculated. It is noticed that increasing the Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, the Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. Also, interesting features of the flow dynamics are elaborated and new future pathways for extension of the study identified in bio-magneto-nano polymers (BMNPs) for solar coatings.

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