scholarly journals New exact and numerical solutions for the effect of suction or injection on flow of nanofluids past a stretching sheet

2019 ◽  
Vol 8 (1) ◽  
pp. 172-178
Author(s):  
Nader Y. Abd Elazem
Keyword(s):  
Nusselt Number ◽  
Exact Solutions ◽  
Sherwood Number ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Lewis Number ◽  
Suction Or Injection ◽  
Wall Mass ◽  
Good Agreement

Abstract The flow of nanofluids past a stretching sheet has attracted much attention due to its wide applications in industry and engineering. Theoretical and numerical solutions have been discussed in this paper for studying the effect of suction or injection on flow of nanofluids past a stretching sheet. In the absence of thermophoresis the analytical exact solution of the stream function was obtained in terms of exponential function, while the exact solutions for temperature and nanoparticle volume fraction were obtained in terms of the generalized incomplete gamma function. In addition, in the presence of thermophoresis, the exact solutions are not available. Therefore, the numerical results, carried out by using Chebyshev collocation method (ChCM). It is found that a good agreement exists between the present results and with those published works. Useful results for temperature profile, concentration profile, reduced Nusselt number and reduced Sherwood number are discussed in details graphically. It was also demonstrated that both temperature and concentration profiles decrease by an increase from injection to suction. Finally, the present results showed that increase of the wall mass transfer from injection to suction decreased both reduced Nusselt number and the reduced Sherwood number when Brownian motion parameter and Lewis number increased.

Numerical Solution for the Effect of Suction or Injection on Flow of Nanofluids Past a Stretching Sheet

2016 ◽  
Vol 71 (6) ◽  
pp. 511-515
Author(s):  
Nader Y. Abd Elazem
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Numerical Solution ◽  
Sherwood Number ◽  
Stretching Sheet ◽  
Lewis Number ◽  
Numerical Results ◽  
Injection Parameter ◽  
Suction Or Injection ◽  
Increasing Function

AbstractThe flow of nanofluids past a stretching sheet has attracted much attention owing to its wide applications in industry and engineering. Numerical solution has been discussed in this article for studying the effect of suction (or injection) on flow of nanofluids past a stretching sheet. The numerical results carried out using Chebyshev collocation method (ChCM). Useful results for temperature profile, concentration profile, reduced Nusselt number, and reduced Sherwood number are discussed in tabular and graphical forms. It was also demonstrated that both temperature and concentration profiles decrease by an increase from injection to suction. Moreover, the numerical results show that the temperature profiles decrease at high values of Prandtl number Pr. Finally, the present results showed that the reduced Nusselt number is a decreasing function, whereas the reduced Sherwood number is an increasing function at fixed values of Prandtl number Pr, Lewis number Le and suction (or injection) parameter s for variation of Brownian motion parameter Nb, and thermophoresis parameter Nt.

Coupled Heat and Mass Transfer by Mixed Convection From a Buried Pipe With Leakage

2003 ◽  
Author(s):  
C. C. Ngo ◽  
F. C. Lai
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Sherwood Number ◽  
Numerical Solutions ◽  
Lewis Number ◽  
The Body ◽  
Buried Pipe ◽  
Buoyancy Ratio

Numerical solutions are presented for combined heat and mass transfer by mixed convection induced from a buried pipe with leakage. Two locations of leakage are considered in the present study: one is on top of the pipe and the other is at the bottom of the pipe. The governing equations formulated in the body-fitted coordinates are solved via the finite difference method. A parametric study has been performed to investigate the effects of Rayleigh number, Peclet number, Lewis number, and buoyancy ratio N on the heat and mass transfer results. It is found that both the Nusselt number and Sherwood number increase for the aiding flows (N > 0) and decrease for the opposing flows (N < 0). For aiding flows, Sherwood number increases with the Lewis number but Nusselt number decreases with the Lewis number.

scholarly journals Dual DTM-Padé approximations on free convection MHD mass transfer flow of nanofluid through a stretching sheet in presence of Soret and Dufour Phenomena

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Concentration Profiles ◽  
Temperature Profiles ◽  
Padé Approximations ◽  
Pade Approximations

A theoretical study is made to investigate heat and mass transfer analysis on the single phase flow of an electrically conducting, Al2O3-Water nanofluid over a linearly stretching sheet in presence of Soret and Dufour effects. An applied magnetic field is considered normal to the flow, while the effect of induced magnetic field got neglected for small magnetic Reynolds number’s value of the flow field relative to the applied field. Since voltage difference at the lateral ends of the sheet is very small, the influence of the electric field is thus omitted. The governing equations representing the physical model of the fluid flow is solved by means of DTM-Padé approximations. The acquired results show that an increase in the Soret number (Dufour number) decreases (increases) the temperature profiles but increases (decreases) the concentration profiles. The axial velocity profiles found decreasing with increasing values of the magnetic parameter. Both chemical reaction and thermal radiation parameters maximize the temperature profiles whereas a reverse phenomenon is seen on concentration profiles. The obtained tables show that increasing nanoparticle volume fraction escalates skin-friction coefficient, Nusselt number and Sherwood number whereas an increase in Richardson number decreases the Nusselt number but increases the Sherwood number.

Dual DTM-Padé approximations on free convection MHD mass transfer flow of nanofluid through a stretching sheet in presence of Soret and Dufour Phenomena

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Concentration Profiles ◽  
Temperature Profiles ◽  
Padé Approximations ◽  
Pade Approximations

A theoretical study is made to investigate heat and mass transfer analysis on the single phase flow of an electrically conducting, Al2O3-Water nanofluid over a linearly stretching sheet in presence of Soret and Dufour effects. An applied magnetic field is considered normal to the flow, while the effect of induced magnetic field got neglected for small magnetic Reynolds number’s value of the flow field relative to the applied field. Since voltage difference at the lateral ends of the sheet is very small, the influence of the electric field is thus omitted. The governing equations representing the physical model of the fluid flow is solved by means of DTM-Padé approximations. The acquired results show that an increase in the Soret number (Dufour number) decreases (increases) the temperature profiles but increases (decreases) the concentration profiles. The axial velocity profiles found decreasing with increasing values of the magnetic parameter. Both chemical reaction and thermal radiation parameters maximize the temperature profiles whereas a reverse phenomenon is seen on concentration profiles. The obtained tables show that increasing nanoparticle volume fraction escalates skin-friction coefficient, Nusselt number and Sherwood number whereas an increase in Richardson number decreases the Nusselt number but increases the Sherwood number.

Study of the boundary layer heat transfer of nanofluids over a stretching sheet: Passive control of nanoparticles at the surface

2015 ◽  
Vol 93 (7) ◽  
pp. 725-733 ◽  
Author(s):  
M. Ghalambaz ◽  
E. Izadpanahi ◽  
A. Noghrehabadi ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Heat Transfer Enhancement ◽  
Base Fluid ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Enhancement Ratio ◽  
Transfer Enhancement

The boundary layer heat and mass transfer of nanofluids over an isothermal stretching sheet is analyzed using a drift-flux model. The relative slip velocity between the nanoparticles and the base fluid is taken into account. The nanoparticles’ volume fractions at the surface of the sheet are considered to be adjusted passively. The thermal conductivity and the dynamic viscosity of the nanofluid are considered as functions of the local volume fraction of the nanoparticles. A non-dimensional parameter, heat transfer enhancement ratio, is introduced, which shows the alteration of the thermal convective coefficient of the nanofluid compared to the base fluid. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using the fourth-order Runge–Kutta and Newton–Raphson methods along with the shooting technique. The effects of six non-dimensional parameters, namely, the Prandtl number of the base fluid Prbf, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, variable thermal conductivity parameter Nc and the variable viscosity parameter Nv, on the velocity, temperature, and concentration profiles as well as the reduced Nusselt number and the enhancement ratio are investigated. Finally, case studies for Al2O3 and Cu nanoparticles dispersed in water are performed. It is found that increases in the ambient values of the nanoparticles volume fraction cause decreases in both the dimensionless shear stress f″(0) and the reduced Nusselt number Nur. Furthermore, an augmentation of the ambient value of the volume fraction of nanoparticles results in an increase the heat transfer enhancement ratio hnf/hbf. Therefore, using nanoparticles produces heat transfer enhancement from the sheet.

A Theoretical Formula for the Validity Limits of the Dipole Approximation for a Dielectric Mixture

2014 ◽  
Vol 906 ◽  
pp. 72-80
Author(s):  
Chang He Yang ◽  
Ding Long Cao ◽  
Lin Song Guo
Keyword(s):  
Finite Element Method ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Dipole Approximation ◽  
Empirical Method ◽  
Theoretical Formula ◽  
The Finite Element Method ◽  
Dielectric Mixture ◽  
Good Agreement ◽  
Dielectric Mismatch

A newly criterion for the validity limits of the dipole approximation for a dielectric mixture was presented, based on the comparison between the dipole approximation and the numerical solutions by the finite-element method (FEM). In terms of this criterion and the dipole-enhanced model, a simple theoretical formula for the validity limits was derived. This formula includes three variables: the dielectric mismatch, the volume fraction of particles and the precision. Its calculated results have a good agreement with the limits determined by the empirical method in the range of our interest, which indicates the theoretical formula is creditable. Using this formula, we can approximate the precision of the dipole approximation for an arbitrary dielectric mixture. And we found that the dipole approximation is acceptable with the precision equal to 30% when the dielectric mismatch is less than 2.3 (εi/ εe2.3) for the almost touching spheres.

Magnetohydrodynamics and Soret Effects on Bioconvection in a Porous Medium Saturated With a Nanofluid Containing Gyrotactic Microorganisms

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
S. Shaw ◽  
P. Sibanda ◽  
A. Sutradhar ◽  
P. V. S. N. Murthy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Sherwood Number ◽  
Peclet Number ◽  
Volume Fraction ◽  
Soret Effect ◽  
Magnetic Field Effect ◽  
Lewis Number ◽  
Solute Concentration ◽  
Péclet Number

We investigate the bioconvection of gyrotactic microorganism near the boundary layer region of an inclined semi infinite permeable plate embedded in a porous medium filled with a water-based nanofluid containing motile microorganisms. The model for the nanofluid incorporates Brownian motion, thermophoresis, also Soret effect and magnetic field effect are considered in the study. The governing partial differential equations for momentum, heat, solute concentration, nanoparticle volume fraction, and microorganism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations and solved numerically. The effects of the bioconvection parameters on the thermal, solutal, nanoparticle concentration, and the density of the micro-organisms are analyzed. A comparative analysis of our results with previously reported results in the literature is given. Some interesting phenomena are observed for the local Nusselt and Sherwood number. It is shown that the Péclet number and the bioconvection Rayleigh number highly influence the local Nusselt and Sherwood numbers. For Péclet numbers less than 1, the local Nusselt and Sherwood number increase with the bioconvection Lewis number. However, both the heat and mass transfer rates decrease with bioconvection Lewis number for higher values of the Péclet number.

Nutrient uptake in a suspension of squirmers

2016 ◽  
Vol 789 ◽  
pp. 481-499 ◽  
Author(s):  
Takuji Ishikawa ◽  
Shunsuke Kajiki ◽  
Yohsuke Imai ◽  
Toshihiro Omori
Keyword(s):  
Nutrient Uptake ◽  
Sherwood Number ◽  
Volume Fraction ◽  
Industrial Applications ◽  
Hydrodynamic Interactions ◽  
Energetic Cost ◽  
Unit Energy ◽  
Micro Organisms ◽  
Dilute Limit ◽  
Good Agreement

Nutrient uptake is one of the most important factors in cell growth. Despite the biological importance, little is known about the effect of cell–cell hydrodynamic interactions on nutrient uptake in a suspension of swimming micro-organisms. In this study, we numerically investigate the nutrient uptake in an infinite suspension of squirmers. In the dilute limit, our results are in good agreement with a previous study by Magar et al. (Q. J. Mech. Appl. Maths, vol. 56, 2003, pp. 65–91). When we increased the volume fraction of squirmers, the nutrient uptake of individual cells was enhanced by the hydrodynamic interactions. The average nutrient concentration in the suspension decayed exponentially as a function of time, and the relaxation time could be scaled using the Sherwood number, the Péclet number and the volume fraction of cells. We propose a fitting function for the Sherwood number, which is useful in predicting nutrient uptake in the non-dilute regime. Furthermore, we analyse the swimming energy consumed by individual cells. The results indicate that both the energetic cost and the nutrient uptake increased as the volume fraction of cells was increased, and that the uptake per unit energy was not significantly affected by the volume fraction. These findings are important in understanding the mass transport and metabolism of swimming micro-organisms in nature and for industrial applications.

Boundary-Layer Flow and Heat Transfer of Nanofluid Over a Vertical Plate With Convective Surface Boundary Condition

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Wubshet Ibrahim ◽  
Bandari Shanker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Vertical Plate ◽  
Lewis Number ◽  
Convective Heating ◽  
Flow And Heat Transfer ◽  
Layer Flow

The problem of boundary layer flow and heat transfer induced due to nanofluid over a vertical plate is investigated. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. We used a convective heating boundary condition instead of a widely employed thermal conduction of constant temperature or constant heat flux. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., convective heating parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, buoyancy ratio parameter Nr, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order ordinary differential equations. These equations were solved numerically using Runge-Kutta fourth order method with shooting technique. The effects of the governing parameters on flow field and heat transfer characteristics were obtained and discussed. Numerical results are obtained for velocity, temperature, and concentration distribution as well as the local Nusselt number and Sherwood number. It is found that the local Nusselt number and Sherwood number increase with an increase in convective parameter A and Lewis number Le. Likewise, the local Sherwood number increases with an increase in both A and Le. A comparison with the previous study available in literature has been done and we found an excellent agreement with them.

scholarly journals Numerical Investigation of Heat Transfer Enhancement in a Rectangular Heated Pipe for Turbulent Nanofluid

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hooman Yarmand ◽  
Samira Gharehkhani ◽  
Salim Newaz Kazi ◽  
Emad Sadeghinezhad ◽  
Mohammad Reza Safaei
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Volume Fraction ◽  
Rectangular Channel ◽  
Thermal Characteristics ◽  
Reynolds Numbers ◽  
Constant Heat Flux ◽  
Energy Equations ◽  
Volume Method ◽  
Good Agreement

Thermal characteristics of turbulent nanofluid flow in a rectangular pipe have been investigated numerically. The continuity, momentum, and energy equations were solved by means of a finite volume method (FVM). The symmetrical rectangular channel is heated at the top and bottom at a constant heat flux while the sides walls are insulated. Four different types of nanoparticles Al2O3, ZnO, CuO, and SiO2at different volume fractions of nanofluids in the range of 1% to 5% are considered in the present investigation. In this paper, effect of different Reynolds numbers in the range of 5000 < Re < 25000 on heat transfer characteristics of nanofluids flowing through the channel is investigated. The numerical results indicate that SiO2-water has the highest Nusselt number compared to other nanofluids while it has the lowest heat transfer coefficient due to low thermal conductivity. The Nusselt number increases with the increase of the Reynolds number and the volume fraction of nanoparticles. The results of simulation show a good agreement with the existing experimental correlations.

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