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.

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.

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.

scholarly journals MHD Heat and Mass Transfer Forced Convection Flow along a Vertical Stretching Sheet with Heat Generation and Radiation

1970 ◽  
Vol 46 (2) ◽  
pp. 169-176
Author(s):  
MA Samad ◽  
S Ahmed
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Forced Convection ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Concentration Profiles ◽  
Forced Convection Flow

The present study comprises of steady two dimensional magnetohydrodynamic heat and mass transfer forced convection flow along a vertical stretching sheet in the presence of magnetic field with radiation. The nonlinear partial differential equations governing the flow field occurring in the problem have been transformed to dimensionless nonlinear ordinary differential equations by introducing suitably selected similarity variables. The ensuing equations are simultaneously solved by applying Nachtsheim-Swigert shooting iteration technique with sixth order Runge-Kutta integration scheme. The results in the form of velocity, temperature and concentration profiles are then displayed graphically. The corresponding skin-friction coefficient, Nusselt number and Sherwood number are displayed graphically and also in tabular form as well. Several important parameters such as the prandtl number (Pr), radiation parameter (N), magnetic field parameter (M), heat source parameter (Q), schmidt number (Sc), suction parameter (fw ) and eckert number (Ec) are confronted. The effects of these parameters on the velocity, temperature and concentration profiles are investigated. Key Words: MHD; Forced convection; Stretching sheet; Radiation; Heat generation. DOI: http://dx.doi.org/10.3329/bjsir.v46i2.8183 Bangladesh J. Sci. Ind. Res. 46(2), 169-176, 2011

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.

Double Diffusive Marangoni Convection Flow of Electrically Conducting Fluid in a Square Cavity With Chemical Reaction

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
M. Saleem ◽  
M. A. Hossain ◽  
Suvash C. Saha
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Average Nusselt Number ◽  
Marangoni Convection ◽  
Convection Flow ◽  
Square Cavity ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Double Diffusive

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w causes the average Nusselt number to decrease, and average Sherwood number to increase.

scholarly journals Thermophoresis and suction/injection roles on free convective MHD flow of Ag–kerosene oil nanofluid

2020 ◽  
Vol 7 (3) ◽  
pp. 386-396
Author(s):  
Himanshu Upreti ◽  
Alok Kumar Pandey ◽  
Manoj Kumar
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Mass Transfer Rate ◽  
Brownian Diffusion ◽  
Particle Volume ◽  
Ohmic Dissipation ◽  
Surface Mass

Abstract In this article, the mass and heat transfer flow of Ag–kerosene oil nanofluid over a cone under the effects of suction/injection, magnetic field, thermophoresis, Brownian diffusion, and Ohmic-viscous dissipation was examined. On applying the suitable transformation, PDEs directing the flow of nanofluid were molded to dimensionless ODEs. The solution of the reduced boundary value problem was accomplished by applying Runge–Kutta–Fehlberg method via shooting scheme and the upshots were sketched and interpreted. The values of shear stress and coefficients of heat and mass transfer were attained for some selected values of governing factors. The obtained results showed that when the amount of surface mass flux shifts from injection to the suction domain, the heat and mass transfer rate grew uniformly. However, they have regularly condensed with the rise in the magnitude of the magnetic field and particle volume fraction. Several researches have been done using cone-shaped geometry under the influence of various factors affecting the fluid flow, yet, there exists no such investigation that incorporated the response of viscous-Ohmic dissipation, heat absorption/generation, suction/blowing, Brownian diffusion, and thermophoresis on the hydro-magnetic flow of silver-kerosene oil nanofluid over a cone.

scholarly journals The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1014 ◽  
Author(s):  
Essam R. EL-Zahar ◽  
Ahmed M. Rashad ◽  
Laila F. Seddek
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Surface Temperature ◽  
Drag Coefficient ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Grid Points ◽  
The Impact ◽  
Sinusoidal Surface ◽  
The Magnetic Field

The spotlight of this investigation is primarily the effectiveness of the magnetic field on the natural convective for a Fe3O4 ferrofluid flow over a vertical radiate plate using streamwise sinusoidal variation in surface temperature. The energy equation is reduplicated by interpolating the non-linear radiation effectiveness. The original equations describing the ferrofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-differential quadrature method (HLDQM). HLDQM is a high order semi-analytical numerical method that results in analytical solutions in η -direction, and so the solutions are valid overall in the η domain, not only at grid points. The dimensionless velocity and temperature curves are elaborated. Furthermore, the engineering curiosity of the drag coefficient and local Nusselt number are debated and sketched in view of various emerging parameters. The analyzed numerical results display that applying the magnetic field to the ferroliquid generates a dragging force that diminishes the ferrofluid velocity, whereas it is found to boost the temperature curves. Furthermore, the drag coefficient sufficiently minifies, while an evolution in the heat transfer rate occurs as nanoparticle volume fraction builds. Additionally, the augmentation in temperature ratio parameter signifies a considerable growth in the drag coefficient and Nusselt number. The current theoretical investigation may be beneficial in manufacturing processes, development of transport of energy, and heat resources.

scholarly journals Effects of a Rotating Cone on the Mixed Convection in a Double Lid-Driven 3D Porous Trapezoidal Nanofluid Filled Cavity under the Impact of Magnetic Field

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 449 ◽  
Author(s):  
Ali J. Chamkha ◽  
Fatih Selimefendigil ◽  
Hakan F. Oztop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Mixed Convection ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Rotational Velocity ◽  
Rotating Cone ◽  
The Impact

Effects of a rotating cone in 3D mixed convection of CNT-water nanofluid in a double lid-driven porous trapezoidal cavity is numerically studied considering magnetic field effects. The numerical simulations are performed by using the finite element method. Impacts of Richardson number (between 0.05 and 50), angular rotational velocity of the cone (between −300 and 300), Hartmann number (between 0 and 50), Darcy number (between 10 − 4 and 5 × 10 − 2 ), aspect ratio of the cone (between 0.25 and 2.5), horizontal location of the cone (between 0.35 H and 0.65 H) and solid particle volume fraction (between 0 and 0.004) on the convective heat transfer performance was studied. It was observed that the average Nusselt number rises with higher Richardson numbers for stationary cone while the effect is reverse for when the cone is rotating in clockwise direction at the highest supped. Higher discrepancies between the average Nusselt number is obtained for 2D cylinder and 3D cylinder configuration which is 28.5% at the highest rotational speed. Even though there are very slight variations between the average Nu values for 3D cylinder and 3D cone case, there are significant variations in the local variation of the average Nusselt number. Higher enhancements in the average Nusselt number are achieved with CNT particles even though the magnetic field reduced the convection and the value is 84.3% at the highest strength of magnetic field. Increasing the permeability resulted in higher local and average heat transfer rates for the 3D porous cavity. In this study, the aspect ratio of the cone was found to be an excellent tool for heat transfer enhancement while 95% enhancements in the average Nusselt number were obtained. The horizontal location of the cone was found to have slight effects on the Nusselt number variations.

scholarly journals A Computational Analysis of Two-Phase Casson Nanofluid Passing a Stretching Sheet Using Chemical Reactions and Gyrotactic Microorganisms

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Rizwan Akhtar ◽  
Zhu Zhiyu ◽  
Muhammad Umar ◽  
Ali Imran ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Porous Media ◽  
Nusselt Number ◽  
Chemical Reactions ◽  
Stretching Sheet ◽  
Field Parameter ◽  
Two Phase ◽  
Gyrotactic Microorganisms ◽  
Magnetic Field Parameter ◽  
Casson Nanofluid

In this study, an attempt is made to explore the two-phase Casson nanofluid passing through a stretching sheet along a permeable surface with the effects of chemical reactions and gyrotactic microorganisms. By utilizing the strength of similarity transforms the governing PDEs are transformed into set of ODEs. The resulting equations are handled by using a proficient numerical scheme known as the shooting technique. Authenticity of numerical outcomes is established by comparing the achieved results with the MATLAB built-in solver bvp4c. The numerical outcomes for the reduced Nusselt number and Sherwood number are exhibited in the tabular form, while the variations of some crucial physical parameters on the velocity, temperature, and concentration profiles are demonstrated graphically. It is observed that Local Nusselt number rises with the enhancement in the magnetic field parameter, the porous media parameter, and the chemical reactions, while magnetic field parameter along with porous media parameter retards the velocity profile.

Effects of Magnetic Field on an Unsteady Mixed Convection Flow of Nanofluids Containing Spherical and Cylindrical Nanoparticles

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Kalidas Das ◽  
Pinaki Ranjan Duari ◽  
Prabir Kumar Kundu
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Mixed Convection ◽  
Time Dependent ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Mixed Convection Flow ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Unsteady Mixed Convection

The present article gives a ray of light on the effects of magnetic field on an unsteady mixed convection flow of nanofluids containing nanoparticles which are spherical and cylindrical in nature. The unsteadiness in the flow is mainly caused by time dependent stretching velocity and temperature of the sheet at the surface. The governing transportation equations are first transformed into ordinary differential equations by using similarity transformations and then solved by employing Runga–Kutta–Frelberg method with shooting technique. The influence of various parameters on velocity and temperature profiles as well as wall shear stress and the rate of mass transfer are discussed through graphs and tables. The results for regular fluid (water) from the study are in excellent agreement with the results reported in the literature.

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