Numerical Investigation of Slip Effects on Hydromagnetic Flow Due to a Rotating Porous Disk in a Nanofluid with Internal Heat Absorption

2017 ◽  
Vol 33 (3) ◽  
pp. 375-386
Author(s):  
S. P. Anjali Devi ◽  
T. Elakkiya Priya

AbstractIn recent days, nanofluids have derived the attention of researchers, scientists and engineers due to their abundant applications in Engineering and technology and specific applications such as Electronics cooling, vehicle cooling, medical applications including cancer therapy and so on. Motivated by these applications of nanofluids, this work is mainly concerned with the convective heat transfer of nanofluids. MHD slip flow of nanofluids with heat absorption over a rotating disk subjected to suction has been analyzed. Two types of nanofluids such as copper-water nanofluid and silver-water nanofluid are considered for the present study. The system of axisymmetric nonlinear partial differential equations governing the hydromagnetic steady flow and heat transfer are reduced to nonlinear ordinary differential equations by introducing suitable similarity transformations. The resulting non-linear ordinary differential equations are solved numerically by most efficient Nachtsheim-Swigert shooting iteration technique for satisfaction of asymptotic boundary conditions along with Runge – Kutta Fehlberg Method. The flow field is affected by the presence of physical parameters, such as magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, whereas the temperature field is addionally affected by magnetic interaction parameter, suction parameter, internal heat absorption parameter and solid volume fraction. With the amplifying effect in magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, the radial and tangential velocities decline. Axial velocity gets decelerated for increasing magnetic interaction parameter and slip parameter whereas it gets accelerated for growing effect of suction parameter and solid volume fraction. The temperature of the fluid within the boundary layer enhances with the increasing effect of magnetic interaction parameter and solid volume fraction while it reduces for increasing values of the suction parameter and internal heat absorption parameter. Also the values of radial and tangential skin friction coefficients and Nusselt number are obtained numerically and are tabulated.

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Winifred Nduku Mutuku-Njane ◽  
Oluwole Daniel Makinde

We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration. Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (fw), Biot number (Bi), and slip parameter (β), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.


2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Umair Rashid ◽  
Thabet Abdeljawad ◽  
Haiyi Liang ◽  
Azhar Iqbal ◽  
Muhammad Abbas ◽  
...  

The focus of the present paper is to analyze the shape effect of gold (Au) nanoparticles on squeezing nanofluid flow and heat transfer between parallel plates. The different shapes of nanoparticles, namely, column, sphere, hexahedron, tetrahedron, and lamina, have been examined using water as base fluid. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by suitable transformations. As a result, nonlinear boundary value ordinary differential equations are tackled analytically using the homotopy analysis method (HAM) and convergence of the series solution is ensured. The effects of various parameters such as solid volume fraction, thermal radiation, Reynolds number, magnetic field, Eckert number, suction parameter, and shape factor on velocity and temperature profiles are plotted in graphical form. For various values of involved parameters, Nusselt number is analyzed in graphical form. The obtained results demonstrate that the rate of heat transfer is maximum for lamina shape nanoparticles and the sphere shape of nanoparticles has performed a considerable role in temperature distribution as compared to other shapes of nanoparticles.


2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Navid Freidoonimehr ◽  
Behnam Rostami ◽  
Mohammad Mehdi Rashidi ◽  
Ebrahim Momoniat

A coupled system of nonlinear ordinary differential equations that models the three-dimensional flow of a nanofluid in a rotating channel on a lower permeable stretching porous wall is derived. The mathematical equations are derived from the Navier-Stokes equations where the governing equations are normalized by suitable similarity transformations. The fluid in the rotating channel is water that contains different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The differential transform method (DTM) is employed to solve the coupled system of nonlinear ordinary differential equations. The effects of the following physical parameters on the flow are investigated: characteristic parameter of the flow, rotation parameter, the magnetic parameter, nanoparticle volume fraction, the suction parameter, and different types of nanoparticles. Results are illustrated graphically and discussed in detail.


1990 ◽  
Vol 68 (3) ◽  
pp. 284-292 ◽  
Author(s):  
Y. N. Joshi ◽  
A. J. J. Raassen ◽  
A. A. Van der Valk

The spectra of thallium, lead, and bismuth were photographed in the region 600–2000 Å using sliding spark and triggered spark sources. The (5d10 + 5d96s)–5d96p transitions in Tl IV, Pb V, and Bi VI were investigated. Earlier level values were revised and new lines were classified. Hyperfine structure splittings were observed for many lines in Tl IV and Bi VI. Least squares fitted calculations were done for each spectra. The deviations between the calculated and observed level values showed that parametric descriptions using only the spin-orbit magnetic interaction parameter to describe magnetic effects is not sufficient in the 5d-shell spectra.


2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
D. R. V. S. R. K. Sastry ◽  
A. S. N. Murti ◽  
T. Poorna Kantha

The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.


2018 ◽  
Vol 387 ◽  
pp. 51-62 ◽  
Author(s):  
Jawad Reza ◽  
Fateh Mebarek-Oudina ◽  
Oluwole Daniel Makinde

In this paper, rheology of laminar incompressible Copper-Kerosene nanofluid in a channel with stretching walls under the influence of transverse magnetic field is investigated. The main structure of the partial differential equations was taken from the law of conservation of mass, momentum and energy equations. Governing boundary layer equations are transformed into nonlinear ordinary differential equations by using similarity variables and then solved with 3-stage Lobatto IIIA formula. Numerical results were compared with another numerical method (Runge-Kutta-Fehlberg) and found excellent agreement. The influence of physical parameters Reynolds number, magnetic number, solid volume fraction, momentum and thermal slip parameters on velocity and temperature profile considered. Numerical results revealed that solid volume fraction decreases the velocity of nanofluid particles near the lower wall of the channel and increase the thermal boundary layer thickness in the channel.


1998 ◽  
Vol 358 ◽  
pp. 299-333 ◽  
Author(s):  
OLEG ZIKANOV ◽  
ANDRE THESS

The transformation of initially isotropic turbulent flow of electrically conducting incompressible viscous fluid under the influence of an imposed homogeneous magnetic field is investigated using direct numerical simulation. Under the assumption of large kinetic and small magnetic Reynolds numbers (magnetic Prandtl number Pm[Lt ]1) the quasi-static approximation is applied for the computation of the magnetic field fluctuations. The flow is assumed to be homogeneous and contained in a three-dimensional cubic box with periodic boundary conditions. Large-scale forcing is applied to maintain a statistically steady level of the flow energy. It is found that the pathway traversed by the flow transformation depends decisively on the magnetic interaction parameter (Stuart number). If the magnetic interaction number is small the flow remains three-dimensional and turbulent and no detectable deviation from isotropy is observed. In the case of a strong magnetic field (large magnetic interaction parameter) a rapid transformation to a purely two-dimensional steady state is obtained in agreement with earlier analytical and numerical results for decaying MHD turbulence. At intermediate values of the magnetic interaction parameter the system exhibits intermittent behaviour, characterized by organized quasi-two-dimensional evolution lasting several eddy-turnover times, which is interrupted by strong three-dimensional turbulent bursts. This result implies that the conventional picture of steady angular energy transfer in MHD turbulence must be refined. The spatial structure of the steady two-dimensional final flow obtained in the case of large magnetic interaction parameter is examined. It is found that due to the type of forcing and boundary conditions applied, this state always occurs in the form of a square periodic lattice of alternating vortices occupying the largest possible scale. The stability of this flow to three-dimensional perturbations is analysed using the energy stability method.


2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Waqar A. Khan ◽  
Richard Culham ◽  
A. Aziz

A model based on the works of Buongiorno, which includes the effects of Brownian motion and thermophoresis, is used to develop the governing equations for convection in nanofluids. The analysis includes examples with water and ethylene glycol as the base fluids and nanoparticles of Cu and Al2O3. An assumption of zero nanoparticle flux is used at the surface of the plate to make the model more physically realistic. The model accounts for the effects of both Brownian motion and thermophoresis in the mass boundary condition. Using suitable transformations, the governing partial differential equations are converted into ordinary differential equations which are solved numerically. The dimensionless velocity, temperature, and concentration gradients are used in the second law analysis to determine heat and mass transfer rates. It is shown that the dimensionless entropy generation rate strongly depends upon the solid volume fraction of the nanoparticles, local Reynolds number, and group parameters.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sumera Dero ◽  
Hisamuddin Shaikh ◽  
Ghulam Hyder Talpur ◽  
Ilyas Khan ◽  
Sayer O. Alharbim ◽  
...  

AbstractIn this paper, the heat transfer properties in the three-dimensional (3D) magnetized with the Darcy-Forchheimer flow over a shrinking surface of the $$Cu + Al_{2} O_{3} /$$ C u + A l 2 O 3 / water hybrid nanofluid with radiation effect were studied. Valid linear similarity variables convert the partial differential equations (PDEs) into the ordinary differential equations (ODEs). With the help of the shootlib function in the Maple software, the generalized model in the form of ODEs is numerically solved by the shooting method. Shooting method can produce non-unique solutions when correct initial assumptions are suggested. The findings are found to have two solutions, thereby contributing to the introduction of a stability analysis that validates the attainability of first solution. Stability analysis is performed by employing if bvp4c method in MATLAB software. The results show limitless values of dual solutions at many calculated parameters allowing the turning points and essential values to not exist. Results reveal that the presence of dual solutions relies on the values of the porosity, coefficient of inertia, magnetic, and suction parameters for the specific values of the other applied parameters. Moreover, it has been noted that dual solutions exist in the ranges of $$F_{s} \le F_{sc}$$ F s ≤ F sc , $$M \ge M_{C}$$ M ≥ M C ,$$S \ge S_{C} ,$$ S ≥ S C , and $$K_{C} \le K$$ K C ≤ K whereas no solution exists in the ranges of $$F_{s} > F_{sc}$$ F s > F sc , $$M < M_{c}$$ M < M c , $$S < S_{c}$$ S < S c , and $$K_{C} > K$$ K C > K . Further, a reduction in the rate of heat transfer is noticed with a rise in the parameter of the copper solid volume fraction.


2019 ◽  
Vol 35 (6) ◽  
pp. 851-862
Author(s):  
A. Aghbari ◽  
H. Ali Agha ◽  
D. Sadaoui

ABSTRACTNumerical analysis was investigated for steady two-dimensional double diffusive mixed convection boundary layer flow over a semi-infinite vertical plate embedded non-Darcy porous medium filled with nanofluid, in presence of thermal dispersion and under convective boundary conditions. The Buongiorno nanofluid model is used, while the porous medium is described by the Darcy-Forchheimer extension. The governing partial differential equations are transformed into four coupled nonlinear ordinary differential equations using an appropriate similarity transformations and the resulting system of equations is then solved numerically by the finite-difference method. Numerical results are presented to illustrate how the physical parameters affect the flow field, temperature, concentration and solid volume fraction profiles. In addition, the variation of heat, mass and nanoparticle transfer rates at the plate are exhibited graphically for different values of pertinent parameters.


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