Purpose
The purpose of this paper is to examine the combined effects of thermal radiation and magnetic field of molybdenum disulfide nanofluid in a channel with changing walls. Water is considered as ...a Newtonian fluid and treated as a base fluid and MoS2 as nanoparticles with different shapes (spherical, cylindrical and laminar). The main structures of partial differential equations are taken in the form of continuity, momentum and energy equations.
Design/methodology/approach
The governing partial differential equations are converted into a set of nonlinear ordinary differential equations by applying a suitable similarity transformation and then solved numerically via a three-stage Lobatto III-A formula.
Findings
All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters. The validations of numerical results have been taken into account with other works reported in literature and are found to be in an excellent agreement. The study reveals that the Nusselt number increases by increasing the solid volume fraction for different shapes of nanoparticles, and an increase in the values of wall expansion ratio α increases the velocity profile f′(η) from lower wall to the center of the channel and decreases afterwards.
Originality/value
In this paper, a numerical method was utilized to investigate the influence of molybdenum disulfide (MoS2) nanoparticles shapes on MHD flow of nanofluid in a channel. The validity of the literature review cited above ensures that the current study has never been reported before and it is quite new; therefore, in case of validity of the results, a three-stage Lobattoo III-A formula is implemented in Matlab 15 by built in routine “bvp4c,” and it is found to be in an excellent agreement with the literature published before.
With an objective to unfold the flow and heat transfer characteristics of carbon nanotubes between two stretchable coaxial rotating disks, the present investigation has been carried out. The behavior ...of single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs) taking water as the base fluid is analyzed. To formulate the energy equation, we have incorporated Cattaneo–Christov heat flux model. Consideration of such kind of model accounts the contribution by thermal relaxation. von Karman transformation has been implemented in order to reconstruct the governing partial differential equations into a system of ordinary differential equations. Employing optimal homotopy analysis method series solutions are obtained. Error analysis has also been performed and presented in tabular form. The physical clarifications for the behavior of fluid velocity, temperature, skin friction coefficient and Nusselt number are well demonstrated with the help of graphs and contour plots. One of the major outcomes of the present study signifies that water-based SWCNTs have a tendency to cause less drag and higher rate of heat transfer as compared to water-based MWCNTs. This investigation finds numerous applications in different mechanisms of thermal conversion for nuclear propulsion and spacecraft.
The current work concentrates on the transient entropy generation and mixed convection due to a rotating hot inner cylinder within a square cavity having a flexible side wall by using the finite ...element method and arbitrary Lagrangian-Eulerian formulation. Effects of various relevant parameters like Rayleigh number (104 ≤ Ra ≤ 107), angular rotational velocity (-1 ≤ Ω ≤ 1), dimensionless elasticity modulus (1012 ≤ E ≤ 1015) on the convective heat transfer characteristics and entropy generation rates are analyzed for dimensionless time 10-8 ≤ τ ≤ 3.5. It is observed that various complex shaped wall deformations are established depending on the non-dimensional elastic modulus of the flexible right wall and cylinder rotation direction. The local and average Nusselt numbers rise with Ra and secondary peaks in the local Nusselt number are established for lower values of Ra. The local heat transfer along the hot cylinder does not change for the case of clockwise rotation of the heated cylinder even if there is a wall deformation in the positive x-direction. The highest average heat transfer and global entropy generation rates are achieved for the case of counter-clockwise rotation of the circular cylinder and for lower values of the flexible wall deformation.
In this study, heat transfer though a porous fin with rectangular cross section is investigated. The Darcy model is utilized to simulate heat transfer in this porous media. It is assumed that the fin ...is one-dimensional, homogenous, the flow is laminar, and the generated heat is a linear function of temperature. In this research, three different analytical methods are used to obtain the temperature distribution after deriving the heat transfer equation. In order to validate the obtained solution the collocation method (CM) is compared with the results by a numerical method, in order to validate the solutions, homotopy perturbation method (HPM) and homotopy analysis method (HAM) are employed. This problem is solved for the general case, and the output is obtained as a relationship for one iteration. The effects of various parameters including convection (Nc), porosity (Sh), Rayleigh number (Ra) are examined in this research.
In this work, the influences of heat generation/absorption and nanofluid volume fraction on the entropy generation and MHD combined convection heat transfer in a porous enclosure filled with a ...Cu–water nanofluid are studied numerically with of partial slip effect. The finite volume technique is utilized to solve the dimensionless equations governing the problem. A comparison with already published studies is conducted, and the data are found to be in an excellent agreement. The minimization of entropy generation and the local heat transfer according to various values of the controlling parameters are reported in detail. The outcome indicates that an augmentation in the heat generation/absorption parameter decreases the Nusselt number. Also, when the volume fraction is raised, the Nusselt number and entropy generation are reduced. The impact of Hartmann number on heat transfer and the Richardson number on the entropy generation and the thermal rendering criteria are also presented and discussed.
Purpose
Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor ...can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism.
Design/methodology/approach
A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation.
Findings
Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 ≤ Ha ≤ 80), inclination angles (0 ≤ γ ≤ 90°) and radii ratios λ ≤ 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at γ = 30°.
Practical implications
This numerical model is selected for its various applications in technology and industry.
Originality/value
To the best of the authors’ knowledge, the influence of the inclination of the cylindrical annulus (ring), with various radii ratio, on natural oscillatory convection under a radial magnetism has never been investigated.
A study of natural convective flow, heat transfer and entropy generation in an odd-shaped geometry is presented here. The geometry considered is a combination of the horizontal and vertical enclosure ...shapes. The cavity is filled with Cu–water nanofluid. The numerical study focuses specifically on the effect of natural convection parameter and solid volume fraction of nanoparticle on the average Nusselt number, total entropy generation and Bejan number. Also isotherms, stream function and entropy generation due to heat transfer are presented for various Rayleigh number and solid volume fraction. The governing equations are solved by using penalty finite element method with Galerkins weighted residual technique. The results reveal that increasing Rayleigh number causes increase of the average Nusselt number as well as the heat transfer term of entropy generation and decrease of the viscous term. The proper choice of Rayleigh number could be able to maximize heat transfer rate simultaneously minimizing entropy generation.
•Local thermal non-equilibrium (LTNE) heat transfer in a porous medium is studied.•There is a conjugate heat transfer between the cavity walls and LTNE porous medium.•The influence of the location of ...hot and cold walls is addressed.•There is an optimum location of elements for maximum heat transfer.
The problem of conjugate natural convection heat transfer in a cavity filled with a porous medium is addressed by considering the local thermal non-equilibrium effects. The thickness of the solid walls of the cavity is taken into account, and the vertical walls are assumed to be partially active. The effect of the heat transfer bifurcation in the interface of the solid walls and the porous medium is also taken into account. The governing equations for the heat and momentum of the fluid in the porous space, heat transfer in the porous matrix, and heat transfer in the solid walls are represented in the form of partial differential equations. The governing equations along with the corresponding boundary conditions are transformed into a generalized form of the non-dimensional equations and solved by the finite element method. Considering various values of the non-dimensional parameters, the effect of the location of the active walls on the flow patterns and the local and overall heat transfer are addressed. The results demonstrate that the location of the active walls can significantly affect the streamlines and the fluid isotherm contours in the porous space and the isotherms in the solid walls. Moreover, it is found that in most of the cases the highest total rate of heat transfer corresponds to the case in which the elements are in the center of the active wells. In contrast, the lowest total rate of the heat transfer corresponds to a case, in which the active hot element is at the top of the wall, and the cold element is at the bottom.
The aim of this paper is to examine the effects of Cu–Al
2
O
3
/water hybrid nanofluid and Al
2
O
3
/water nanofluid on the mixed convection inside a square cavity caused by a hot oscillating ...cylinder. The governing equations are first transformed into dimensionless form and then discretized over a non-uniform unstructured moving grid with triangular elements. The effects of several parameters, such as the nanoparticle volume fraction, the Rayleigh number, the amplitude of the oscillation, and the period of the oscillation of the cylinder are investigated numerically. The results indicate that the motion of the oscillating cylinder toward the top and bottom walls increases the average Nusselt number when the Rayleigh number is low. Furthermore, the presence of Al
2
O
3
and Cu–Al
2
O
3
nanoparticles leads to an increase in the values of the average Nusselt number
Nu
avg
for cases of low values of the Rayleigh number. It is found that the natural convection heat transfer rate of a simple Al
2
O
3
/water nanofluid is better than that of Cu–Al
2
O
3
/water hybrid nanofluid.
The aim of the present study is to investigate the effects of a hybrid nanofluid in a square cavity that is divided into two equal parts by a vertical flexible partition in the presence of a magnetic ...field. A numerical method called the Galerkin finite element method is utilized to solve the governing equations. The effects of different parameters, namely the Rayleigh number (10
6
≤
Ra
≤ 10
8
) and the Hartmann number (0.0 ≤
Ha
≤ 200) as well as the effects of nanoparticles concentration (0.0 ≤
φ
≤ 0.02) and magnetic field orientation (0 ≤
γ
≤
π
), on the flow and heat transfer fields for the cases of pure fluid, nanofluid and hybrid nanofluid are investigated. The results indicate that the streamline patterns change remarkably and the convective heat transfer augments with increasing values of the Rayleigh number. Additionally, the maximum stress imposed on the flexible partition resulting from the interaction of the partition and pure fluid is more than those caused by the nanofluid and the hybrid nanofluid. Furthermore, the increase in the magnetic field strength decreases the fluid velocity in the cavity, which declines the fluid thermal mixing and heat transfer effects.
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