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Article
Publication date: 28 October 2014

M. Sheikholeslami, R. Ellahi, Mohsan Hassan and Soheil Soleimani

The purpose of this paper is to study the effects of natural convection heat transfer in a cold outer circular enclosure containing a hot inner elliptic circular cylinder. The…

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Abstract

Purpose

The purpose of this paper is to study the effects of natural convection heat transfer in a cold outer circular enclosure containing a hot inner elliptic circular cylinder. The fluid in the enclosure is Cu-water nanofluid. The main emphasis is to find the numerical treatment for the said mathematical model. The effects of Rayleigh number, inclined angle of elliptic inner cylinder, effective of thermal conductivity and viscosity of nanofluid, volume fraction of nanoparticles on the flow and heat transfer characteristics have been examined.

Design/methodology/approach

A very effective and higher order numerical scheme Control Volume-based Finite Element Method (CVFEM) is used to solve the resulting coupled equations. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and inclined angle of elliptic inner cylinder. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively.

Findings

The results reveal that Nusselt number increases with an increase of nanoparticle volume fraction, Rayleigh numbers and inclination angle. Also it can be found that increasing Rayleigh number leads to a decrease in heat transfer enhancement. For high Rayleigh number the minimum heat transfer enhancement ratio occurs at.

Originality/value

To the best of the authors’ knowledge, no such analysis is available in the literature which can describe the natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder by means of CVFEM.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 11 February 2021

J.N. Reddy, Matthew Martinez and Praneeth Nampally

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear…

Abstract

Purpose

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.

Design/methodology/approach

In the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).

Findings

Numerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.

Originality/value

To the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 17 October 2018

A.S. Dogonchi, Mikhail A. Sheremet, Ioan Pop and D.D. Ganji

The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the…

Abstract

Purpose

The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using control volume finite element method (CVFEM).

Design/methodology/approach

Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with Brinkman correlation for the effective dynamic viscosity and Hamilton and Crosser model for the effective thermal conductivity have been solved numerically by CVFEM.

Findings

The impacts of control parameters such as the Rayleigh number, Hartmann number, nanoparticles volume fraction, local triangular heater size, shape factor on streamlines and isotherms as well as local and average Nusselt numbers have been examined. The outcomes indicate that the average Nusselt number is an increasing function of the Rayleigh number, shape factor and nanoparticles volume fraction, while it is a decreasing function of the Hartmann number.

Originality/value

A complete study of the free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using CVFEM is addressed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 August 2018

Mohsen Sheikholeslami and Shirley Abelman

The purpose of this paper is to examine the effect of magnetic field on ferrofluid convective mode with radiation.

Abstract

Purpose

The purpose of this paper is to examine the effect of magnetic field on ferrofluid convective mode with radiation.

Design/methodology/approach

Viscosity of Fe3O4 ferrofluid is considered as a function of magnetic field. Solutions of the governing equations are obtained by a powerful numerical method, namely, control volume finite element method (CVFEM). Roles of radiation parameter (Rd), number of undulations (N), Fe3O4–water volume fraction (ϕ), Hartmann (Ha) and Rayleigh numbers are illustrated graphically. A correlation for Nuave is extracted.

Findings

The inner wall temperature decreases with increasing buoyancy forces, but increases with increasing Rd and Ha. Also increasing Rd results in increasing nanofluid motion. This influence is more evident when convection flow is dominant. As nanofluid temperature increases, the nanofluid begins moving from the warm surface to the outer one and dropping along the circular cylinder. At low Rayleigh number, conduction is more significant than convection. |Ψmax| increases as buoyancy force increases and it decreases as the Lorentz force increases. As Hartmann number increases, the center of the vortices moves to x = 0. As Ra increases, convection becomes stronger. Thus, |Ψmax| and temperature gradient increase with increasing Ra. As N increases, the distortion of isotherms reduces and vortices become weaker. Increasing Hartmann number results in a reduction in the thermal plume and the heat transfer mechanism changes from convection to conduction. Nusselt number decreases with increasing NNu decreases with increasing Lorentz force. At N = 5 , increasing the Lorentz force causes the main vortices to convert into three smaller ones. As the Lorentz force increases, the two upper vortices merge together and the thermal plume vanishes. The number of extrema in the Nuloc profile matches the existence of the thermal plume and the number of undulations. Nuave increases with increasing Rd. As buoyancy forces increase, the temperature decreases and in turn Nuave increases with increasing Ra.

Originality/value

Nanofluids are an innovative way to enhance radiation heat. In this paper, MHD Fe3O4–water nanofluid natural convection with radiation source term is examined. Magnetic field-dependent (MFD) viscosity is considered. Using the CVFEM, numerical simulations are carried out for various values of the radiation parameter (Rd = 0 to 0.8), volume fraction of Fe3O4–water (ϕ = 0 to 0.04), Rayleigh number (Ra = 103, 104 and 105), number of undulations (N = 3,4 and 5) and Hartmann number (Ha = 0 to 40).

Details

Engineering Computations, vol. 35 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 7 August 2017

M. Sheikholeslami

The effect of a magnetic field on nanofluid natural convection in a porous annulus is simulated. Control volume-based finite element method (CVFEM) is applied to find the…

Abstract

Purpose

The effect of a magnetic field on nanofluid natural convection in a porous annulus is simulated. Control volume-based finite element method (CVFEM) is applied to find the influence of tilted angle and Darcy, Rayleigh and Hartmann numbers on nanofluid hydrothermal behavior. Vorticity stream function formulation is taken into account. Also, Brownian motion effect on nanofluid thermal conductivity is considered. Results reveal that Hartmann number and tilted angle make changes in nanofluid flow style. Nusselt number enhances with augment of Darcy number and buoyancy forces but reduces with rise of tilted angle and Hartmann number.

Design/methodology/approach

The influence of adding CuO nanoparticles in water on the velocity and temperature distribution in an inclined half-annulus was studied considering constant heat flux. CVFEM is applied to the simulation procedure.

Findings

Influences of CuO volume fraction, inclination angle and Rayleigh number on hydrothermal manners are presented.

Originality/value

Results indicate that inclination angle makes changes in flow style. The temperature gradient enhances with rise of buoyancy forces, whereas it reduces with augment of inclination angle.

Details

Engineering Computations, vol. 34 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 2003

H. Abbassi, A. Boughamoura and S. Ben Nasrallah

In this paper, we present a comparison of linear and exponential interpolation functions for control volume finite element method. The exponential interpolation function is…

Abstract

In this paper, we present a comparison of linear and exponential interpolation functions for control volume finite element method. The exponential interpolation function is expressed in the elemental local coordinate system whereas the classic linear interpolation function is expressed in the global coordinate system. The comparison is achieved in the case of the Green‐Taylor vortex, a flow from which we know the analytical solution. Firstly, the two functions are applied to a triangular element of the domain to compare the results given by each interpolation function to the exact value. Secondly, these two functions are compared when used to solve the discretized equations over the entire domain.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 10 July 2018

Mohsen Sheikholeslami

The purpose of this paper is to simulate nanofluid laminar steady flow in a lid-driven porous cavity under the impact of Lorentz forces.

Abstract

Purpose

The purpose of this paper is to simulate nanofluid laminar steady flow in a lid-driven porous cavity under the impact of Lorentz forces.

Design/methodology/approach

Shape effect of nanoparticles and magnetic field impact on nanofluid properties are taken into consideration. The solutions of final equations are obtained by control volume based finite element method (CVFEM).

Findings

Graphs are depicted for different values of Darcy number, Fe3O4-water volume fraction, Reynolds and Hartmann numbers.

Originality/value

Results illustrated that using Platelet-shaped nanoparticles results in the highest Nusselt number. Nusselt number augments with rise of Darcy and Reynolds number.

Details

Engineering Computations, vol. 35 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 May 2016

Bantwal R. (Rabi) Baliga and Iurii Yuri Lokhmanets

The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical…

Abstract

Purpose

The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains.

Design/methodology/approach

Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed.

Findings

Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner.

Originality/value

Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 November 2017

M. Sheikholeslami

This main purpose of this paper is to investigate the influence of Lorentz forces on magnetic nanofluid free convection in a porous media. Control volume based finite element…

Abstract

Purpose

This main purpose of this paper is to investigate the influence of Lorentz forces on magnetic nanofluid free convection in a porous media. Control volume based finite element method (CVFEM) is chosen to simulate the purpose of this paper. Influences of Darcy number, Fe3O4–water volume fraction, Hartmann and Rayleigh numbers on hydrothermal behavior are presented.

Design/methodology/approach

Magnetic nanofluid flow in a permeable medium is studied numerically using the non-Darcy model. Outputs are obtained by means of CVFEM.

Findings

Results indicated that isotherms become denser near the inner cylinder with augmentation of the permeability of the porous media. The Nusselt number enhances with an increase in buoyancy forces, Darcy number but it detracts with augment of Lorentz forces.

Originality/value

Results depict that the effect of the Hartmann number on rate of heat transfer is more observable in a medium with higher permeability.

Details

Engineering Computations, vol. 34 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 August 2015

Alexandre Lamoureux and Bantwal R. (Rabi) Baliga

The purpose of this paper is to first present the key features of hybrid numerical methods that enable cost-effective simulations of complex thermofluid systems, and then…

1967

Abstract

Purpose

The purpose of this paper is to first present the key features of hybrid numerical methods that enable cost-effective simulations of complex thermofluid systems, and then demonstrate the formulation and application of such a method.

Design/methodology/approach

A hybrid numerical method is formulated for simulations of a closed-loop thermosyphon operating with slurries of a micro-encapsulated phase-change material suspended in distilled water. The slurries are modeled as homogeneous mixtures, with inputs of effective properties and overall heat-loss coefficients. Combinations of an axisymmetric two-dimensional (2D) control-volume finite-element method and a segmented-quasi-one-dimensional (1D) model are used to achieve cost-effective simulations. Proper matching of the solutions at the interfaces between adjacent axisymmetric 2D and quasi-1D zones is ensured by incorporating and heuristically determining suitable lengths of pre- and post-heating (and also pre- and post-cooling) sections.

Findings

In the demonstration problem, which would strictly require full three-dimensional simulations of the fluid flow and heat transfer phenomena, the proposed hybrid 1D/2D numerical method produces results that are in very good agreement with those obtained in a complementary experimental investigation.

Originality/value

The hybrid numerical methods discussed in this paper allow cost-effective computer simulations of complex thermofluid systems. These methods can therefore serve as very useful tools for the design, parametric studies, and optimization of such systems.

1 – 10 of 78