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Article
Publication date: 18 May 2021

J.I. Ramos

The purpose of this paper is to determine both analytically and numerically the existence of smooth, cusped and sharp shock wave solutions to a one-dimensional model of…

Abstract

Purpose

The purpose of this paper is to determine both analytically and numerically the existence of smooth, cusped and sharp shock wave solutions to a one-dimensional model of microfluidic droplet ensembles, water flow in unsaturated flows, infiltration, etc., as functions of the powers of the convection and diffusion fluxes and upstream boundary condition; to study numerically the evolution of the wave for two different initial conditions; and to assess the accuracy of several finite difference methods for the solution of the degenerate, nonlinear, advection--diffusion equation that governs the model.

Design/methodology/approach

The theory of ordinary differential equations and several explicit, finite difference methods that use first- and second-order, accurate upwind, central and compact discretizations for the convection terms are used to determine the analytical solution for steadily propagating waves and the evolution of the wave fronts from hyperbolic tangent and piecewise linear initial conditions to steadily propagating waves, respectively. The amplitude and phase errors of the semi-discrete schemes are determined analytically and the accuracy of the discrete methods is assessed.

Findings

For non-zero upstream boundary conditions, it has been found both analytically and numerically that the shock wave is smooth and its steepness increases as the power of the diffusion term is increased and as the upstream boundary value is decreased. For zero upstream boundary conditions, smooth, cusped and sharp shock waves may be encountered depending on the powers of the convection and diffusion terms. For a linear diffusion flux, the shock wave is smooth, whereas, for a quadratic diffusion flux, the wave exhibits a cusped front whose left spatial derivative decreases as the power of the convection term is increased. For higher nonlinear diffusion fluxes, a sharp shock wave is observed. The wave speed decreases as the powers of both the convection and the diffusion terms are increased. The evolution of the solution from hyperbolic tangent and piecewise linear initial conditions shows that the wave back adapts rapidly to its final steady value, whereas the wave front takes much longer, especially for piecewise linear initial conditions, but the steady wave profile and speed are independent of the initial conditions. It is also shown that discretization of the nonlinear diffusion flux plays a more important role in the accuracy of first- and second-order upwind discretizations of the convection term than either a conservative or a non-conservative discretization of the latter. Second-order upwind and compact discretizations of the convection terms are shown to exhibit oscillations at the foot of the wave’s front where the solution is nil but its left spatial derivative is largest. The results obtained with a conservative, centered second--order accurate finite difference method are found to be in good agreement with those of the second-order accurate, central-upwind Kurganov--Tadmor method which is a non-oscillatory high-resolution shock-capturing procedure, but differ greatly from those obtained with a non-conservative, centered, second-order accurate scheme, where the gradients are largest.

Originality/value

A new, one-dimensional model for microfluidic droplet transport, water flow in unsaturated flows, infiltration, etc., that includes high-order convection fluxes and degenerate diffusion, is proposed and studied both analytically and numerically. Its smooth, cusped and sharp shock wave solutions have been determined analytically as functions of the powers of the nonlinear convection and diffusion fluxes and the boundary conditions. These solutions are used to assess the accuracy of several finite difference methods that use different orders of accuracy in space, and different discretizations of the convection and diffusion fluxes, and can be used to assess the accuracy of other numerical procedures for one-dimensional, degenerate, convection--diffusion equations.

Details

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

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Article
Publication date: 25 February 2021

Leo Lukose and Tanmay Basak

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of…

Abstract

Purpose

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

Design/methodology/approach

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Findings

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

Originality/value

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 14 December 2020

Mostafa Safdari Shadloo

Convection is one of the main heat transfer mechanisms in both high to low temperature media. The accurate convection heat transfer coefficient (HTC) value is required for…

Abstract

Purpose

Convection is one of the main heat transfer mechanisms in both high to low temperature media. The accurate convection heat transfer coefficient (HTC) value is required for exact prediction of heat transfer. As convection HTC depends on many variables including fluid properties, flow hydrodynamics, surface geometry and operating and boundary conditions, among others, its accurate estimation is often too hard. Homogeneous dispersion of nanoparticles in a base fluid (nanofluids) that found high popularities during the past two decades has also increased the level of this complexity. Therefore, this study aims to show the application of least-square support vector machines (LS-SVM) for prediction of convection heat transfer coefficient of nanofluids through circular pipes as an accurate alternative way and draw a clear path for future researches in the field.

Design/methodology/approach

The proposed LS-SVM model is developed using a relatively huge databank, including 253 experimental data sets. The predictive performance of this intelligent approach is validated using both experimental data and empirical correlations in the literature.

Findings

The results show that the LS-SVM paradigm with a radial basis kernel outperforms all other considered approaches. It presents an absolute average relative deviation of 2.47% and the regression coefficient (R2) of 0.99935 for the estimation of the experimental databank. The proposed smart paradigm expedites the procedure of estimation of convection HTC of nanofluid flow inside circular pipes.

Originality/value

Therefore, the focus of the current study is concentrated on the estimation of convection HTC of nanofluid flow through circular pipes using the LS-SVM. Indeed, this estimation is done using operating conditions and some simply measured characteristics of nanoparticle, base fluid and nanofluid.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 6 July 2018

Ismail Arroub, Ahmed Bahlaoui, Abdelghani Raji, Mohammed Hasnaoui and Mohamed Naïmi

The purpose of this paper is to investigate numerically mixed convection of Al2O3-water nanofluids flowing through a horizontal ventilated cavity heated from below by a…

Abstract

Purpose

The purpose of this paper is to investigate numerically mixed convection of Al2O3-water nanofluids flowing through a horizontal ventilated cavity heated from below by a temperature varying sinusoidally along its lower wall. The simulations focus on the effects of different key parameters, such as Reynolds number (200 ≤ Re ≤ 5,000), nanoparticles’ concentration (0 ≤ ϕ ≤ 0.1) and phase shift of the heating temperature (0 ≤ γ ≤ π), on flow and thermal patterns and heat transfer performances.

Design/methodology/approach

The Navier–Stokes equations describing the nanofluid flow were discretized using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the stream function were obtained by using the point successive over-relaxation method.

Findings

The simulations were performed for two modes of imposed external flow (injection and suction). The main findings are that the dynamical and thermal fields are affected by the parameters Re, ϕ, γ and the applied ventilation mode; the addition of nanoparticles leads to an improvement of heat transfer rate and an increase of mean temperature inside the enclosure; the heat exchange performance and the better cooling are more pronounced in suction mode; the phase shift of the heating temperature may lead to periodic solutions for weaker values of Re and contributes to an increase or a decrease of heat transfer depending on the value of ϕ and the convection regime.

Originality/value

To the best of the authors’ knowledge, the problem of mixed convection of a nanofluid inside a vented cavity using the injection or suction technics and submitted to non-uniform heating conditions has not been treated so far.

Details

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

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Article
Publication date: 4 December 2018

Alireza Rahimi, Ali Dehghan Saee, Abbas Kasaeipoor and Emad Hasani Malekshah

The purpose of this paper is to carry out a comprehensive review of some latest studies devoted to natural convection phenomenon in the enclosures because of its…

Abstract

Purpose

The purpose of this paper is to carry out a comprehensive review of some latest studies devoted to natural convection phenomenon in the enclosures because of its significant industrial applications.

Design/methodology/approach

Geometries of the enclosures have considerable influences on the heat transfer which will be important in energy consumption. The most useful geometries in engineering fields are treated in this literature, and their effects on the fluid flow and heat transfer are presented.

Findings

A great variety of geometries included with different physical and thermal boundary conditions, heat sources and fluid/nanofluid media are analyzed. Moreover, the results of different types of methods including experimental, analytical and numerical are obtained. Different natures of natural convection phenomenon including laminar, steady-state and transient, turbulent are covered. Overall, the present review enhances the insight of researchers into choosing the best geometry for thermal process.

Originality/value

A comprehensive review on the most practical geometries in the industrial application is performed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 5 March 2018

Minh Tuan Nguyen, Abdelraheem M. Aly and Sang-Wook Lee

This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions…

Abstract

Purpose

This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the incompressible smoothed particle hydrodynamics (ISPH) method.

Design/methodology/approach

In the ISPH method, the pressure evaluation is stabilized by including both of divergence of velocity and density invariance in solving pressure Poisson equation. The authors prevented the particles anisotropic distributions by using the shifting technique.

Findings

The proposed ISPH method exhibited good performance in natural/mixed convection in a cavity with fixed, moving and free-falling rigid body. In natural convection, the authors investigated the effects of an inner sloshing baffle as well as fixed and moving circular cylinders on the heat transfer and fluid flow. The heated baffle has higher effects on the heat transfer rate compared to a cooled baffle. In the mixed convection, a free-falling circular cylinder over a free surface cavity and heat transfer in the presence of a circular cylinder in a lid-driven cavity are simulated. Fixed or moving rigid body in a cavity results in considerable effects on the heat transfer rate and fluid flow.

Originality/value

The authors conducted numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the ISPH method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 November 2003

I. Pop, T. Groşan and M. Kumari

An analysis of steady laminar mixed convection boundary layer flow along a vertical cone of constant wall temperature is presented. A mixed convection parameter ξ, as…

Abstract

An analysis of steady laminar mixed convection boundary layer flow along a vertical cone of constant wall temperature is presented. A mixed convection parameter ξ, as proposed by Lin and Chen, is used to serve as a controlling parameter that determines the relative importance of the forced and the free convection flows. New coordinates and dependent variables are then defined in terms of ξ, so that the transformed non‐similar boundary layer equations give computationally efficient numerical solutions which are valid over the entire range of mixed convection flow from the forced convection limit to the free convection limit for fluids of any Prandtl number. The effects of the mixed convection parameter ξ and the Prandtl number Pr on the velocity and temperature profiles as well as on the skin friction and heat transfer coefficients are shown for both cases of buoyancy assisting and buoyancy opposing flow conditions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 May 1995

H. Schweiger, A. Oliva, M. Costa, C.D. Pérez Segarra and A. Ivancić

Two‐dimensional finite difference calculations are carried out tostudy laminar flow in longitudinal and transverse convection rolls for threedifferent geometries: a single…

Abstract

Two‐dimensional finite difference calculations are carried out to study laminar flow in longitudinal and transverse convection rolls for three different geometries: a single rectangular cavity with high aspect ratio; a double cavity with a thin separation sheet; and a double cavity with a separation sheet and a honeycomb structure. The equations for the convection‐diffusion in the fluid and conduction in the solid region are solved simultaneously. Good agreement with experimental data is achieved for Rayleigh numbers not too high above the critical value for the onset of secondary convection rolls (Ra < 8500 for vertical and Ra < 2700 for horizontal cavities filled with air). Simulation fails for inclined cavities, where the flow structure is essentially three‐dimensional.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 August 1999

Rama Subba Reddy Gorla and Mahesh Kumari

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power‐law type non‐Newtonian fluids along a vertical wedge with variable wall…

Abstract

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power‐law type non‐Newtonian fluids along a vertical wedge with variable wall temperature distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 25 November 2019

Shihua Lu, Jianqi Zhu, Dongyan Gao, Weiwei Chen and Xinjun Li

This study aims to show the importance of natural convection of supercritical fluid in an inclined cavity. The heat transfer performance of natural convection can be improved.

Abstract

Purpose

This study aims to show the importance of natural convection of supercritical fluid in an inclined cavity. The heat transfer performance of natural convection can be improved.

Design/methodology/approach

A model of an inclined cavity was set up to simulate the natural convection of supercritical fluid. The influence of inclined angles (30 to approximately 90°) and pressures (8 to approximately 12 MPa) are analyzed. To ascertain flow and heat transfer of supercritical fluid natural convection, this paper conducts a numerical investigation using the lattice Boltzmann method (LBM), which is proven to be precise and convenient.

Findings

The results show that the higher heat transfer performance can be obtained with an inclined angle of 30°. It is also presented that the heat transfer performance under pressure of 10 MPa is the best. In addition, common criterion number correlations of average Nusselt number are also fitted.

Originality/value

These study results can provide a theoretical reference for the study of heat transfer of supercritical fluid natural convection in engineering.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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