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Article
Publication date: 1 May 1995

M.A.I. El‐Shaarawi, M.A. Al‐Nimr and M.A. Hader

The paper presents a finite‐difference scheme to solve thetransient conjugated heat transfer problem in a concentricannulus with simultaneously developing hydrodynamic and…

Abstract

The paper presents a finite‐difference scheme to solve the transient conjugated heat transfer problem in a concentric annulus with simultaneously developing hydrodynamic and thermal boundary layers. The annular forced flow is laminar with constant physical properties. Thermal transient is initiated by a step change in the prescribed isothermal temperature of the inner surface of the inside tube wall while the outer surface of the external tube is kept adiabatic. The effects of solid‐fluid conductivity ratio and diffusivity ratio on the thermal behaviour of the flow have been investigated. Numerical results are presented for a fluid of Pr = 0.7 flowing in an annulus of radius ratio 0.5 with various values of inner and outer solid wall thicknesses.

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: 4 May 2012

S.M. Aminossadati and B. Ghasemi

The purpose of this paper is to numerically examine the conjugate natural convection in an inclined enclosure with a conducting centred block. This enclosure is filled…

Abstract

Purpose

The purpose of this paper is to numerically examine the conjugate natural convection in an inclined enclosure with a conducting centred block. This enclosure is filled with an Ethylene Glycol‐copper nanofluid. This study utilises numerical simulations to quantify the effects of pertinent parameters such as the Rayleigh number, the solid volume fraction, the length and the thermal conductivity of the centred block and the inclination angle of the enclosure on the conjugate natural convection characteristics.

Design/methodology/approach

The SIMPLE algorithm is utilised to solve the governing equations with the corresponding boundary conditions. The convection‐diffusion terms are discretised by a power‐law scheme and the system is numerically modelled in FORTRAN.

Findings

The results show that the utilisation of the nanofluid enhances the thermal performance of the enclosure and that the length of the centred block affects the heat transfer rate. The results also show that the higher block thermal conductivity results in a better heat transfer that is most noticeable at low Rayleigh numbers, and that increasing the inclination angle improves the heat transfer, especially at high Rayleigh numbers.

Originality/value

This paper presents an original research on conjugate natural convection in nanofluid‐filled enclosures.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 March 1996

Hongjun Li, C.K. Hsieh and D.Y. Goswami

A method has been developed for conjugate heat transfer analysis offluid flow inside parallel channels formed by a phase change material (PCM)separated from the fluid by a…

Abstract

A method has been developed for conjugate heat transfer analysis of fluid flow inside parallel channels formed by a phase change material (PCM) separated from the fluid by a wall. The phase change in the PCM is two dimensional and a hybrid analysis consisting of an analytical solution in one direction and a finite‐difference method in another direction is used to solve for the temperature in the PCM. The heat transfer fluid (HTF) inlet temperature is given and the heat transfer between the HTF and the PCM is treated as a conjugate problem that requires no iterations to obtain a solution. The numerical results are found to be stable, convergent, and accurate. Application of the method to the solution of heat extraction from a phase‐change energy storage unit is given in detail and the numerical results are shown to be accurate, based on an energy conservation analysis, to within 3%.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 4 January 2016

Abderrahim Bourouis, Abdeslam Omara and Said Abboudi

The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical…

Abstract

Purpose

The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer. The effect of the relevant parameters: Richardson number (Ri=0.1, 1, 10) and thermal conductivity ratio (Rk=0.1, 1, 10, 100) are investigated.

Design/methodology/approach

The studied system is a two dimensional lid-driven enclosure with thick vertical porous layer. The left vertical wall of the enclosure is allowed to move in its own plane at a constant velocity. The enclosure is heated from the right vertical wall isothermally. The left and the right vertical walls are isothermal but temperature of the outside of the right vertical wall is higher than that of the left vertical wall. Horizontal walls are insulated. The governing equations are solved by finite volume method and the SIMPLE algorithm.

Findings

From the finding results, it is observed that: for the two studied cases, heat transfer rate along the hot wall is a decreasing function of thermal conductivity ratio irrespective of Richardson numbers contrary to the heat transfer rate along the fluid-porous layer interface which is an increasing function of thermal conductivity ratio. At forced convection dominant regime, the difference between heat transfer rate for upward and downward moving wall is insensitive to the thermal conductivity ratio. For downward moving wall, average Nusselt number is higher than that of upward moving wall.

Practical implications

Some applications: building applications, furnace design, nuclear reactors, air solar collectors.

Originality/value

From the bibliographic work and the authors’ knowledge, the conjugate mixed convection in lid-driven partially porous enclosures has not yet been investigated which motivates the present work that represent a continuation of the preceding investigations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 February 2002

W. Song and B.Q. Li

This paper describes the finite element solution of conjugate heat transfer problems with and without the use of gap elements. Direct and iterative methods to incorporate…

Abstract

This paper describes the finite element solution of conjugate heat transfer problems with and without the use of gap elements. Direct and iterative methods to incorporate gap elements into a general finite element program are presented, along with their advantages and disadvantages of the two gap element treatments in the framework of finite elements. The numerical performance of the iterative gap element treatment is discussed in detail in comparison with analytical solutions for both 2‐ and 3‐D gap conductance problems. Numerical tests show that the number of iterations depends on the non‐dimensional number Bi = hL/k, and it increases approximately linearly with Bi for Bi≥0.6. Here, for gap heat transfer problems, h is taken to be the inverse of the contact resistance. This conclusion holds true for both 2‐ and 3‐D problems, for both linear and quadratic elements and for both transient and steady state calculations. Further numerical results for conjugate heat transfer problems encountered in heat exchanger and micro chemical reactors are computed using the gap element approach, the direct numerical simulations and analytical solutions whenever solvable. The results reveal that for the standard heat exchanger designs, an accurate prediction of temperature distribution in the moving streams must take into consideration the radial temperature distribution and the accuracy of the calculations depends on the non‐dimensional number Bi = hR/2k. From gap element calculations, it is found that classical analytical solutions are valid for a heat transfer analysis of an exchanger system, only when Bi<0.1. This important point so far has been neglected in virtually all the textbooks on heat transfer and must be included to complete the heat transfer theory for heat exchanger designs. Results also suggest that for thermal fluids systems with chemical reactions such as micro fuel cells, the gap element approach yields accurate results only when the heat transfer coefficient that accounts for the chemical reactions is used. However, when these heat transfer coefficients are not available, direct numerical simulations should be used for an accurate prediction of the thermal performance of these systems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 July 2005

K.J. Hsieh and F.S. Lien

Performance of various kε models on turbulent forced convection in a channel with periodic ribs is assessed.

Abstract

Purpose

Performance of various kε models on turbulent forced convection in a channel with periodic ribs is assessed.

Design/methodology/approach

The influence of the Yap correction and the non‐linear stress‐strain relation on the predictions of mean‐flow, turbulence quantities and local heat transfer rate is examined. The effect of thermal boundary conditions on the heat transfer predictions is investigated by employing both the prescribed heat flux approach and the conjugate heat transfer approach.

Findings

It was found that the inclusion of the Yap correction in the ε‐equation significantly improves the predictions of mean velocity and wall heat transfer for both high‐Reynolds number and low‐Reynolds number kε models in the present ribbed channel flow with massive flow separation. The employment of the non‐linear stress‐strain relation only marginally improves the predictions of turbulence quantities: the turbulence anisotropy is reproduced although the level of turbulence intensity is still too low. In general, the conjugate heat transfer approach predicts better average Nusselt number than the prescribed heat flux approach. However, both approaches under‐predict the experimental value by about 28‐33 percent when the low‐Reynolds number kε model of Lien and Leschziner (1999) with the Yap term is adopted.

Originality/value

Thorough numerical treatments of the thermal boundary conditions at the solid‐liquid interface, and detailed periodic condition in the periodic regime, were given in the paper to benefit researchers interested in solving similar problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 19 June 2007

Maged A.I. El‐Shaarawi, Esmail M.A. Mokheimer and Ahmad Jamal

To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection…

Abstract

Purpose

To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal boundary conditions with one cylinder heated isothermally while the other cylinder is kept at the inlet fluid temperature.

Design/methodology/approach

A finite‐difference algorithm has been developed to solve the bipolar boundary‐layer equations for the conjugate laminar free convection heat transfer in vertical eccentric annuli.

Findings

Numerical results are presented for a fluid of Prandtl number, Pr=0.7 in eccentric annuli. The geometry parameters of NR2 and E (the fluid‐annulus radius ratio and the eccentricity, respectively) have considerable effects on the results.

Practical implications

Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.

Originality/value

The paper presents results that are not available in the literature for the problem of conjugate laminar free convection in open‐ended vertical eccentric annular channels. Geometry effects having been investigated by considering fluid annuli having radii ratios NR2=0.1 and 0.3, 0.5 and 0.7 and four values of the eccentricity E=0.1, 0.3, 0.5 and 0.7. Moreover, practical ranges of the solid‐fluid conductivity ratio (KR) and the wall thicknesses that are commonly available in pipe standards have been investigated. Such results are very much needed for design purposes of heat transfer equipment.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 2 October 2017

Zimeng Wang, Fabrice Colin, Guigao Le and Junfeng Zhang

The purpose of this paper is to develop a counter-extrapolation approach for computational heat and mass transfer with the interfacial discontinuity considered at conjugate

Abstract

Purpose

The purpose of this paper is to develop a counter-extrapolation approach for computational heat and mass transfer with the interfacial discontinuity considered at conjugate interfaces.

Design/methodology/approach

By applying finite-difference approximations for the interfacial gradients along the local normal direction, the conjugate system can be simplified to the Dirichlet boundary problems for individual domains. A suitable method for the Dirichlet boundary value condition can then be used. The lattice Boltzmann method has been used to demonstrate the method. The model has been carefully validated by comparing the simulation results and theoretical solutions for steady and unsteady systems with flat or circular interfaces. Furthermore, the cooling process of a hot cylinder in a cold flow, which involves unsteady flow and heat transfer across a curved interface, has been simulated as an example to illustrate the practical usefulness of this model.

Findings

Good agreement has been observed in comparisons of simulations and theoretical solutions. The convergence and stability of the method have also been examined and satisfactory results have been obtained. Results of the cylinder cooling process show that a surface insulation layer can effectively reduce the heat transfer process and slow down the cooling process.

Originality/value

This method possesses several technical advantages, including the simple and straightforward algorithm, and accurate representation of the interface geometry. The basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems with interface discontinuity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 10
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 9 January 2009

E. Vishnuvardhanarao and Manab Kumar Das

The purpose of this paper is to consider the conjugate heat transfer from a flat plate involving a turbulent plane wall jet. The bottom wall of the solid block is heated

Abstract

Purpose

The purpose of this paper is to consider the conjugate heat transfer from a flat plate involving a turbulent plane wall jet. The bottom wall of the solid block is heated by a constant heat flux.

Design/methodology/approach

High Reynolds number two‐equation model (κϵ) has been used for turbulence modeling. The parameters considered are the conductivity ratio of solid and fluid, the solid slab thickness and the Prandtl number. The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then is independent of the Reynolds number. The range of parameters considered are: conductivity ratio = 1‐1,000, solid slab thickness = 1‐10 and Prandtl number = 0.01‐100.

Findings

The non‐dimensional bottom surface temperature is high for high‐Prandtl number fluid and vice versa. As conductivity ratio increases, it decreases whereas it increases with the increase in slab thickness. Similar trend is observed for the distribution of the interface temperature. The Nusselt number computed based on the interface temperature increases with Prandtl number. It is observed that for the range of parameters considered, local Nusselt number distribution superimposes with each other. The average heat flux at the interface has been computed and found to be equal with average heat flux at the bottom which ensures the overall heat balance.

Originality/value

The study of conjugate heat transfer with a turbulent wall jet will be useful for cooling of heated body.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 2 June 2020

Amin Kardgar

The purpose of this paper is to investigate conjugate heat transfer of natural convection and entropy generation of nanofluid in the presence of external magnetic field…

Abstract

Purpose

The purpose of this paper is to investigate conjugate heat transfer of natural convection and entropy generation of nanofluid in the presence of external magnetic field via numerical approach in an inclined square cavity enclosure.

Design/methodology/approach

Control volume finite volume method with collocated arrangement of grids was used for discretization of continuity, momentum, solid and fluid energy equations. Rhie and Chow interpolation technique was applied to avoid checkerboard problem in pressure field and the well-established SIMPLE algorithm was followed to deal with the pressure and velocity coupling. The cavity is filled with water and nanoparticles of the aluminum oxide (Al2O3). This study has been conducted for the certain pertinent parameters of the volume fraction of nanoparticle (φ = 0–0.08), the angle of inclination (ϴ = 0°–330°), the Ra number (Ra = 103–108), the solid to fluid conductivity ratio (ksf = 1–400), the Ha number (Ha = 0–80) and the wall thickness ratio (δ/L = 0–0.3).

Findings

The results indicate that averaged Nu number increases by approximately 9% by increasing volume fraction from 0.0 to 0.08. Nu increases with an increasing inclination angle to 40° and decreases abruptly in 90° because of the formation of two weaker vorticity with opposite circulation pattern intensifying the density of isotherm curves in a vertical direction. Nu increases sharply with increasing Ra more than 105. Nu also augments almost 67% by increasing ksf = 1 to ksf = 50 and remains constant by increasing ksf more than 50. Nu number reduction is almost 72% with a variation of wall thickness ratio from d/L = 0 to 0.3. Entropy generation because of fluid flow, magnetic field and heat transfer reduces linearly almost 30%, 19% and 16% by increasing volume fraction, respectively. With increasing ksf, entropy generation because of fluid flow, magnetic field and heat transfer increases asymptotically, but Bejan number decreases.

Originality/value

A brief review of conducted research studies in nanofluid flow and heat transfer reveals that the effect of wall thermal inertia was not investigated in MHD natural convection of nanofluids in an inclined enclosure. The aim of the present study is to analyze conjugate heat transfer in an inclined cavity filled with water and Al2O3.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 736