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Article

H. Amiri, S.H. Mansouri and P.J. Coelho

The solution of radiative heat transfer problems in participating media is often obtained using the standard discrete ordinates method (SDOM). This method produces…

Abstract

Purpose

The solution of radiative heat transfer problems in participating media is often obtained using the standard discrete ordinates method (SDOM). This method produces anomalies caused by ray effects if radiative boundary conditions have discontinuities or abrupt changes. Ray effects may be mitigated using the modified discrete ordinates method (MDOM), which is based on superposition of the solutions obtained by considering separately radiation from the walls and radiation from the medium. The purpose of this paper is to study the role of ray effects in combined conduction‐radiation problems and investigate the superiority of the MDOM over SDOM.

Design/methodology/approach

The MDOM has been used to calculate radiative heat transfer in irregular geometries using body‐fitted coordinates. Here, the blocked‐off region concept, originally developed in computational fluid dynamics, is used along with the finite volume method and SDOM or MDOM to solve combined conduction‐radiation heat transport problems in irregular geometries. Enclosures with an absorbing, emitting and isotropically or anisotropically scattering medium are analyzed.

Findings

The results confirm the capability of the MDOM to minimize the anomalies due to ray effects in combined heat transfer problems, and demonstrate that MDOM is more computationally efficient than SDOM.

Originality/value

The paper demonstrates the application of MDOM to combined conduction‐radiation heat transfer problems in irregular geometries using blocked‐off method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

He Ya‐Ling, Ding Wen‐Jing and Tao Wen‐Quan

The effect of the tube wall heat conduction on the natural convection in a tilted long cylindrical envelope with constant, but different temperature of the two ends and an…

Abstract

The effect of the tube wall heat conduction on the natural convection in a tilted long cylindrical envelope with constant, but different temperature of the two ends and an adiabatic outer surface was numerically investigated. The envelope is supposed to be a simplified model for the pulse tube in a pulse tube refrigerator when the pulse tube is positioned at different orientations. It is found that the cylindrical envelope lateral wall heat conduction can enhance the heat transfer from the hot end to the cold end, not only because of the increase in pure heat conduction in the wall, but more importantly, also the intensification of the natural convection within the enclosure. This enhancement is resulted from the big temperature difference between the tube wall and the adjacent fluid near the hot and cold ends. Adoption of low thermal conductivity tube can effectively reduce such additional heat transfers from hot to cold end, thus reducing the loss of cooling capacity for the pulse tube refrigerator.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14 no. 8
Type: Research Article
ISSN: 0961-5539

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Article

Mas Irfan Purbawanto Hidayat, Bambang Ariwahjoedi and Setyamartana Parman

The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction

Abstract

Purpose

The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems.

Design/methodology/approach

In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique.

Findings

Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate the effectiveness of the present approach. Comparison of the obtained results with solutions from other numerical method available in literature is given. Excellent agreement with reference numerical method has been found.

Research limitations/implications

The method is presented for 2D problems. Nevertheless, it would be also applicable for 3D problems.

Practical implications

A transient two dimensional heat conduction in complex domains which represent for extended surfaces in industrial applications is presented.

Originality/value

The presented new meshless local method is simple and accurate, while it is also suitable for analysis in domains of arbitrary geometries.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
ISSN: 0961-5539

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Article

Mohammed Q. Al‐Odat

In this study, the purpose was to introduce two‐dimensional hyperbolic heat conduction equations in order to simulate the fast precooling process of a cylindrically shaped…

Abstract

Purpose

In this study, the purpose was to introduce two‐dimensional hyperbolic heat conduction equations in order to simulate the fast precooling process of a cylindrically shaped food product with internal heat generation. A modified model for internal heat generation due to respiration in the food product was proposed to take the effect of relaxation time into account. The obtained governing equations were solved numerically using an efficient finite difference technique. The influence of Biot number and heat generation parameters on thermal characteristics was examined and discussed. The results based on hyperbolic model were compared with the classical parabolic heat diffusion model. The present numerical code was validated via comparison with analytical solution and a good agreement was found.

Design/methodology/approach

The obtained governing equations were solved numerically using an efficient finite difference technique.

Findings

The influence of Biot number and heat generation parameters on thermal characteristics was examined and discussed. The results based on hyperbolic model were compared with the classical parabolic heat diffusion model. The present numerical code was validated via comparison with analytical solution and a good agreement was found.

Originality/value

Two‐dimensional analysis of fast precooling of cylindrical food product based on hyperbolic heat conduction model has not been investigated yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Ahmed E. Abouelregal

In this work, a modified thermoelastic model of heat conduction, including higher order of time derivative, is constructed by extending the Roychoudhuri model (TPL…

Abstract

Purpose

In this work, a modified thermoelastic model of heat conduction, including higher order of time derivative, is constructed by extending the Roychoudhuri model (TPL) (Choudhuri, 2007). In this new model, Fourier’s law of heat conduction is replaced by using Taylor series expansions, including three different phase lags for the heat flux, the thermal displacement and the temperature gradient. The generalized thermoelasticity models of Lord–Shulman (Lord and Shulman, 1967), Green and Naghdi (1991), dual-phase lag (Tzou, 1996) and three-phase lag (TPL) (Choudhuri, 2007) are obtained as special cases. The paper aims to discuss these issues.

Design/methodology/approach

The aim of this work is to establish a new generalized mathematical model of thermoelasticity that includes TPL in the vector of heat flux, and in the thermal displacement and temperature gradients extending TPL model (Li et al., 2019e). In this model, Fourier law of heat conduction is replaced by using Taylor series expansions to a modification of the Fourier law with introducing three different phase lags for the heat flux vector, the temperature gradient, and the thermal displacement gradient and keeping terms up with suitable higher orders.

Findings

The established high-order three-phase-lag heat conduction model reduces to the previous models of thermoelasticity as special cases.

Originality/value

In this paper, a TPL thermoelastic model is developed by extending the Roychoudhuri (Sherief and Raslan, 2017) model (TPL) considering the Taylor series approximation of the equation of heat conduction. This model is an alternative construction to the TPL model. The new model includes high order of TPL in the vector of heat flux, and in the thermal displacement and temperature gradients.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

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Article

S. BRANDON and J.J. DERBY

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate…

Abstract

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 4
Type: Research Article
ISSN: 0961-5539

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Article

Nishant Tiwari and Manoj Kumar Moharana

This paper aims to emphasize on studying various geometrical modification performed in wavy and raccoon microchannel by manipulating parameters, i.e. waviness (γ)…

Abstract

Purpose

This paper aims to emphasize on studying various geometrical modification performed in wavy and raccoon microchannel by manipulating parameters, i.e. waviness (γ), expansion factor (α), wall to fluid thermal conductivity ratio (ksf), substrate thickness to channel height ratio (dsf) and Reynolds number (Re) for obtaining optimum parameter(s) that leads to higher heat dissipation rate.

Design/methodology/approach

A three-dimensional solid-fluid conjugate heat transfer numerical model is designed to capture flow characteristics and heat transfer in single-phase laminar flow microchannels. The governing equations are solved using finite volume method.

Findings

The results are presented in terms of average base temperature, average Nusselt number, pressure drop, dimensionless local heat flux, dimensionless wall and bulk fluid temperature, local Nusselt number and performance factor including axial conduction number. Heat dissipation rate with raccoon microchannel configuration is found to be higher compared to straight and wavy microchannel. With waviness of γ = 0.167, and 0.267 in wavy and raccoon microchannel, respectively, performance factor attains maximum value compared to other waviness for all values of Reynolds number. It is also found that the effect of axial wall conduction in wavy and raccoon microchannel is negligible. Additionally, thermal performance of wavy and raccoon microchannel is compared with straight microchannel.

Practical implications

In recent past years, much complex design of microchannel has been proposed for heat transfer enhancement, but the feasibility of available manufacturing techniques to fabricate complex geometries is still questionable. However, fabrication of wavy and raccoon microchannel is easy, and their heat dissipation capability is higher.

Originality/value

This makes the difference in wall and bulk fluid temperature smaller. Thus, present work highlighted the dominance of axial wall conduction on thermal and hydrodynamic performance of wavy and raccoon microchannel under conjugate heat transfer situation.

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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Article

Antonio Campo and Yunesky Masip

The purpose of this study is to address one-dimensional, unsteady heat conduction in a large plane wall exchanging heat convection with a nearby fluid under “small time”…

Abstract

Purpose

The purpose of this study is to address one-dimensional, unsteady heat conduction in a large plane wall exchanging heat convection with a nearby fluid under “small time” conditions.

Design/methodology/approach

The Transversal Method of Lines (TMOL) was used to reformulate the unsteady, one-dimensional heat conduction equation in the space coordinate and time into a transformed “quasi-steady”, one-dimensional heat conduction equation in the space coordinate housing the time as an embedded parameter. The resulting ordinary differential equation of second order with heat convection boundary conditions is solved analytically with the method of undetermined coefficients.

Findings

Semi-analytical TMOL dimensionless temperature profiles of compact form with/without regressed terms are obtained for the whole spectrum of Biot number (0 < Bi < ∞) in the “small time” sub-domain. In addition, a new “large time” sub-domain is redefined, that is, setting a smaller critical dimensionless time or critical Fourier number τcr = 0.18.

Originality/value

The computed dimensionless center, surface and mean temperature profiles in the large plane wall accounting for all Biot number (0 < Bi < ∞) in the “small time” sub-domain τ < τcr = 0.18 exhibit excellent quality while carrying reasonable relative errors for engineering applications. The exemplary level of accuracy indicates that the traditional evaluation of the center, surface and mean temperatures with the standard infinite series retaining a large number of terms is no longer necessary.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

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Article

A. Kassab, E. Divo, J. Heidmann, E. Steinthorsson and F. Rodriguez

We report on the progress in the development and application of a coupled boundary element/finite volume method temperature‐forward/flux‐back algorithm developed to solve…

Abstract

We report on the progress in the development and application of a coupled boundary element/finite volume method temperature‐forward/flux‐back algorithm developed to solve conjugate heat transfer arising in 3D film‐cooled turbine blades. We adopt a loosely coupled strategy where each set of field equations is solved to provide boundary conditions for the other. Iteration is carried out until interfacial continuity of temperature and heat flux is enforced. The NASA‐Glenn explicit finite volume Navier‐Stokes code Glenn‐HT is coupled to a 3D BEM steady‐state heat conduction solver. Results from a CHT simulation of a 3D film‐cooled blade section are compared with those obtained from the standard two temperature model, revealing that a significant difference in the level and distribution of metal temperatures is found between the two. Finally, current developments of an iterative strategy accommodating large numbers of unknowns by a domain decomposition approach is presented. An iterative scheme is developed along with a physically‐based initial guess and a coarse grid solution to provide a good starting point for the iteration. Results from a 3D simulation show the process that converges efficiently and offers substantial computational and storage savings.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Ajay Vadakkepatt, Sanjay R. Mathur and Jayathi Y. Murthy

Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity…

Abstract

Purpose

Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems.

Design/methodology/approach

Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid).

Findings

Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains.

Originality/value

In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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