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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

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Article

Zdzisław Włodarski, Jadwiga Włodarska and Andrzej Brykalski

The increase of the accuracy of a mathematical model of hysteresis by the choice of the optimum saturation curve for a given material.

Abstract

Purpose

The increase of the accuracy of a mathematical model of hysteresis by the choice of the optimum saturation curve for a given material.

Design/methodology/approach

Hysteresis loops of typical soft magnetic materials are approximated with the help of the Taka´cs magnetization model using different saturation curves. The quality of approximations is determined by the deviation of computed magnetic induction amplitudes, iron losses, apparent remanences and coercivities from the measured values.

Findings

By the proper choice of saturation curve, the relative inaccuracy of approximations can be reduced with reference to the original model based on tangent hyperbolic function.

Research limitations/implications

The accuracy of approximations worsens close to saturation because of the excessive rise of magnetization due to the linear term of the model. This effect should be minimized by the application of complex saturation curves using greater number of parameters.

Practical implications

Owing to the convenient analytical form and increased accuracy, the model equations can be used in simpler practical evaluations of hysteresis effects and for teaching purposes.

Originality/value

Presented form of model equations enables approximation of hysteresis loops and the evaluation of main characteristics of magnetic materials on the basis of any saturation curve.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 24 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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Article

Kesha K. Coker, Deepa Pillai and Siva K. Balasubramanian

Rewards from sales promotions may be either immediate (e.g. instant savings, coupons, instant rebates) or delayed (e.g. rebates, refunds). The latter type is of interest…

Abstract

Purpose

Rewards from sales promotions may be either immediate (e.g. instant savings, coupons, instant rebates) or delayed (e.g. rebates, refunds). The latter type is of interest in this study. The purpose of this paper is to present the hyperbolic discounting framework as an explanation for how consumers delay‐discount rewards, and test whether this holds for both high‐price and low‐price product categories.

Design/methodology/approach

Data were collected by administering two online surveys to respondents. One survey presented choice scenarios between sales promotion formats for a high‐priced product (a laptop, n=154) and the other for a low‐priced product (a cell phone, n=98). Hyperbolic and exponential functions were then fitted to the data.

Findings

The hyperbolic function had a better fit than the exponential function for the low‐priced product. However, this effect was not evident in the case of the high‐priced product; no significant difference was found between the functions. The rate of discounting was greater for the high‐priced product than for the low‐priced product. Thus, for low‐priced products, rather than discount a reward rationally, consumers tend to discount the value of the reward at a decreasing rate.

Originality/value

This study addresses delay discounting in the context of a typical consumer buying situation. It also addresses the possibility of consumers applying different forms of discounting to products at different price levels and tests for the same. The results are of considerable significance for marketers wishing to offer price discounts to consumers. For low‐priced products, marketers seem to have more flexibility in delaying the reward, since the rate of discounting decreases for longer delay periods. At the same time, the discount rate for high‐priced products is higher than that for low‐priced products, hence delay periods may have a more critical role as discounted values fall steeply with an increase in delay to reward.

Details

Journal of Product & Brand Management, vol. 19 no. 7
Type: Research Article
ISSN: 1061-0421

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Article

Alice de Jesus Kozakevicius, Dia Zeidan, Alex A. Schmidt and Stefan Jakobsson

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The…

Abstract

Purpose

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods.

Design/methodology/approach

This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme.

Findings

Hyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures.

Originality/value

Resolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

V.M Wheeler and K K Tamma

The purpose of this paper is to provide an overview and some recent advances in the models, analysis and simulation of thermal transport of phonons as related to the field…

Abstract

Purpose

The purpose of this paper is to provide an overview and some recent advances in the models, analysis and simulation of thermal transport of phonons as related to the field of microscale/macroscale heat conduction in solids. The efforts focus upon a fairly comprehensive overview of the subject matter from a unified standpoint highlighting the various approximations inherent in the thermal models. Subsequently, the numerical formulations and illustrations using the current state-of-the-art are provided.

Design/methodology/approach

This paper is dedicated to the approximate solution to the relaxation time phonon Boltzmann equation (BE). While original contributions are pointed out and addressed appropriately, the efforts and contributions will be focussed on a relatively complete overview highlighting the field from one unified standpoint and clearly stating all assumptions that go into the approximations inherent to existing models. The contents will be divided as follows: In the first section the authors will give an overview of semi-classical phonon transport physics. Then the authors will discuss the equation of phonon radiative transport (EPRT) and its approximations—the ballistic-diffusive approximation (BDA) and the new heat equation (NHE). Next the authors derive and discuss the C-F model. A numerical discretization method valid for all models is then presented followed by results to numerical simulations and discussion.

Findings

From a unified treatment based on the introduction of an energy distribution function, the authors have derived the EPRT and its two well-known approximations: BDA and NHE. For completeness and to provide a vehicle for a general numerical discretization approach, the authors have also included analysis of the C-F model and the parabolic and hyperbolic descriptions of heat transfer along with it. The approximation of angular dependence of phonons in radiation-like descriptions of transport has been given special attention. The assumption of isotropy was found to be of paramount importance in the formulation of position space models for phononic thermal transport. For the thin film problem considered here, the NHE along with the proper boundary condition appears to be the best choice to approximate the phonon BE. Not only does it provide predictions that are in excellent agreement with EPRT, it does not require the discretization of phase space making it far more computationally efficient.

Originality/value

The authors hope this work will help dispel the idea that since Fourier’s law describes diffusion (under limiting assumptions) and it has shown to be ineffective in describing heat transfer for very thin films, that diffusion cannot describe heat transfer in thin films and one should look to a radiative description instead. If one considers diffusion in the sense of random motion, as invisaged by the original builders of the subject (Smoluchowski, Einstein, Ornstein et al.), instead of a temperature gradient, the idea that diffusion can govern thermal transport at this scale is not surprising. Indeed, the NHE is essentially a diffusion equation that describes the motion of particles up to the point of true randomness (isotropy) as well as thereafter.

Details

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

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Article

Azizeh Jabbari, Hossein Kheiri and Ahmet Yildirim

– The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method.

Abstract

Purpose

The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method.

Design/methodology/approach

The authors used Maple Package to calculate the solutions obtained from the homotopy Padé method.

Findings

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m, m] homotopy Padé technique are often independent of auxiliary parameter h and this technique accelerates the convergence of the related series. Finally, numerical results for some test problems with known solutions are presented and the numerical results are given to show the efficiency of the proposed techniques.

Originality/value

The paper is shown that homotopy Padé technique is a promising tool with accelerated convergence for complicated nonlinear differential equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

Mehrdad T. Manzari and Majid T. Manzari

Using a non‐Fourier heat conduction (NFHC) hypothesis, the governing equations of thermal wave propagation are established. The resulting differential equations are…

Abstract

Using a non‐Fourier heat conduction (NFHC) hypothesis, the governing equations of thermal wave propagation are established. The resulting differential equations are transformed to integral forms using the Galerkin weighted residual method and then are discretized by a finite element technique. The proposed finite element formulation is verified by comparing the results of analytical and numerical solutions to a number of selected 1‐D problems. A couple of 2‐D sample problems are solved and the responses of the system to various input signals are studied. The proposed mixed approach shows superiority to the conventional finite element solution of hyperbolic heat conduction equation, because of the simultaneous determination of heat fluxes and temperature at each nodal point. The mixed approach is also shown to be capable of capturing the sudden temperature jump due to heat pulses.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

M. Moshiri, M.T. Manzari, S.K. Hannani and A. Rasouli

In this paper, the flow of multiphase fluids in a one-dimensional homogeneous porous media involving the gravity effects is numerically studied using the dominant wave…

Abstract

Purpose

In this paper, the flow of multiphase fluids in a one-dimensional homogeneous porous media involving the gravity effects is numerically studied using the dominant wave method. The paper aims to discuss these issues.

Design/methodology/approach

The numerical scheme used for solving the pressure equations, obtained for the black-oil model, is a backward Euler scheme while the hyperbolic mass conservation equations, derived for both black-oil and Buckley-Leverett models, are solved using the dominant wave method. Higher-order schemes are achieved using either variable derivatives along with the minmod limiter or a MUSCL type interface construction scheme using the Fromm's limiter. The mass conservation equations are solved using the first-order forward Euler method in time. Harten's entropy correction procedure is employed to avoid non-physical expansion shocks.

Findings

It was found that the dominant wave method can accurately solve multiphase flow equations involving gravity effects. Numerical experiments also show that both minmod and Fromm's limiters can be successfully used to construct higher-order schemes while the minmod limiter gives slightly more diffuse solutions.

Research limitations/implications

The flow models considered here include two- and three-phase Buckley-Leverett and the black-oil models and the capillary effects are neglected.

Practical implications

The proposed scheme can be efficiently used for solving problems involving non-convex flux functions especially those experienced during gravity drainage process in hydrocarbon reservoirs.

Originality/value

To the best of authors knowledge, this is the first time that the dominant wave method has been used to tackle multiphase flow problems involving gravity effect.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

G.M. Deheri, P.I. Andharia and R.M. Patel

The effect of longitudinal surface roughness on the behaviour of slider bearing with squeeze film formed by a magnetic fluid has been analysed. The roughness of the…

Abstract

The effect of longitudinal surface roughness on the behaviour of slider bearing with squeeze film formed by a magnetic fluid has been analysed. The roughness of the bearing surface is modelled by stochastic random variable with non‐zero mean, variance and skewness. The concerned Reynolds' equation is stochastically averaged with respect to the random roughness parameter. Results for bearing performance characteristics such as load carrying capacity of the bearing, centre of pressure, frictional force and coefficient of friction for different values of α (mean), σ (standard deviation) and ε (measure of symmetry) are numerically computed. In order to investigate the quantitative effect of roughness on the performance characteristics, four shapes namely; plane slider, exponential slider, hyperbolic slider and secant slider for the lubricant film are considered. The results are presented in tabular form as well as graphically. It is observed that the bearing performance is significantly affected by all the three parameters characterizing the surface roughness.

Details

Industrial Lubrication and Tribology, vol. 56 no. 3
Type: Research Article
ISSN: 0036-8792

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Article

Mohammad Mortezazadeh and Liangzhu (Leon) Wang

The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.

Abstract

Purpose

The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.

Design/methodology/approach

The semi-Lagrangian-based solvers are typically PB, i.e. semi-Lagrangian pressure-based (SLPB) solvers, where a Poisson equation is solved for obtaining the pressure field and ensuring a divergence-free flow field. As an elliptic-type equation, the Poisson equation often relies on an iterative solution, so it can create a challenge of parallel computing and a bottleneck of computing speed. This study proposes a new DB semi-Lagrangian method, i.e. the semi-Lagrangian artificial compressibility (SLAC), which replaces the Poisson equation by a hyperbolic continuity equation with an added artificial compressibility (AC) term, so a time-marching solution is possible. Without the Poisson equation, the proposed SLAC solver is faster, particularly for the cases with more computational cells, and better suited for parallel computing.

Findings

The study compares the accuracy and the computing speeds of both SLPB and SLAC solvers for the lid-driven cavity flow and the step-flow problems. It shows that the proposed SLAC solver is able to achieve the same results as the SLPB, whereas with a 3.03 times speed up before using the OpenMP parallelization and a 3.35 times speed up for the large grid number case (512 × 512) after the parallelization. The speed up can be improved further for larger cases because of increasing the condition number of the coefficient matrixes of the Poisson equation.

Originality/value

This paper proposes a method of avoiding solving the Poisson equation, a typical computing bottleneck for semi-Lagrangian-based fluid solvers by converting the conventional PB solver (SLPB) to the DB solver (SLAC) through the addition of the AC term. The method simplifies and facilitates the parallelization process of semi-Lagrangian-based fluid solvers for modern HPC infrastructures, such as OpenMP and GPU computing.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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