An exponential heat balance integral method

Mosally, F.; Wood, Alastair S.; Al-Fhaid, A. S.

doi:10.1016/s0096-3003(01)00083-2

Cited by 31 publications

(38 citation statements)

References 8 publications

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“…However, there are numerous other possible approximating functions, perhaps the two most standard are the quadratic of Goodman, see Ref. 27, for example, and the exponential approximation of Mosally et al 30 In fact, even in the simple case of the quadratic there are seven different formulations. 29 In Fig.…”

Section: Resultsmentioning

confidence: 99%

Unsteady contact melting of a rectangular cross-section material on a flat plate

2008

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The work in this paper concerns a mathematical model of the contact melting process of a rectangular material in contact with a hot plate. The problem is described by a coupled system of heat equations in the solid and melt layer, fluid flow in the melt, a Stefan condition at the melt interface, and a force balance between the weight of the solid and the fluid pressure. Since the melt layer remains thin throughout the process, we use the lubrication approximation to the fluid equations and assume that the heat flow in the fluid is dominated by conduction across the thin film. In the solid we employ a heat balance integral method. Results show that the film height has initial and final rapid increases, whereas for intermediate times the height slowly increases. The quasisteady state of previous models is never attained: This is shown to be an effect of neglecting the change in mass and conduction in the solid. The previously observed initial infinite velocity of the melt is shown to be a result of the perfect thermal contact assumption. For a water-ice system the melting rate is shown to be approximately linear, this allows us to reduce the problem to solving a single first order differential equation for the liquid layer thickness. The main analysis is carried out in two dimensions, but we briefly highlight the extension to three dimensions. The method is verified by comparison with previously published experimental results on the melting of n-octadecane.

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Section: Resultsmentioning

confidence: 99%

Unsteady contact melting of a rectangular cross-section material on a flat plate

2008

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“…Jet unit technology which injects cold air into the cabin is applied to adjust the cabin temperature distribution 8,9 . The arrangement of jet units is a critical factor for the heat balance of the cabin.…”

Section: Introductionmentioning

confidence: 99%

Heat Balance Research of 3mw Marine Wind Turbine's Engine Room

Kang

Jiang

Zhou

et al. 2012

Int. J. Mod. Phys. Conf. Ser.

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The increment of heat load in Wind Turbine's engine room could cause the system shut down. In this paper the heat balance of Wind Turbine's engine room is investigated according to the structure of the engine room, environmental operating requirements as well as heat-dissipating of different components of a 3MW Wind Turbine System. The heat load of the engine room is analyzed and the physical model is developed based on finite volume method. After that, the temperature distribution of the cabin is obtained under different conditions with/without the jet unit. The temperature distribution in engine compartments with different number and the arrangement of jet units is compared in this paper. Based on the analysis, the cabin cooling design is carried out to achieve the purpose of stopping heat gathering and keeping heat balance of the cabin. This work puts forward the heat balance maintenance and completes the corresponding research, which could be helpful for the optimization of large-capacity Wind Turbine cooling system.

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“…Mosally et al [27] note that many thermal problems have exponentially decaying solutions, and consequently use an exponential form. This performs well for the problem that motivated the choice, however for the melting problem investigated in [35] it is the worst of the choices investigated.…”

Section: Introductionmentioning

confidence: 99%

“…This is not necessarily the same as the liquidsubstrate heat transfer coefficient. The HBI method for boundary condition (i) is considered in [13,27,38,43], but case (ii) with either Q = 0 or h s = 0 is only briefly discussed in [13] and no comparisons are given with a numerical solution.…”

Section: Introductionmentioning

confidence: 99%

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Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems

Mitchell¹,

Myers²

2010

SIAM Rev.

106

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Abstract. The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

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An exponential heat balance integral method

Cited by 31 publications

References 8 publications

Unsteady contact melting of a rectangular cross-section material on a flat plate

Unsteady contact melting of a rectangular cross-section material on a flat plate

Heat Balance Research of 3mw Marine Wind Turbine's Engine Room

Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems

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