Determination of wall decay times by use of a polynomial equation

Urbikain, M. Karmele; Davies, M.G.

doi:10.1016/j.ijheatmasstransfer.2010.04.019

Cited by 7 publications

(3 citation statements)

References 3 publications

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“…Essentially three approaches have been taken to deriving CTF data and these differ in their robustness, computational burden and accuracy [18]. These approaches can be classed as Frequency Domain [9,21,22], Time Domain [23][24][25][26][27] and State-space [28][29][30] formulations. The original frequency domain approach was to use Laplace transforms for multi-layer constructions and search for the roots of the hyperbolic characteristic function using a 'direct root-finding method'.…”

Section: Response Factor Methodsmentioning

confidence: 99%

“…The formulation by Singh and Bhadauria allows steps of varying size but retains second order accuracy [44]. For the current time step size, ∆t n and previous time step size, ∆t n−1 , the temporal differential is approximated according to, (27) where T n−1 and T n−2 are the temperatures at the two previous time steps. In the case of thermally massive structures increasing the time step allows the total number of steps required to be reduced by at least two orders of magnitude compared to using one that is fixed.…”

Section: Numerical Conduction Modelmentioning

confidence: 99%

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A numerical implementation of the Dynamic Thermal Network method for long time series simulation of conduction in multi-dimensional non-homogeneous solids

Rees

Fan

2013

International Journal of Heat and Mass Transfer

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Article:Rees, SJ orcid.org/0000-0003- 4869-1632 andFan, D (2013) A numerical implementation of the Dynamic Thermal Network method for long time series simulation of conduction in multi-dimensional non-homogeneous solids. ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.A numerical implementation of the Dynamic Thermal Network method for long time series simulation of conduction in multi-dimensional non-homogeneous solids AbstractThe Dynamic Thermal Network (DTN) approach to the modelling of transient conduction was conceived by Claesson (1999Claesson ( , 2003 as an extension of the network representation of steady-state conduction processes. The method is well suited to the simulation of building fabric components such as framed walls and thermally massive structures such as basements but can also be applied to the long timescale simulation of other conduction problems. The theoretical basis of the method and its discretized form is outlined in this paper and a new numerical procedure for the calculation of the necessary weighting factor data is presented. Such data has previously been generated for three-dimensional bodies by a heuristic process of blending analytical solutions and numerical data. The numerical approach reported here has the advantage of accommodating parametric representations of multi-dimensional geometries and allows the data to be produced in an automated fashion and so more easily incorporated into simulation tools. Enhancements to the data reduction procedure and a generalised approach to representing complex boundary conditions are also presented. The numerical procedure has been validated by a series of comparisons with analytical conduction heat transfer solutions and discretization errors were found to be acceptably small. Compared to numerical methods, calculations using the DTN method were found to be up to four orders of magnitude quicker but with comparable accuracy.

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