Notes on Non-Steady-State Heat Flow in Walls and Roofs

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Publisher’s version / Version de l'éditeur:

Technical Note (National Research Council of Canada. Division of Building Research), 1958-05-01

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NATIONAL RESEARCH COUNCIL OF CANADA

DIVISION OF BUILDING RESEARCH

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NOTJE

No. 251

NOT FOR PUBLICATION

PREPARED BY D.G.stephenson _CHECKED _BY _A.G.W.

FOR INTERNAL USE

APPROVED BY N.D.H.

PREPARED FOR

n. c.

Haychuu0JlUrit Con'i;J:'ul Building

Rosearch Institute. India. DATE lTay 1958

SUBJECT _notes _{on non-s'teody-state heat}

i'loVi _{in walls and} _roofs

The best method of solution for a non-stcac1_;y'-statc

heat floVi problom depends on the da.lca unO. the gua:u-aty t'lhlch nust be calculated. ｾｾ･ tollowing table Gives ono way of

classifyiTlG tho problems and a sugGested method ai' solution.

2. Calculation of instan-tanoous heat flux across any plano in a rwll ｜ＧＭｖｬｬｃｾｾｬ

inside and outsido tempercltures aro specified.

Description of Problem

and Iklta

1. Oalculation of instan-taneous heating or cooli116 load villen outside conditions oro specified.

- Surface heat "transfer cocff'iclents are constm1"t, hea.t l'loi': 0110 Ciimcnsion['ll,

temperature variation is periodic.

- Surface heat transfer

coefficients oro constant,

heat flow one diuwnsional, temperature variation now periodic.

- Surface heat tronsfcr cocff'iciellts ere variable, heat f'loH one dirJcl'lsional.

Suggosted l:lothod of' Solution

Use thermol circuit approach and either onalogue or digi-tal computer.

I.;.atrix Nethod

(outlined in DBR Report 132.)

or ReGponse Factor rJcthod (reference 9)

Response Factor tlothod

ProlJlems arc nOV"l linear emu fillst be solved for specific oond1 tiono. A ｬｬｗｾｃｬﾷｩｯＺＮｬＱ )'lc<.llOd

is usually ｢ｯｾＺｲＨ［Ｎ Vm: o·r' Lio'bL:ann

E'.nnlo,:;uc OJ: n ｣ｊｩＨｾｩＭｌ｣Ｚｬ GOi;:yULQ:t'

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-- 2 ..

For walls made up

ot

_{homogeneous layers the matrix} elements or response faotors can be oaloulated in a straight-forward way but the arithmetio mllY be oonsiderable. However, for oonstruotions oontaining oavities, studs, eto., it is

diffioult to oalculate an aocurate non-steady-state heat flux. For walls of this type it is proposed to caloulate the response factors from the results of tests done With the Wall Panel

Test Unit. The measured valves of temperatures and hea't"flows for N consecu"tiva hours oan be used jco form N equations oontaining

Nunknown response factors and the response faotors oan be found

by solving the set of simultaneous algebraio equations. When a oavity wall must be represented in a ｴｨ･ｾ｡ｬ

cirouit 'the equivalent resistanoe-oapacitanoe network is

required. To find a good representation it would be possible to first 'determine the thermal impedanoes of the wall with the Wall Panel Test Unit and then oaloulate the resistanoe-capaoi-tance network which would simulate the test wall. We have no1;

as yet carried out these measurements with the Wall Panel Test

Unit since the equlpnent has just come into servioe.

Studies to determine the sol-air temperature ｾｯｲ different walls with different orientations form a part of our general

program on heat flow through walls. For this the solar

radiation on vertical surfaces is reoorded along with air tem-perature and wind speed and direction. DBR Internal Report No. 121 is 'the most reoent note on this phase

ot

_{-the work.}

The following list of referenoes is oertainly not exhaustive but 'they may be useful.

(1) New eleotrical analog method for solution of transient heat-oonduction problems by G. Liebmann. Amor. Soc. o! Mech. Engineers, Transactions, V. 78, n.3, April 1956, p.655-665.

(2) Solution of transient heat-transfer problems by resistanoe-, network analog method by G. Liebmann. ａｭ･ｾＮ Soo. of Mech. Engineers, Transactions, V. 78, n.6, August 1956,

p.1267-1272. .

(3) An iterative analogue computer for use with resistance network analogues by 1.0. Hutcheon. Eritish Journal of Applied ｾｬｙｳｩ｣ｓｴ Vol. 8, 1957, p.370.

(4) Limits of accuracy of electrical analog circuits used in solution of transient heat conduction problems by

E.O.P. Klein, Y.S. Toulouldan and J.R. Eaton. Amer. SOOt

of Mech. Engineers, paper 52-A-65.

The transient flow of heat through a two-layer ,wall by

M.V. Griffith and G.K. Horton. Proc. PhYs. SOOt London, V. 58, pt.4, n.;28, July 1946, p.48l.

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-

.

,

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-(6) Matrix analysis of heat 'transfer problems by L.A. Pipes. Journal of Franklin Inst1tute, Vol. 263, n.3, March

1957, p.l95.

(7) The calculation of temperatures· inside buildings having variable external conditions by R. W. Muncey. Australian

Journal of Applied Science, 1953, Vol. 4, #4, p.la9.

(8) calculation of temperature rise with intermittent heating by R.W. 14uncey. Australian Journal of Applied Scienoe,

, 1956, Vol.

7,

#1, p.29.

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Heat load oalculations by thermal response by W.R. Br1sken and S.G. Reque. Amor. Soc. of Heating and Mr-Conditio Engineers, Transactions, Vol. 62, 1956, p.39l.

(10) Oircuit analysis applied to load estimating by H.B. Wottage and G.V. Parmelee. Amer. Soo. of Heating and Ventilating

Engineers, Transactions, Vol. 60, 1954, p.59.

(11) A method of oomputing the transient temperature of thick walls from arbitrar.y variation of adiabatio-wall tempera-ture and heat-transfer ooefficient, by P.R. Hill. National Advisory Committee for Aeronaut1cs, Teohnioal Note 4105. ｾ

,

(12) llwnerical ana].ysisof heat flow by G.M. Dusinberre. McGraw-' Hill, Bew York, 1949.

,

(13) Conduotion heat transfer by :P•.1. Schneider. Addison-Wesley,