M.G. Davies

WALL TRANSIENT HEAT FLOW USING TIME-DOMAIN ANALYSIS

Abstract If values of ambient temperature and room temperature are known at hourly intervals, the heat flow to or from the room at some specified time can be computed in terms of the values of recent temperatures and heat flows, weighted by values of a series of N wall transfer coefficients, bk, or ck, and dk, (k = 0 to N). These coefficients have hitherto been found by frequency domain methods. It is shown here that they can be evaluated using elementary time domain solutions for wall heat flow. A multi-layer wall with surface films representing radiant and convective exchange is discussed. Using suitable transmission matrices, solutions for the steady-progressive and transient temperature profiles through the wall are derived. The value of N and the wall dk values follow immediately from the wall decay times of the transient solution, together with the choice of 1 hour as time interval. Using a development of Fourier analysis, the steady-progressive and transient solutions are combined so as to provide the time-domain solution for the response to an imposed ramp in ambient or room temperature. Combination of three such ramps forms a triangular temperature pulse of excitation and the infinite series of wall response factors—hourly values of heat flow at and after the temperature peak—serve to describe the response of the wall when excited by such a pulse. The values of bk and ck follow from the response factors. The procedure is illustrated numerically.

The thermal admittance of layered walls

Abstract A procedure is developed for computing thermal admittance, the ratio of the sinusoidal component of heat flux at the surface of some building construction to the corresponding temperature variation there. A chart and tables are presented to enable computation of the change of admittance which results when a layer (or an air film) is added to some pre-existing construction of known admittance.

Qualitative Comparison of North American and U.K. Cooling Load Calculation Methods

A qualitative comparison is presented between three current North American and U.K. design cooling load calculation methods. The methods compared are the ASHRAE Heat Balance Method, the Radiant Time Series Method and the Admittance Method, used in the U.K. The methods are compared and contrasted in terms of their overall structure. In order to generate the values of the 24 hourly cooling loads, comparison was also made in terms of the processing of the input data and the solution of the equations required. Specific comparisons are made between the approximations used by the three calculation methods to model some of the principal heat transfer mechanisms. Conclusions are drawn regarding the ability of the simplified methods to correctly predict peak-cooling loads compared to the Heat Balance Method predictions. Comment is also made on the potential for developing similar approaches to cooling load calculation in the U.K. and North America in the future.

The thermal response of an enclosure to periodic excitation: The CIBSE approach

Abstract In order to relate the temperatures and heat flows at the surface of a slab when it undergoes sinusoidal excitation, five quantities (conductivity, specific heat, density, thickness and driving period) have to be specified. They can however be reduced to just two groups, (i) the characteristic admittance, a, which has the usual units of thermal transmittance (W/m2K) but also takes account of the fact that heat flows and temperatures are not in phase, and (ii) the cyclic thickness, τ, a non-dimensional form of the thickness of the slab. The slab transmission matrix can be expressed in terms of a and τ, and the overall transmission matrix for a wall, including films, is formed by multiplying the slab matrices. From this, the wall admittance and cyclic transmittance can be found. An example is given. Equations are then developed for the response of an enclosure when subjected to periodic excitation. It is shown that the response of a wall can be expressed exactly in thermal circuit terms, either as a pair of lumped elements (units W/K) (to express admittance), or as three pairs of lumped elements to express two admittances and the cyclic transmittance. The relations between various temperature and heat flows in an enclosure can be shown graphically in the form of vector diagrams. The special status of ventilation in estimating room response is mentioned. These considerations serve to support methods currently advanced in the CIBSE Guide to estimate periodic changes in room temperature.

Optimal designs for star circuits for radiant exchange in a room

Abstract For accurate calculation of the radiation exchange between the surfaces of a room a ‘delta’ network of resistances based on view factor values is used. In design calculations involving building heat transfer, the network is often simplified to a ‘star’ network in which all radiation ‘passes’ through a ‘star’ point. The star point temperature is usually lumped with the room air temperature to yield a room index temperature. This article is concerned with finding the values for the radiation star resistances. Optimal values are arrived at by minimising the difference between the responses of the exact delta network and of the star network. Three bases for the comparison are put forward, one based on surface area, one on view factor considerations and one in which the above dofference is minimised individually for each surface. There is little to choose in performance between the first and second of these methods. The third is much more accurate and a formula is supplied to size the resistance. Current design techniques which involve U values and their dynamic equivalents derive from a thermal model where the radiation transfer in star from is lumped with the convective exchange and the index temperature so formed is regarded as room temperature. This index temperature is compared with estimates of the mean temperature of a sensor placed within a simple enclosure as it responds to heat input either at the walls of the enclosure or within the enclosure itself. Significant differences are noted.

Optimum design of resistance and capacitance elements in modelling a sinusoidally excited building wall

Abstract A procedure is described to calculate the optimum values of the lumped elements of a T section ladder network which models a multilayer one-dimensional building wall or roof when subjected to sinusoidal excitation. The transmission matrices of the real wall and a chain of simple T sections (1, 2, 3 or 4 units) are evaluated and the T section elements are systematically varied so as to minimise the sums of squares of the differences between the corresponding pairs of the 4 vector elements in the 2 matrices. For a thin wall this procedure is demonstrated analytically for up to 3 sections. The sum of squares is proportional to the fourth power of the slab thickness. Tables are provided of the optimum values for the elements of a homogeneous slab when represented by 1–4 T sections. The investigation is extended to a homogeneous slab flanked by equal and unequal surface films, and the possibility of a degenerate solution for a thin slab is demonstrated. Finally, the case of an entire wall construction is discussed; of a group of 29 walls and roofs, most can be satisfactorily modelled by a 3 T section network consisting of 6 lumped elements. Exact modelling may be possible.

Heat loss from a solid ground floor

Abstract Heat losses from solid uninulated ground floors are often calculated using Maceys formula which involves the floor length and breadth, and the thickness of the wall surrounding it. The origins of the formula are examined. It is shown that in deriving it, an assumption is implicitly made that a semi-circular section of the floor beneath the wall is composed of perfectly insulating material. Further, the adjustment which is used to make the formula apply to a floor of finite length leads to an internally inconsistent expression. Procedures are advanced that tend to correct for both these defects. An exact expression has been advanced by Delsante, Stokes and Walsh against which five simplified forms can be tested and one of them is compact and provides 1% accuracy.

Room heat needs in relation to comfort temperature: Simplified calculation methods

Definitions are set up of local and space-averaged air and radiant temperatures and certain derived temperatures, together with the conductances that are needed to estimate building heat needs. Expressions are derived for the radiant and convective heat inputs Q r and Q a which are needed to establish a particular value of comfort temperature; they are given for each of three models for room internal heat exchange. They are easy to derive and simple to state. The method currently advanced in the CIBSE Guide (Section A5) to compute these needs is summarised: quite apart from the fundamental flaws in its basis, its exposition is more protracted and convoluted than is necessary.

A thermal circuit for radiant exchange

Abstract The radiant heat exchange in an enclosure can be expressed using a circuit approach. It distinguishes between the separate effects of enclosure geometry and surface emissivity. By a simple linearisation of the thermal driving force, the radiant exchange conductances can be expressed in the same units as those describing convective, conductive and ventilation heat exchanges.

On the basis of the environmental temperature procedure

Abstract The procedure advanced by Danter and developed by Loudon at the Building Research Establishment, Watford, represents a major improvement in the means available to the building services engineer and architect to estimate the thermal response of some part of a building. This paper re-examines its basis. The twin roles of radiation and convection as means of transferring heat within an enclosure are first discussed. The concept of a single representative temperature to describe heat loss from the enclosure, the conductances between this central temperature and its several constituents, and the possibility of taking all heat to be input at this temperature are introduced step-by-step. It is then shown that in an enclosure so idealised to entail two surface and one air temperature, these conductances appear simultaneously by a delta to star transformation of the physical conductances, and that the star temperature tec so introduced is an overall measure of the enclosure temperature without an internal heat source. The environmental temperature tei calculated by equation (A5.18) of the IHVE 1970 Guide is shown to be nearly equal to the duly weighted combination of tec and the temperature thb of a suitable hot body source of heat contained within the enclosure. tei thus serves as the temperature at which this heat can be considered to be input, and from which it is lost by conduction through the fabric or by ventilation. If the heat is input by some other source (such as a convector) it may be convenient to scale it to make it equivalent to an input at tei. Account can be taken of periodic variation in an internal source by including the admittance of the wall construction in a manner formally similar to the steady state transmittance of the wall.