SOME STUDIES ON HEAT AND MASS TRANSFER THROUGH BUILDINGS BY ANALYTICAL ANALOGUE AND COMPUTATIONAL METHODS

Abstract

In tropical countries like India, the problems of heat and mass transfer through buildings assumes great importance especially due to wide diurnal and seasonal variations of weather elements. This thesis is mainly concerned with pro viding solutions to problems of heat transfer through buildings under natural boundary conditions by analytical, analogue and digital computational methods and also on the interaction be tween heat and mass transfer processes. The work reported in this thesis is conveniently divided into nine chapters each dealing with a specific aspect. The introductary chapter covers the basic mechanism of heat transfer,combined heat and mass transfer through building elements and the heat exchange phenomenon at the boundaries. A critical review of the computational methods which in clude analytical and numerical methods of solving heat transfer problems of buildings has been presented in chapter two. A system function approach based on Matrix method for deriving the essential thermal characteristics of homogeneous and multi layer building elements, has been introduced and dis cussed in chapter three. Chapter four deals with the application aspects of thermal system functions for the prediction of thermal behaviour of un conditioned and conditioned buildings under natural exposure conditions. Precise methods developed for the estimation of heating and cooling loads and temperature swings in enclosed spaces have been presented. An improved method which removes the limitations of the existing methods and permits the deter mining of the temperature variations within individual rooms of any large multiroomed building has been evolved. Anelectrical analogue technique, employing resistance capacitance, lumped parameter passive network for solving one and two dimensional heat flow problems through slabs and hollow panels or blocks, has been described with illustrative examples in chapter five. Mathematical expressions for thermal transient charac teristics as defined by delay and rise times of any single or multilayered building section based on Eleraore's definitions have been derived in Chapter six. These expressions have also been validated by a comparison of the results obtained from the step response method. Generalised system function Laplace transform polynomials have been formulated for building, sections of any number of layers. Methods for obtaining time response factors for step, triangular pulse and sinusoidal excitations and system response for any arbitrary temperature wave form, have been described in chapter seven. In chapter eight, temperature gradient functions have been derived for the determination of space time distribution of tem perature in thick slabs under periodically varying exposure con ditions. Their application to thermal stress problems have also been dealt with. 1)1 The complex problem of combined heat and mass transfer in building elements under naturally occuring boundary condi tions has been stated. The mathematical formulation of the problem and its simulation on an electrical R-C network ana logue has been discussed in chapter nine. A number of digital computer programs developed on the basis of the mathematical models derived in the thesis are included in the appendix. The methods described in this thesis provide a basis for reliable and accurate prediction of temperature variations in enclosed spaces of single or multiroomed buildings. This method can also be used in studying the effect of various design, climatic and utilization factors on indoor air temperatures and air conditioning loads. The analogue method used for the study of one and two dimensional heat flow problems can further be extended to solve problems of design of hollow bricks and blocks from thermal considerations. The modified definitions of thermal delay and rise times eleminate the tedious process of extracting all the roots of system function polynomials and to construct the complete transient response. The thermal gradient functions evolved provide an exact method of finding space, time distribution and the resultant thermal stress in thick slabs. The problem of combined heat and mass transfer can be studied by analogue techniques with special reference to the effect of moisture in porous bodies. 11/ The subject matter of the following chapters have been published and the available reprints of the papers are atta ched at the end. Chapter -III t Digital Computer Determination of Thermal Frequency Response of Building Sections*. Bldg. Sc. 1, 299-307. 1966. Chapter - IV •Thermal Performance Rating and Classification of Roof Sections*. Bldg. Digest 94, CBRI,Roorkee, India. •Thermal Performance Rating and classification of Walls* Bldg. Digest 101, CBRI, Roorkee, India. •Application of Thermal System Functions in Predicting Thermal Behaviour of Buildings1. Proc. 14th Cong. 1STAM, Kurukshetra, 1969. «A Computer programme for the Calculation of Indtoldual Room Air Temperature of Multi-roomed Buildings1. 1st Syra. on the use of Computers for Environmental Engg. related to Buildings. Buld. Sc. Series 39, NBS, Washington, 1970