Individual and overall coefficients of heat transfer

At first sight, equation 9.1 implies that the relationship between Q and AT is linear. Whereas this is approximately so over limited ranges of temj ature difference for which U is nearly constant, in practice U may well be influenced both by the temperauire difference and by the absolute value of the temperatures. 

If it is required to know the area needed for the transfer of heat at a specified rate, the temperature difference AT, and the value of the overall heat-transfer coefficient must be known. Thus the calculation of the value of U is a key requirement in any design probleni in which heating or cooling is involved. A large part of the study of heat transfer is therefore devoted to the evaluation of this coefficient. 

The value of the coefficient will depend on the mechanism by which heat is transferred, on the fluid dynamics of both the heated and the cooled fluids, on tine prcq)erties of the materials through which the heat must pass, and on the geometry of the fluid paths. In solids, heat is normally transferred by conduction some materials such as metds have a high thermal conductivity, whilst others such as cer unics have a low conductivity. Transparent solids like glass also transmit radiant energy particularly in the visible part of the spectrum. 

If heat is being transferred through three media, each of area A, and individual coefficients for each of the media are h, hi, and /13, and the corresponding tem rature changes are AT, ATi, and AT2 then, provided that there is no accumulation of heat in the media, the heat transfer rate Q will be the same through each. Three equations, analogous to equation 9.1 can therefore be written  

The reciprocals of the heat transfer coefficients are resistances, and equation 9.6 therefore illustrates that the resistances are additive. 

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