CHAPTER 3
PREDICTIVE THERMAL MODELING W.A. LOTENS
CONTENTS SUMMARY
SUMMARY
The various kinds of predictive thermal models are classified according to the calculation steps involved, in the chain: environment - skin heat transfer - physiological strain - performance. Each class of model is discussed, including validity and differences between representative examples.
Key Words: thermoregulation, mathematical model, mass and heat transfer, clothing, thermal physiology, performance criteria, thermal sensation
1. INTRODUCTION
It was perhaps Burton in 1934 who first published a mathematical model to predict temperature response. Many models have been developed ever since at an exponentially growing rate. Only few of those have been put into use by people other than the authors, for various reasons. Lack of understanding, lack of confidence, lack of input data and lack of ready-to-use program files are probably the main reasons. It is the purpose of this chapter to touch on various models, explain the context and differences and to go into some more detail regarding the most popular models, in an attempt to remove some of the obstacles mentioned.
The general scheme of Fig. 1 may serve as a means for classification of the various models. In this scheme, the environmental conditions are related to operational performance by means of a long process that starts with the heat exchange between the skin and the environment. This is in fact pure physics, but by no means a static process. The heat and moisture transfer depends on the ventilation due to motion and wind, the properties of the clothing change with wetting of the clothing, and, due to posture and behaviour, the exposed surface area may change.
Fig. 1 A general scheme of calculation steps to relate environmental conditions to operational performance.
The next step, from skin to physiological strain, is partly physical and for a large part physiological. In the tissue of the body, heat is transferred by conduction and circulatory convection. The heat flow is controlled by the physiological processes of sweating, shivering, vasomotor action and metabolic heat production. The latter depends on the work load evolving from the task and the impeding effect of the clothing. The resulting effect of the physiological system is called the physiological strain. Physiological strain is not represented by a unique parameter, but rather shows itself in many more or less related variables such as
heart rate, blood pressure, sweat production, body temperature, metabolic waste products, etc. The main physiological system involved is probably the circulation, including body fluids, but the nervous system (pain, muscle control) is important as well.
In the third step in Fig. 1 the physiological strain, or better the spare capacity in the physiological system, is used as a criterion to decide whether a task can still be continued. In general, the strain will increase in the course of time until the maximum of the individual is reached. The maximum is dependent on the individual's state of acclimatization, fitness and various other factors of minor importance. Mental aspects play a role as well. Due to motivation, the performance may be kept level until it breaks down completely. With less motivation the performance will decrease gradually.
The various existing models may be classified according to the calculation steps involved. Some do one step only, some take two or more, either implicitly or explicitly. Some are mechanistic, taking an engineering view on the matter. Others do not deal with the processes that are going on, but relate results to input conditions in an empirical approach. In the next sections, this classification will be made, but first a few remarks on models in general.
Considerations in modeling
Models increase in value when they take verifiable steps. Verifiable means in this respect that the results can be checked with experimental methods, methods that preferably do not require difficult techniques like invasive measurements. Some investigators may have access to the required facilities, but the majority do not and consequently difficult-to-check models will otherwise be of disputable value for many potential users. The argument for verifiable steps demands a block building concept of models. Any block should deal with a single or a few coupled variables only and have a clearly defined interface of input and output variables. Another advantage is that blocks of various models may be coupled and give room for investigators to play with them.
A related topic is the availability of input data. Any model will require input data, at least about the environmental conditions, the clothing and the activity. Some require many more parameters, dealing with the shape and thermal properties of the body and with physiological control functions. A model can run only when all input parameters are available. In default of actual measured values, literature or even estimated values have to be used. These are usually provided by the author of the model. It is tempting, however to fit the model to experimental data by changing those parameter values in the expectation that the model will be improved. What it really boils down to is that a different model has been used and moreover, it becomes a one shot model, for just one experiment. If every investigator acts this way, chaos results in the literature, if not in his own archives. The utmost care has to be exercised in this matter.
Few authors will claim that their model is close to reality. In fact, it is rather a mathematical description of observed phenomena than a representation of the real process.
However, the assumption underlying the model, together with the fit of the data give confidence to interpolations and some extrapolation. The non-expert user of the model is not
might be well outside the validity range. Moreover, he will probably believe that the results are as good as reality. It is advisable, therefore, to accompany a model with a definition of the validity domain and the level of validation. A typical correct use of a model would be the estimation of the range of conditions for an experiment.
Types of models
The various types of models will be classified according to the included steps, referring to Fig. 1. Class 1-2 are the models dealing with the physics of clothing only. Class 2-3 are the purely physiological models and class 3-4 the performance criteria. Models that do not make the separation between physics and physiology, jumping directly from environment to physiological strain are data regression models (class 1-3). Models that use the skin condition to predict performance are relatively rare, but thermal sensation models fall into this class (2-4). Models that predict performance directly from the environmental conditions, without clear steps in between, are unknown to the author.
The mentioned classes will be discussed in more detail in the following sections. It must be emphasized that this is not a complete inventory of existing models, however.