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148    Cha pte r  F o u r

                   Van de Braak et al. (1998) considered the slow response caused by
               a large thermal mass to be a significant disadvantage; a slow response
               time may mean that ventilation during the day will be required.
               Moreover, on sunny days, the temperature is more difficult to control
               because of the relatively fast changes that occur in the radiant thermal
               load compared to the rate of cooling of the soil (Hanan 1998). In
               warm-water distribution systems, the control of the heating system is
               conducted based on simple parameters such as temperature (Bailey
               1985), solar radiation (Calvert and Slack 1975), or based on the simu-
               lation of the energy flow in the greenhouse (Duncan et al. 1981; Fuller
               et al. 1987). Different authors have developed and studied models of
               localized heating systems for growing substrates. Some of these models
               apply warm air (Boulard et al. 1989; Kurpaska and Slipek 1996), warm
               water (Ahmed et al. 1983; Kurpaska and Slipek 2000), or electric
               cables (Rikbost et al. 1975; de la Plaza et al. 1999; Rodriguez et al.
               2004; Fernandez et al. 2005a, 2005b).
                   The aim of all these models is to supply heat to the substrate in
               order to achieve the temperature required for appropriate plant
               growth. To quantify the amount of heat that must be supplied for
               adequate substrate heating, the use of heat needs to be known. The
               amount of heat supplied to the substrate depends on many external
               factors (Kurpaska and Slipek 2000), among which are (1) type and
               physical conditions of the greenhouse substrate, (2) room tempera-
               ture inside the facilities, (3) technical parameters and type of soil-
               heating system, and (4) properties and characteristics of use of the
               materials used, such as flow rate and water temperature, etc.
                   Many authors have been concerned with these types of heating
               systems, mainly warm-water heating systems, but also with electric-
               cable heating systems. Electric-cable heating provides great opportu-
               nities for greenhouse soil heating. Currently, other systems show
               cheaper operating costs. However, this drawback is largely offset by
               the following advantages: simplicity and low cost of initial installa-
               tion, low costs of system maintenance, easy and comfortable handling,
               clean use, and high flexibility of the control functions. Moreover,
               growers can obtain an efficient use of electric energy by directly heat-
               ing the growing substrate (Rodriguez et al. 2006), or by including a
               heat accumulator that allows for heat-energy storage during the
               hours when electric energy is cheaper (de la Plaza et al. 1999).


          4.5  Models for Predicting Temperature
                 in Heated Substrates
               As discussed earlier in the chapter, many models have been designed
               to predict soil temperature under natural conditions. Yet such models
               do not enable the introduction of the heat supplied by the heating
               system, and they do not consider the effects of the heat supplied.
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