in Soil Warming in a Buried

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(1)論. 文. 農業気象(J.Agr.Met.)45(4):217‑226,1990,. Heat. and. Moisture. Circulating. Transfer. Warm. Hirakazu. Water. in Soil Warming in a Buried. SEKI and Tomoaki. by. Pipe. Line. KOMORI. Department of Civil Engineering, Faculty of Technology, Kanazawa University, Kanazawa 920, Japan In ing. warming. warm. were. the water,. predicted were by. empirical. constants.. difference. region. an. soil. as. Tl. around. planning. the. Key. words:. protected and. by. Philip. applying. systematically,. It. was. the. the. of. shown. that. higher, pipe.. warming Heat. and cases. The system. transfer,. of the. and. of. moisture. content. and. deVries'. the. basis. the. rate dry. results. in. a greenhouse.. Moisture. transfer,. model.. of. the. 50•Ž. the. out. of. of. soil. shown. be. potential. here. the. Protected. of and. warm. become. Soil. water several. Tl. , assuming. pipe. finite. becomes. extremely. useful. cultivation,. soil the by. water an. time. of. calculated. within. would. with transport. temperature. limited. circulat-. soil. moisture. were. water. by. the. content,. around. would. and. matric. distributions. and. retentivity. Heat. moisture. content. 40•Ž. water. distributions. and. moisture 30•Ž,. a typical. of. temperature. drying. that. calculated. cultivation. on. function. Temperature for. becomes. soil. the. temperature. approximate. technique. bare. for of. estimated. expressed. larger. bed. theoretically. properties. the. soil changes. narrow. information. on. warming.. キーワード:施設栽培,水分移動,熱移動,土壌加温. for. cultivation.. Shapiro. (1975). investigated. the. 1. Introduction problem. In the regions where it is cold in winter because of low intensity of solar radiation such as Hokuriku district, soil warming is introduced to the protected cultivation in order to prevent an undesirable temperature drop in the soil. In the cultivation of plants, it is not permitted that moisture content falls extremely with warming the soil, since plants become unable to grow if the moisture content of the soil falls below the wilting point. Accordingly, in planning the operation of soil warming, it is important to predict exactly how the temperature and moisture content of the soil vary spatially with time. Several reports (Abdel-Hadi and Mitchel, 1981; Baradi et al., 1981; Radhakrishna et al., 1984) were published regarding the change of moisture content around heat sources buried in the soil, however, these reports were not for the soil bed. of. with. the. warm. the. that. the. at. steady. the. is. profile. Slegel irrigation. the. wheat. for. corn,. large. field.. scale. The. warming the. soil. soil. Among. papers theoretical. warming. the. sub-. prevent. the. These. inves-. cultivation. of. grains. results. such. in. only in. for. the. open. content. similarly. as. obtained. almost. moisture. cultivation, on. to. system. would. 15•Ž.. the. out.. available. soil. than. protected. the. in. bed. protected few. that. decrease. the. drying the. are. the between. greater. culture. so. of. investigated. from. investigations. a very. 217. pipe. zone. moisture. bottom. pipe. the. root. difference. porous. open-field. and. those. the. than. plant. volumetric. is. to. theoretically. the. the. (1977). not. the. the at. soil. heat. lower. in. surface. of. were for. predicted. temperature soil. effect. tigations. been. 15%. Davis. around. in. when. the. waste. becomes. than. in. plant. loam. state. and and. and. a silty. the. transfer. power. content. less. and. but. soil,. for. water. soil. moisture of. moisture point. the. and. field. wilting. content. Read at a Hokuriku Chapter Meeting on 8 October 1986 and Annual Meeting on 26 July 1989 Received December 8, 1988. heat. application. with. occurs. however,. even. there. has. subject. models. for. problems. of. the.

(2) 農. 業. simultaneous, heat and moisture transfer in th soil, a model of Philip and deVries (1959) is the most well known, which is the basis of most of the above referenced papers. It has been pointed out that the model of Philip and deVries does not apply directly to moisture transfer in the regions considerably deeper under the ground and to moisture transfer in extremely clayey soils. 気象 All. the. DTv, of. the. which. osmotic. of ƒ³p. ground such as the soil bed for cultivation. In applying Philip and deVries' model, it is important to estimate the heat and moisture transport pro-. teristic. a. function. that. been. perties properly, however, a tractable estimation procedure of them has not be so fax arranged satisfactorily. From the above view point, a problem of simultaneous heat and moisture transfer in soil warming by the circulation of warm water for the protected cultivation is solved numerically by applying Philip and deVries' model. The transport properties of heat and moisture were estimated systematically by using the mathematical expression of the matric. w. on. soil. water.. be. and. T. in. the to. order. the. soil. to. trans-. estimate ƒ³ theore-. curve. has. moisture. must. in. predict. between. the. soil. functions. well-established relation. the. water, , the. as desirable. Dwl,. functions If. ignored. characteristic. of. DTl,. pure. is. Therefore,. curve. k, are. a. regarded. the. moistute. have. op. and. not. yet. characbeen. deter-. experimentally.. Fig. 1. Schematic illustration of the moisture characteristic curve of soil. moisture. presented of. soil. considered. ing. of. other. of. relatively. occupied. high with. considering p,. free the. the. authors. potential. of temperature. the. the. parts low. adsorptive is. at. (Mitsuno,. express (w). water ƒ³PT0 the. region. primarily 1979).. soil. by. water, the. Then,. characteristics. approximately. T0. flection. content. content. general. be curve. correspond-. to. moisture water. the. capillary. corresponding. many. may. moisture. and. above. it. the is. been. for. and of. separating of. has. sigmoid 1,. region. relatively. part. be. Fig.. whole. One of. involving the. in. parts. region. and. tial. the. PFc).. the. curve to. shown. two. (we, to. mainly. tative. as. that. consists point. characteristic. semi-empirically. types. (1). of. it. of. developed.. The. According to Philip and deVries (1959), transfer of heat and of moisture in the soil are mutually influenced with each other, so that the following differential equations of moisture and heat transfer are given.. (2),. properties,. is,. mined. be. Although. formulation. w,. and. can. may. is,. (1). by. potential. transport. tical. that. Eqs.. approximated. only.. p as. in. potential. be. properties. the. 2. Mechanism of simultaneous heat and moisture transfer in the soil and equations for estimating transport properties. Keff. moisture can. port. properties,. and. water. (Dakshanamurthy and Fredlund, 1981), however, the model would be useful to apply to moisture transfer in relatively shallow regions from the surface to the position at most 1m below the. potential of soil water. Then, from the calculated results of temperature and moisture profiles in the soil, the decrease of moisture content in the soil around warm water pipe is mainly investigated.. transport. Dwv. the at. following. of matric ƒ³. a represenexponen-. functions.. (2). (5). (3). (6). where. (4). where A is an empirical 218. constant. regarding as soil.

(3) H. Seki and T. Komori: Heat and Moisture Transfer in Soil Warming. texture.. Eq.. similar. to. (5). of. Gardner's. applicable. to. a. the. above. two. equation. relatively. equations. (1970),. narrow. which. range. of. is. The. is. expressed. moisture. content. Assuming is of as. 6. that. the. determined only. as. a function. by pointed of. temperature the out. T. and. w. dependence. temperature by. dependence. Philip. and. a. value. of. wi. ƒ³p. tion. and. by. Fig.. by. Using and. Eq.. (7),. all. the. moisture. in. by. following. sively. According conductivity following. the. the. to. Green. of. an. function. transport soil. properties. can. be. of. obtained. the the. types following. heat. at. a. by. was. (8). on. of. to. k may. if. interpola-. ki+1. and of of v. approximately and. The. linear. dependence. w. m>10.. paper. Raudkivi. (8). between. and. is. Eq.. content. dependence be of. k. by ki. a semi-logarithmic. temperature. function. here. values. which. symbol ƒÀ. of. estimated. According. soil,. factor,. a. moisture. temperature of. matching. certain. the. 2.. a. approximation. k. Eq.. is briefly. good. wi+1. since. (7). /kstc. between. from. is. kst here. gives. of. deVries, ƒ³p. ratio. obtained as. U'u k is. governed in. given. shown (1976),. many by. the. T.. succes-. procedure. and. Corey. unsaturated of ƒ³p. (1971), soil. as. illustrated. is. (10) Then, using Eqs. (7) and (10), DTl , Dwl,p wvDTv and pwvDwvdefined by Philip and deVries (1959),. hydraulic given in. by Fig.. the 2.. are. (11) (8) where i = pore class of the soil, m=total number of (12) (13) (14). pore classes, n=mwst/(wst -w1) , ket= measured saturated hydraulic conductivity, and kstc= theoretical saturated hydraulic conductivity defined as follows :. There are several methods for estimating Keff, of which the following equation (Seki and Komori, 1984) that had been slightly simplified the series-. (9). parallel-combined model by Krischer (1963) was used here. (15) where. (16). (17) The foregoing equations, Eqs. (5)-(15), were not obtained through the purely theoretical consideration, so that the several empirical constants, A in Eqs. (5) and (6), i, that is, kst/kstc in Eq. (8) and B in Eq. (15), are involved. Therefore, the constants must be given experimentally in advance. The systematic estimation procedure of transport properties proposed here requires not so many empirical constants, and would be available for. Fig. 2. Relation between hydraulic conductivity and moisture content estimated from Eq. (8) proposed by Green and Corey.. practical calculation of heat and moisture transfer in the soil. 219.

(4) 農. 3. A problem of simultaneous moisture. 業. heat and. transfer in soil warming. Suppose that the pipes for soil warming are arranged within the soil bed in a greenhouse at a constant depth a below the surface of the soil with an equal space p as shown in Fig. 3.. 気象 (7) The temperature and moisture content are uniform initially. Upon these assumptions, a mathematical treatment of this problem may be defined only for the region indicated by //// in Fig. 3. The differential equations for w and T are. (18). (19) Fig. 3.. Schematic rangement analysis. representation and the region of heat. and moisture. of the defined. The. pipe arfor the. boundary. are. heat. surface.. transfer.. the. In the soil warming system, flow rate of water circulated in the pipe is usually set large enough to make the temperature difference of water between the inlet and outlet of the pipe as small as possible. Therefore, a two dimensional analysis with respect to the soil profile perpendicular to the pipes may be available to give a good approximation of the temperature and moisture content distributions in the soil. In treating the problem mathematically, the following several assumptions for simplification are made.. conditions. and. and. given.. Moreover, also. to. at. assumptions. of. and. at. the. at. the. the. pipe. both. soil (6),. the. are. soil. easily. conditions. account. the. soil. and. of. boundary. taking. w. of. (5). bottom. of. other. easily,. T. the. surface the. surface equations. at. the. given. metry. the. conditions. profile. the. balance. According. boundary. are. at. moisture. of sides. the. of. sym-. the. soil. profile. Since. Eqs.. tions,. it. tions. of. is. (18). T. and. temperature the. soil as. (1) The soil does not shrink during the soil warming process, and 1d is held constant.. tions. and. (2) The hysteresis in the relation between op and w is not taken into account because the soil warming is related to the drying process only,. equations,. (3) A bare soil is assumed here, and the effect of suction of water in the plant root zone can be ignored.. the. (4) Since the difference of Tl between the inlet and outlet of the pipe is relatively small under the usual operating conditions of soil warming, Tl is regarded to be constant approximately.. numerical. the. is. divided Fig.. boundary. w. the. is. Physical. basic. cultivation reference previously. 220. into. grid of Ti. value. be of. equa-. difference-form-. values. to. square. rewritten. individual. the. account. properties. operating. and. of. differential. increment. initial. the. and. wi. .. In. of ‡™ƒÆ against. 0.1(‡™z)2/k the. points time ‡™ƒÆ. ‡™z or 0.1. stability. of. the. solutions.. 4.. (6) Thermal resistance at the interface between the warm water pipe and soil can be ignored.. number. the. the. determined. taking. calculating. are. small. calculation,. or ‡™x. The. at. solu-. distributions,. the. Using. every from. (‡™x)2/k,. a. and. conditions. and. numerical. in. into 4,. equa-. analytical. content. forms. T. non-linear. the. Therefore,. in. calculated. are. moisture. shown. successively. (5) The temperature and moisture content at the bottom of the soil profile are held constant during the soil warming process.. obtain. profile. difference. are. (19). to w ,. and. parts. and. difficult. Miyazaki,. physical are to. of. the. soil. and. conditions. properties. assumed the. (Maeda 1979).. as. shown. experimental and. the. in. Table. results. Matsuo, Based. of. 1974; on. the. soil. 1 with reported. Kasubuchi basic. for. physical.

(5) H. Seki and T. Komori;. Heat. and Moisture. properties, heat and moisture transport properties of the soil were estimated from Eqs. (5)-(17). Several empirical constants necessary for estimation of the transport properties are shown in Table 2. The value of A was determined so that the curve expressed by Eqs. (5) and (6) coincides the. vation.. primary and permanent wilting points and the point of field capacity for the soil for cultivation of typical in Japan (SAMJ, 1986). Fig. 5 shows the calculated results of pF againts w and the experimental results by the thermocouple psychrometer (Wescor, HR-33T) for a sample soil for culti-. rated. extent,. relatively. The. ,. value. ft. cal. Specifications. of the. pipe. Eq.. (15). sample. constants,. was. A. Keff. to condition. container.. For The. hydraulic. k,. be. available. from. and. satu-. The. value. measured. conductivity test 0.0315 of. falling. with the densely. order. of. a. were. slight. sample. soil packed. magnitude of. Using Dw. of. by. the. m/hr. DT. the. the. the. conductivity. 10-1-10-2 Keff,. experimental. from. 0.0032. smaller.. are. conditions.. permeability. packing. to. results. both. hydraulic. by. scattered. estimated. under. estimated. saturated. the. would. was. dried. becomes saturated kst. of. from in. with of. in. soil. varies. the. B. are. calculated. agreement value. was. the. difference a. good. completely. which. sample. head,. results the. results. of. the. sample. 1. of. and. of ƒÀ. experimental. the. experimental. of. Table. and value. in Soil Warming. however, in. results,. soil,. for the numerical. The. some. into. Fig. 4. Grid network. Transfer. the. the. soil. empiri-. calculated. solution. arrangement.. Fig. 5. Comparison of the calculated results of pF -w relationship with the experimental results for the soil sample (ps=2500kg/ m3; pd=1256kg/m3). Table 2. Physical properties. of the typical soil for cultivation.. 221.

(6) 農. 業. 気. from Eqs. (10)-(15), and the calculated results of them are illustrated in Figs. 6 and 7. Table 3 shows the dimensions of the soil profile and specifications of the soil warming pipes. The values listed in Table 3 would be the representative ones, which were determined with reference to the previous repoets (Itaki,1976; Okada,1980). The soil warming pipes are to be the plastic. 象. pipes. made. mm. in. of. I.D.. practical. In. winter. of (Seki. and and. upon. As. is. related so. ks. for in. Komori,. that ƒÀ. the. is. moisture. Table 3. of the calculated. against. Fig.. results. of. Plots. of. the. calculated. of. 222. k,. DT. and. near. soil. was. and. discussion. the. transfer the. hr. results. from with. the. Eqs. k. but. most. transfer. (11) also. and with. important in. the. ground. calculated. (12), ƒÀ Dwl. factor soil.. and. is DTl. affecting. Therefore,. to. Values of several empirical constants for estimation of heat and moisture trans-. Keff. results. cor-. from. and. w.. 7.. the is. typical. estimated. port properties.. Fig. 6. Plots. wo. law.. evident only. over. and. layer. the. warming. convective. air. 1985),. Calculated. not. soil. the. 30. shows. average. of. were. natural. moisture. the. the. capacity. and. Stefan-Boltzman's. 5.. is. are 4. district,. field hs. equations. heat. dimensions Table of. T0. Hokuriku. the. cultivation.. empirical. 4,. in to. which in O.D.. conditions. Table. season. responding. of. 38mm. operating. process.. for. P.V.C.,. and. Dw. against. w at. T=20•Ž.. ,.

(7) H. Seki and T. Komori: Heat and Moisture Transfer Table 4. inverstigate ing,. the. the. mum. two. of. were. moisture. chosen. results. and. 0.0032, the. protected to. Fig.. is. 8,. ordinary. it. time. is. found. due. to. the. inward. gradient. becomes. larger,. the. pipe.. to. the. For around. and. the. considerably For. from. the. pipe. transfer. larger. than. in. to. mois-. in. due of. warm. drop. Tl=30•Ž,. of. occurs. is. not. a. considerable. so. of. near. the. the. pipe,. decrease. of. 50•Ž,. w.. the. the. The with 5. days.. however, =5-10days the. soil. be. the. water. is. the. soil. soil. profilt. gradual Cp. increase decrease. and. shown. p. decreases. of. of w. in. with. and. T. of. Tl=40•Ž. 2cm. 50•Ž,. the. upper. region ƒÆ. in. Fig.. 8. (c).. T. is. related. upper. decreasing. region, w.. fer. the. water. 50•Ž;. so. 2). different. results. at. that. so. mois-. much. on. the. bare. warming. temperature. heat soil. distributions. calculated. practically transfer or so. with. if. continuously surface. 10. 50•Ž.. is suggested. as. a. suitable. intermittently not. to. decrease. The. is. the. the. the. 2). because 10-1. 223. content the. distributions. protected. retentivity, results. cultivation were. obtained. calculated. are. of. constants.. properties. soil,. and. of it. summarized. are and. necessary. moisture to. get a. conductivity factor. of. affecting. the. to trans-. the. Especially,. hydraulic important. heat. is important. properly. the. most. content. However,. for. empirical. the. constants. factor. The. Conclusions. moisture. soil water. Several. in. cal of. with. typical. estimate. T during. in. (b),. There. follows: 1). atate or. of. the. numerically. as. increase. the. a. increase. quasi-steady. and. warming. of. limited. almost. gradually. 1). surface.. Temperature in. becomes is. within. a continuous. as. w. point. the. case. Tl=40•Ž. which. case. warm. not. or. moisture. account. or. were. for. that. the. large. pipe.. of. especially. continuous. the. reach. the. is. of. region of. would In. there. case in. results. and. not. wilting. surface. calculated time,. the. region. annular. outer. is. primary. a narrow. from. in. the. than. within. there. Even. however,. smaller. in. and. be. calculated. the. influence. pipe. 6. near. T. it. not. may. near. except. and. to. not. on the. Tl=40•Ž. of. the. of. conven-. for. follows:. w. of. w here. of. Tl=40•Ž. does. soil. a. undesirable may. and. as. in. results,. a greenhouse,. w. near. of. around. supplied. so. is. case. above. transfer. the. T. summary. drop. the. case. the. amount. pipe. A. results. the. disregard. tem-. larger, w. -DT•ÞT. Tl,. water. becomes. larger. in. an. shown. for ƒÀ=0.0032. From ture. value. -DT•ÞT. days near pipe. is. in. those. adequately in. region. of not. 0.0315. calculated. from. upper. results were. a significant. even. The. be. soil. such. the. space.. not. will. the. practically.. for ƒÀ=. the. pipe. higher. and. in. 0.0315. limited. near. -DT•ÞT. flux. -Dw•Þw. perature. a. flux. gradient. moisture. w. calculated. pipe a. gradually pipe. of. in. According. decreases. decrease. 50•Ž, ƒÀ. warming. water. moisture. temperature. that. w. warm. outward. gradient. soil. induced. The. was. for or. 1980).. that. the The. the. for. (Okada,. surface.. because. distributions 40•Ž. value. around. soil. ture. content Tl=30•Ž,. cultivation. with the. moisture. rise. results. water of. cultivation,. possibly. of of. of. surface. protected. of ƒÀ=. limiting results. the. temperature. calcu-. two. calculated. amount. to. tional. profile. the. above. the. where. is. the. shows. of. moisture. between. a suitable. sprinkled. and. soil and. lie. mini-. value. the. for the soil warming process.. since. warm-. the. temperature in. under. 8. is,. maximum the. conditions. soil. that. temperature. obtained. temperature. with ,0,. and. would. Fig.. which. the. Actual. situations.. =. and here,. distributions. lated. of. distributions. calculated.. content. values. 0.0032. content. were. transfer. limiting. value. 0.0315,. moisture. Operating. in Soil Warming. empiri-. matching the. soil,. moisture. distribution. The m/hr,. soil. of. which. relatively corresponds. high. order to. value the. of kst, case ƒÀ=.

(8) 農. 業. 気. 象. Fig.. 8.. Calculated. results. moisture. of. content. the. temperature. distributions. and. for. the. case. of ƒÀ=0.0032.. 0.0315,. would. water of. pipe, kst,. not. while. 10-2. m/hr,. of ƒÀ=0.0032 equal. or. case. of. soil. dry. out. within. the. narrow. warm. water. pipe.. 3). The. around. warm. distribution. be. of that. However, low. order. would. be. is. almost. on. calculated ignoring. value limited near. small,. the. the. temperature and. distribution by. is in. movement. the. relatively. case Tl. even. moisture. pipe. soil. problem. if. the. temperature. approximately. conduction. out. dried. region. the. value. be. annular. the. warm. order the. relatively. of. the. low. to. warming. water. near. corresponds. 40•Ž.. of by. influence the. suggested. than. the. the. out. relatively. possibly. greater. of. kst,. dried of. which. may. to. the. be that. solving moisture. it. is. would the. heat move-. ment.. 4) According to the above two items 2) and 3), the drop of soil moisture content with soil warming would not be so serious, and it seems rather plausible for the protected cultivation, since the soil moisture control is easier in a greenhouse than in an open field. 224.

(9) H. Seki and T. Komori:. The. authors. Takami. would. for. his. like. helpful. to. Heat. acknowledge. and Moisture. Transfer. in Soil Warming. kstc. = theoretical. L. = latent. and. p. = distance. [-]. q. =. [-]. qr. =. Dr,. S.. saturated. hydraulic. conductivity. advice.. [m2/hr] heat. of. vaporization. between. pipes. of. water. Nomenclature [kcal/kg] A. =. empirical. constant. defined. by. Eqs.. (5). (6) B. =. empirical. constant. a. = depth. b. = distance. Cp. = heat. capacity. of. soil. Cps. = heat. capacity. of. a soil. Cpw. = heat. capacity. of. water. DT. = water. of. the. defined. buried. by. pipe. Eq.. from. (15) the. soil. sur-. face. bottom. of. the. soil. buried. = temperature. water. Ti. = initial. Ti. vapor. due. to. due. diffusivity. [kcal/kg•Ž] temperature. to. soil. warming. soil. bed. = temperature. of. water. T0. = temperature. at. the. vapor. due. diffusivity. Dw. = water. conductivity. Dwl. = liquid. Dwv. = water. in due. T•‡. = atmospheric. w. = moisture. wi. =. initial. wc. =. moisture. gradient. wf. = moisture. moisture. wst. = saturated. x. =. horizontal. z. =. vertical. =. porosity. hr•Ž]. to. moisture. water. diffusivity. due. to. vapor. diffusivity. due. to. gradient. in. the. soil. of. the. atmosphere. bed. h. = relative. humidity. br. = radiative. heat. [kg-H20/kg-dry. air]. [kg-H2O/kg-dry. =. free. convective. heat. transfer. =. thermal. Kdif. =. thermal. conductivity. of. conductivity. air. Keff. =. thermal. conductivity. hr•Ž]. = thermal. conductivity. of. a soil. =. thermal. k. = hydraulic. ks. = mass. kst. = measured. conductivity. of. v. to. vapor. soil. saturated. p. = matric. at. of. the. soil]. soil. the. flection. bed soil]. point. corresponding. moisture. soil] to. field. [kg-H2O/kg-dry. soil]. [kg-H2O/kg-dry. soil]. content. distance. [m] [m]. moisture. content. volumetric. [-]ƒÕ. moisture. potential. of. content. (=ƒÕ) ƒÕ. soil. water. [cmH2O] ƒ³ ƒÆ. thermal. surface. diffusivity. tension. = kinematic. of. of. soil. water. [hr]. bed. K. viscosity. [kg/hr2 ƒÐ. of. water. = matching. factor. (=kst/kstc). = effective. fraction. of. particle. ƒÀ. porosity. available. ƒÌfor. the. in. the. average. particles. temperature and. that. in. medium mass. p. =. apparent. pd. = dry. [-]. [-]. between. =. ]. [m2/hr]. transfer. gradient. [kg/m2 hydraulic. content. saturated. vapor. [m/hr]. coefficient. bed. ƒÕ [ -]. =. = ratio. [kcal/mhr•Ž]. transfer. soil. distance. = volumetric. bed. water. conductivity. content. content. ws. [kcal/mhr•Ž] Kw. the. [m2/hr]. [kcal/mhr•Ž]. of. [•Ž] [•Ž]. o£. moisture. w. =. hr•Ž]. [kcal/mhr•Ž] KS. bed. temperature content. = effective. [kcal/mhr•Ž]. effective. soil. coefficient. equivalent. diffusion. of. = time. [kcal/m2 Ka. pipe. [-]. coefficient [kcal/m2. hs. [•Ž] the. air] [-]. transfer. bed in. bottom. 4w]. [m/hr2]. = humidity. soil. flowing. capacity. [m2/hr ‡™w]. = humidity. the. [m] [•Ž]. [kg-H2O/kg-dry. moisture. acceleration. H. of. pipe. [kg-H2O/kg-dry. [m2/hr. Ho. temperature. [m2/hr]. gradient. = gravitational. of hr]. [kg-H2O/kg-dry. [kg-water/mhr ‡™w]. g. radius. temperature. air. to. hr]. surface. [•Ž]. [m2/hr•Ž]. = water. outer. temperature. gradient Dv. the. [kcal/m2. the. [m2/hr•Ž]. = water. to. [kcal/kg•Ž]. gradient DTv. radiation. the. the [m]. diffusivity. [kcal/m2. of. [kg-water/m. = liquid. solar. [m] bed. of. and. [kcal/kg•Ž]. gradient DTl. soil. bed. =. particle. the. of. T. bed. in. intensity. R. pipe. bed. conductivity. flux. soil. [m] between. heat. ƒÄ the [-]. flow. density. factor. [ƒÅ -]. density of. of soil. soil bed. bed. [kg/m3] [kg/m3. ]. [kg/m3] ps = ofawater soil pw particle [kg/m3] =density density of. hr]. conductivity. pwv = density of water vapor. [m2/hr]. 225. [kg/m3].

(10) 農. p0. = saturated vapor water density. 業. [kg/m3]. References Abdel-Hadi, O. N. and Mitchel, J. K., 1981: Coupled Heat and Water Flows around Buried Cables, ASCE, J. Geotech. Eng. Div., 107, GT11, 146 1-1487. Baradi, J. Y., Ayers, D. L. and Schoenhals, R. J., 1981: Transient Heat and Mass Transfer in Soils, Int. J. Heat Mass Transfer, 24, 449-458. Dakshanamurthy, V. and Fredlund, D. G., 1981: A Mathematical Model for Predicting Moisture Flow in an Unsaturated Soil under hydraulic and Temperature Gradients, Water Resour. Res., 17, 3, 714-722. Gardner, W. R., Hillel, D. and Benyamini, Y.,1970 : Post Irrigation Movement of Soil Water (1. Redistribution), Water Resour. Res., 6, 3, 851861. Green, R. E. and Corey, J. C., 197L Calculation of Hydraulic Conductivity (A Further Evaluation of Some Predictive Methods), Proc. Soil Sci. Soc. Amer., 35, 3-8. Itaki, T., 1976: Studies on the Heating Systems and Control of Air and Soil Temperature for Cucumber and Tomato Culture in Plastic Greenhouses, Kanagawa Horticultural Experimental Station, 34-48 (in Japanese). Kasubuchi, T. and Miyazaki, T., 1979: Chap. 10 Temperature and heat transfer. In Physics of Soil (ed, by Dojou Butsuri Kenkyukai), Morikita Shuppan, Tokyo, 279-293 (in Japanese). Krischer, O., 1963: Die wissenschaftlichen Grundlagen der Trocknungs technik, 2 Aufl., Springer Verlag, 268-277. Maeda, M, and Matsuo, Y., 1974: Dojou no Kisochishiki, Nobunkyo, 49-84. Mitsuno, T., 1979: Chap. 8 Water retentivity of. 気. 象. soil. In Physics of Soil (ed, by Dojou Butsuri Kenkyukai), Morikita Shuppan, Tokyo, 199238 (in Japanese). Okada, M., 1980: Chap. 15 Heating. In Theory and Application for Design of Greenhouse (ed. by Y. Mihara), Yokendo, Tokyo, 182-204 (in Japanese). Philip, J. R. and deVries, D. A., 1959: Moisture Movement in Porous Materials under Temperature Gradients, Trans. Amer. Geophys. Union, 38, 2, 222-232. Radhakrishna, H. S., Ka-Ching Lau and Crawford, A. M., 1984: Coupled Heat and Moisture Flow through Soils, ASME, J. Geotech. Eng. Div., 110, GT12,1766-1784. Raudkivi, A. J. and U'u, N. V., 1976: Soil Moisture Movement by Temperature Gradient, ASCE, J. Geotech. Eng. Div., 102, Gt12,12251244. SAMJ,1986: Nogyokishoyogokaisetsushu, SAMJ, 117-118 (in Japanese). Seki, H, and Komori, T., 1984: Measurement and Prediction of Thermal Conductivity of Soil, Proc. Hokuriku Chapter of Agr. Met. Soc., 9, 43-48 (in Japanese). Seki, H, and Komori, T., 1985: Heat and Moisture Loss at the Surface of the Soil Heated from Below, Proc. Hokuriku Chapter of Agr. Met. Soc., 10, 67-72 (in Japanese). Shapiro, H. N., 1975: Simultaneous Heat and Moisture Transfer in Porous Media with Application to Soil Warming with Power Plant Waste Heat. ph D. thesis presented to the Ohio State University, 1-167. Slegel, D. L. and Davis, L. R., 1977: Transient Heat and Mass Transfer in Soils in the Vicinity of Heated Porous Pipes, Trans. ASME, J. Transfer, 99, 541-546.. 温水循環方式による土壌加温時の熱及び水分移動関. 平和・小森友明. (金沢大学工学部土木建設工学科) 要. 約. 代表的な保水性を有する温室土壌を温水循環方式によ. した。無栽植条件の下で,温水温度Tlを30℃,40℃,. って加温する場合,土壌内の温度及び含水比分布が時間. 50℃ として数値シミュレーションを行ったところ,Tl. 的にどのように変化するかをPhilip&deVriesモ. が高いほど温水管付近の乾燥速度が大きくなること,乾. デル. に基づいて理論的に予測した。熱・水分の移動物性値は,. き上がりは管壁のでく近傍に限られることが予測された。. 温度と含水比の近似関数で表した土中水のマトリックポ. ここに示した計算結果は,温室土壌の加温計画立案のた. テンシャルと幾つかの実験定数に基づいて系統的に推算. めの有用な情報となるであろう。. 226.

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