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Design data for solar heating of air
Design Data for Solar Heating of Air Using a Heat Exchange and Storage System Mohan
Lal Khanna
National Physical Laboratory, New Delhi A n arrangement for heating w i t h solar e n e r g y b y m e a n s o f a heat exchanger and storage c o u p l e d to the two water heaters has b e e n described*. I n the present paper, the a m o u n t of the heat transferred from water to air in the s h e l l - a n d t u b e heat exchanger and the temperature of the outgoing air have been estimated by considering various parameters, viz. flow rate and t e m p e r a t u r e of i n c o m i n g air, temperature of i n c o m i n g and outgoing water, length and diameter o f tubes, etc. Both natural and forced convection mode of heat transfer have been considered. Under boundary conditions of free convection, heat transfer w o u l d be rapid and efficient w i t h a possible reduction in the pipe length. The m a x i m u m permissible limit of pressure drop per foot of each tube for pipes of different diameters a t d i f f e r e n t R e y n o l d s numbers has been given. As c o n d i t i o n s o f d r y i n g vary from material to m a t e r i a l , the data presented will h e l p in arriving at the final d e s i g n o f the shell-and-tube heat exchanger to be used in d r y i n g a p a r t i c u l a r m a t e rial. N EARLIER communications ~' 2 an arrangement for heating air with solar energy by means of a heat exchanger with storage coupled to two solar water heaters was described. In the present paper, the amount of heat transferred from water to air in the shell-and-tube heat exchanger and the temperature of the outgoing air have been estimated by considering the various parameters, viz. flow rate and temperature of incoming air, temperatures of incoming and outgoing water, length and diameter of the tubes, etc. Both natural and forced convection mode of heat transfer have been considered. The over-all heat transfer coefficient, U, is given by the equation:
I
1/U -
( l / U 1 ) -k (l/U=) q- (1/Ua)
(1)
where U1 is the film coefficient for air inside the tube, U=, the film coefficient of water outside the tube; and Ua, the film coefficient of tube material. However, the effect of scale formation has not been taken into account. For forced convection, the value of U~, given in the literature, 3 was taken as 4.0 B t u / h r ft 2 deg F. But for the thermosiphon action, water in the shell of the heat *Solar Energy, 11, March-June, 1967. Manuscript received February 13, 1967
142
exchanger will be more or less stationary and for the purpose of calculation of heat transfer, it is considered to be in a state of natural or free convection. Taking its value 3 to be 30 B t u / h r ft ~ deg F, the value of over-all heat transfer coefficient, U, comes to 3.6 B t u / h r ft 2 deg F indicating thereby that the heat transfer film coefficient for air is the controlling factor. The total amount of heat transferred (Q) by the tube with surface area A is given by the equation (2)
q = U A A T m = mC~, At
The log mean temperature (ATm) is given by the equation ATm ~ (t4
-,,)-
(3)
General purpose tubular heat exchangers ~ and those used in the petroleum industry are designed for operation at 75 lb/in. 2 pressure and higher. But the present heat exchanger operates at atmospheric pressure and water on the shell side is practically stationary except for heating and circulation by thermosiphon action. Use of distilled water in the shell side of the heat exchanger is suggested to avoid reduction of the efficiency of heat transfer by possible scale formation due to impurities dissolved in water. The system of heating water with solar energy and its transfer to the shell side by thermosiphon action may be a closed one. In the initial stages, water would be at the ambient temperature. When thermosiphon action has been in operation for some time, a temperature gradient between the different layers of water would be established with hot water at the top and cold water at the bottom. A steady state would be reached after some time. The following boundary conditions have been asTABLE OF NOMENCLATURE A--surface area of the tube. m--mass of air. Ap--pressure drop. Q--total amount of heat transferred. tl--temperature of air at the inlet of tube. t2--temperature of air at the outlet of tube. t~--temperature of water at the inlet to the shell. t4--temperature of water at the outlet of the shell. At--temperature rise of air. AT,,--log mean temperature. U--over-all heat transfer coefficient. Ul--film coefficient for air inside the tube. U2--film coefficient of water outside the tube. U3--film coefficient of tube material. cp--specific heat of air. Solar Energy
150
140
/
130
I
120
/~
I10
I,~ e._
/
I00
80
t4:122 F
X
$,000
---o-- Io,ooo 70
601
1
0
l
2
I
4
I
I
[
6 8 IO PIPE LENGTH, F't - - ~
12
I
14
Fz~. 1 - - T e m p e r a t u r e of outgoing air versus pipe l e n g t h for different Reynolds N u m b e r s for Case I. 150
Lu
.
.
.
.
.
~.
130
.~,,~,/~?o ~liO
-- ,ooo
s~ii.
~,
t~=149 F
----~---3,300
t4= i22 "F
--X---s.ooo I0,000
I O0
0
I 2
I 4
I d d 6 8 I0 PIPE LFNGTH, Irt
l
12
I 14
FIG. 2 - - T e m p e r a t u r e of outgoing air versus pipe l e n g t h for different Reynold N u m b e r s for Case II.
sumed for the calculation of heat transferred from water to air: Temperature of incoming air, (tl) = 68 deg and 104 deg F. Temperature of outgoing water at bottom, (t3) = 122 deg F. Temperature of incoming water at top, (t4) = 149 deg F. Reynolds numbers = 1000, 2400, 3300, 5000, and 10,000 Mass flow rate of air per tube --- 1.5 to 60.56 lb/hr. Tube diameter = 1, 1, and 2 in. Tube length --- 2, 4, 6, 8, 10, and 12 ft Vol. 11, Nos. 3 and ~ 1967
Under these boundary conditions, the temperature of outgoing air, (h), has been calculated with the help of Eqs. (2) and (3) by the trial and error method and has been plotted against the tube length in a series of graphs for the two sets of boundary conditions (Figs. 1 and 2) with varying Reynolds number. Generally speaking, in general-purpose tubular heat exchangers~ the fluid to be heated meets on entry the hot fluid across the tube. But in the present case, heat transfer to the incoming air through the tube takes place from the hot water leaving the shell-and-tube heat exchanger at the bottom for further heating on its passage through the solar water heater. As air proceeds in the tube, the temperature of water across the tube increases and becomes maximum at the top, where air leaves the tube. All the curves in Figs. 1 and 2 originate at the point corresponding to the temperature of incoming air. Under conditions of natural or free convection prevailing at a low Reynolds number of 1000, there is a steep rise in the curve and the temperature of outgoing air approaches the temperature of incoming hot water at the top corresponding to pipe lengths of 6 to 8 ft. On the other hand, under forced convection conditions prevailing at a high Reynolds number of 10,000 and with pipe length of 12 ft, the temperature of the outgoing air is about 120 and 130 deg F respectively under the two sets of boundary conditions considered. With lowering in Reynolds number and for pipe length of 12 ft, the corresponding temperature of the outgoing air increases. At the intermediate stage of transition from free or natural to forced convection, pipe length greater than 12 ft may be required to ensure that the temperature of the outgoing air approaches the temperature of the incoming hot water at top. It is thus evident from the design of a shell-and-tube heat exchanger that under boundary conditions of natural or free convection, heat transfer would take place quickly with a possible reduction in the pipe length. Taking the viscosity of air to be 0.0182 centipoise, the values of pressure drop at various mass flow rates of air through tubes of different diameters and lengths have been calculated and are given in Table 1. It is possible to accommodate about 200 tubes of ½ in. internal diameter, with triangular pitch at a distance between the centers of the two tubes 1.5 in. in a shell 2 feet in diameter and 6 feet in height. However, in the present equipment operating at atmospheric pressure, about 100 such tubes are used.* Air blowers, generally available, have a delivery * To realize high efficiency of h e a t transfer, free and unres t r i c t e d flow of w a t e r into t h e shell at atmospheric pressure from t h e hot w a t e r inlet a t t o p is necessary and greatly depends on t h e a r r a n g e m e n t of tubes inside the shell. A model can be c o n s t r u c t e d from t r a n s p a r e n t plastic a n d the movem e n t s of water, u n d e r various working conditions, observed. This would greatly help in a r r i v i n g a t t h e final a r r a n g e m e n t of tubes inside t h e shell. 143
TABLE 1--PRESSURE DROP THROUGH TUBES OF DIFFERENT DIAMETERS AT VARIOUS RATES OF MASS AIR FLOW RATES* NRe
Tube dia., in. m, lb/hr Pressurein. water/ft.dr°p'
5000
½ 7.57 0.1
10,000
1 2 ½ 31.028 62.0 15.14 30.28 15.14 56 0.01 0.0015 0.2 0.04 0.006
* Data obtained from Figs. 5-26 page 5-23 in Perry's Chemical Engineers' Handbook McGraw-Hill Book Co. Inc., New York (1963).3 TABLE 2--MAXIMUM LIMIT OF PRESSURE DROP PERMISSIBLE IN PIPES OF DIFFERENT DIAMETERS* Tube diameter, Mass flow rate of in. / air, lb/hr/tube
1_
i /
3.5 2O 130
NRe (approx.)
Max. permissible limit of Ap/tube/ft., in. waler
.
2,400
7,000 20,000
/
0.02 0.02 0.02
* Data obtained from Fig. 21 page 379 in Perry's Chemical Engineers' Handbook, McGraw-Hill Book Co. Inc., New York (1950) Third Ed. TABLE 3--MASS FLOW RATE OF AIR FOR DIFFERENT PIPE DIAMETER AND REYNOLDS NUMBERS NRe
½
1
2
10,000
15.14
30.28
60.56
5,000 3,300
7.57
5.~
15.14 10.00
30.28 20.00
2,400 1,864
3.66 2.83
7.32 5.66 3.04
14.64 11.32 6.08
1,000
1.52
pressure of about 10 to 20 in. of water. Presently, a blower of only 10 in. of water pressure is considered. Ap/tube = 10/100 = 0.1 in. of water and A p / t u b e / f t = 0.1/6.0 = 0.02 in. of water.
(4)
The m a x i m u m permissible limits of pressure drop allowed in pipes of different diameters are given in Table 2. Similarly in Table 3 are given the mass flow rates of air in pipes of different diameters and the corresponding Reynolds numbers. The dotted line drawn in Table 3 corresponds to the m a x i m u m permissible flow rate in individual pipe with the m a x i m u m pressure drop of 0.02 in. of water per foot of the length. The mass flow rate figures below the dotted line have lower than 0.02 in. of water-pressure drop. The use of ½-in. pipe 6 feet long is restricted to mass flow rate of air of 1.52 and 2.33 l b / h r / t u b e corresponding to Reynolds numbers 1000 and 1864 respectively. The rest are ruled out being either close to or above the dotted line. As regards l-in. pipe, it would be advantageous to employ the mass flow rates of 3.04, 5.66 or 144
7.32 l b / h r / t u b e corresponding to Reynolds numbers, 1000, 1864 and 2400 respectively, although higher mass flow rates of 10.00 and 15.14 are also permissible. With respect to 2-in. pipe, the entire range of mass flow rates of air, considered in the present case, is permissible.
Discussion For efficient and uniform drying of materials, a strict control over temperature, relative humidity and rate of flow of air inside the dryers is essential. Two m a j o r factors are involved, namely, the temperature and the quantity of hot air to be circulated in a chamber of a given size. The ultimate use, to which the solar heated air is to be put, demands maintenance of predetermined constant temperature, which is the foremost criterion; while the quantity of hot air required comes next and is related to the dryer's capacity. The aim of this study is to select heat-exchange equipment that will give the temperature of the outgoing air to within 4 deg F of the temperature of the incoming water from the solar water heater. From Figs. 1 and 2, it is evident t h a t for a pipe length of 6 feet, the flow conditions corresponding to Reynolds number lower than 2000 for case I and 1800 for case I I are essential. F r o m Table 3 mass flow rate, corresponding to i in. pipe at Reynolds number 1000 is 1.52 l b / h r / t u b e and the rest are ruled out being either very close to or above the dotted line. For 1-in. pipe, it would be advantageous to adopt mass flow rate of 3.04 l b / h r / t u b e corresponding to Reynolds numbers 1000. With respect to the 2-in. pipe, mass flow rate is 6.08 l b / h r / t u b e for Reynolds numbers 1000. This type of reasoning will greatly help in arriving at the final design of the shelland-tube heat exchanger to be used in drying a particular material, as conditions of drying v a r y from material to material? Taking ½ as a safety factor, the Reynolds n u m b e r of 1000 has been considered for the actual design conditions. This gives about 1.5 l b / h r / t u b e mass flow rate of air in ½ in. i.d. tube. Taking it for granted t h a t the air outlet temperatures, as calculated here, are realized in actual practice, the utilization of the data in the design of the heat exchanger could be employed usefully in drying different materials and will be discussed in subsequent papers.
REFERENCES 1. Khanna, M. L., Solar Energy, I1, 87 (1967). 2. Khanna, M. L., Indian Jour. Tech., In press. 3. Perry, J. H., "Chemical Engineers' Handbook," McGrawHill Book Co. Inc., New York (1963) Fourth Edition. P. 10-30, Tables 10-8 and 10-9; Third Edition (1950) p. 379 Fig. 21. 4. B.S.--3274: 1960, Tubular heat exchangers for general purposes and B.S.--2041: 1953, Tubular heat exchangers for use in the petroleum industry. Solar Energy
Lal Khanna
National Physical Laboratory, New Delhi A n arrangement for heating w i t h solar e n e r g y b y m e a n s o f a heat exchanger and storage c o u p l e d to the two water heaters has b e e n described*. I n the present paper, the a m o u n t of the heat transferred from water to air in the s h e l l - a n d t u b e heat exchanger and the temperature of the outgoing air have been estimated by considering various parameters, viz. flow rate and t e m p e r a t u r e of i n c o m i n g air, temperature of i n c o m i n g and outgoing water, length and diameter o f tubes, etc. Both natural and forced convection mode of heat transfer have been considered. Under boundary conditions of free convection, heat transfer w o u l d be rapid and efficient w i t h a possible reduction in the pipe length. The m a x i m u m permissible limit of pressure drop per foot of each tube for pipes of different diameters a t d i f f e r e n t R e y n o l d s numbers has been given. As c o n d i t i o n s o f d r y i n g vary from material to m a t e r i a l , the data presented will h e l p in arriving at the final d e s i g n o f the shell-and-tube heat exchanger to be used in d r y i n g a p a r t i c u l a r m a t e rial. N EARLIER communications ~' 2 an arrangement for heating air with solar energy by means of a heat exchanger with storage coupled to two solar water heaters was described. In the present paper, the amount of heat transferred from water to air in the shell-and-tube heat exchanger and the temperature of the outgoing air have been estimated by considering the various parameters, viz. flow rate and temperature of incoming air, temperatures of incoming and outgoing water, length and diameter of the tubes, etc. Both natural and forced convection mode of heat transfer have been considered. The over-all heat transfer coefficient, U, is given by the equation:
I
1/U -
( l / U 1 ) -k (l/U=) q- (1/Ua)
(1)
where U1 is the film coefficient for air inside the tube, U=, the film coefficient of water outside the tube; and Ua, the film coefficient of tube material. However, the effect of scale formation has not been taken into account. For forced convection, the value of U~, given in the literature, 3 was taken as 4.0 B t u / h r ft 2 deg F. But for the thermosiphon action, water in the shell of the heat *Solar Energy, 11, March-June, 1967. Manuscript received February 13, 1967
142
exchanger will be more or less stationary and for the purpose of calculation of heat transfer, it is considered to be in a state of natural or free convection. Taking its value 3 to be 30 B t u / h r ft ~ deg F, the value of over-all heat transfer coefficient, U, comes to 3.6 B t u / h r ft 2 deg F indicating thereby that the heat transfer film coefficient for air is the controlling factor. The total amount of heat transferred (Q) by the tube with surface area A is given by the equation (2)
q = U A A T m = mC~, At
The log mean temperature (ATm) is given by the equation ATm ~ (t4
-,,)-
(3)
General purpose tubular heat exchangers ~ and those used in the petroleum industry are designed for operation at 75 lb/in. 2 pressure and higher. But the present heat exchanger operates at atmospheric pressure and water on the shell side is practically stationary except for heating and circulation by thermosiphon action. Use of distilled water in the shell side of the heat exchanger is suggested to avoid reduction of the efficiency of heat transfer by possible scale formation due to impurities dissolved in water. The system of heating water with solar energy and its transfer to the shell side by thermosiphon action may be a closed one. In the initial stages, water would be at the ambient temperature. When thermosiphon action has been in operation for some time, a temperature gradient between the different layers of water would be established with hot water at the top and cold water at the bottom. A steady state would be reached after some time. The following boundary conditions have been asTABLE OF NOMENCLATURE A--surface area of the tube. m--mass of air. Ap--pressure drop. Q--total amount of heat transferred. tl--temperature of air at the inlet of tube. t2--temperature of air at the outlet of tube. t~--temperature of water at the inlet to the shell. t4--temperature of water at the outlet of the shell. At--temperature rise of air. AT,,--log mean temperature. U--over-all heat transfer coefficient. Ul--film coefficient for air inside the tube. U2--film coefficient of water outside the tube. U3--film coefficient of tube material. cp--specific heat of air. Solar Energy
150
140
/
130
I
120
/~
I10
I,~ e._
/
I00
80
t4:122 F
X
$,000
---o-- Io,ooo 70
601
1
0
l
2
I
4
I
I
[
6 8 IO PIPE LENGTH, F't - - ~
12
I
14
Fz~. 1 - - T e m p e r a t u r e of outgoing air versus pipe l e n g t h for different Reynolds N u m b e r s for Case I. 150
Lu
.
.
.
.
.
~.
130
.~,,~,/~?o ~liO
-- ,ooo
s~ii.
~,
t~=149 F
----~---3,300
t4= i22 "F
--X---s.ooo I0,000
I O0
0
I 2
I 4
I d d 6 8 I0 PIPE LFNGTH, Irt
l
12
I 14
FIG. 2 - - T e m p e r a t u r e of outgoing air versus pipe l e n g t h for different Reynold N u m b e r s for Case II.
sumed for the calculation of heat transferred from water to air: Temperature of incoming air, (tl) = 68 deg and 104 deg F. Temperature of outgoing water at bottom, (t3) = 122 deg F. Temperature of incoming water at top, (t4) = 149 deg F. Reynolds numbers = 1000, 2400, 3300, 5000, and 10,000 Mass flow rate of air per tube --- 1.5 to 60.56 lb/hr. Tube diameter = 1, 1, and 2 in. Tube length --- 2, 4, 6, 8, 10, and 12 ft Vol. 11, Nos. 3 and ~ 1967
Under these boundary conditions, the temperature of outgoing air, (h), has been calculated with the help of Eqs. (2) and (3) by the trial and error method and has been plotted against the tube length in a series of graphs for the two sets of boundary conditions (Figs. 1 and 2) with varying Reynolds number. Generally speaking, in general-purpose tubular heat exchangers~ the fluid to be heated meets on entry the hot fluid across the tube. But in the present case, heat transfer to the incoming air through the tube takes place from the hot water leaving the shell-and-tube heat exchanger at the bottom for further heating on its passage through the solar water heater. As air proceeds in the tube, the temperature of water across the tube increases and becomes maximum at the top, where air leaves the tube. All the curves in Figs. 1 and 2 originate at the point corresponding to the temperature of incoming air. Under conditions of natural or free convection prevailing at a low Reynolds number of 1000, there is a steep rise in the curve and the temperature of outgoing air approaches the temperature of incoming hot water at the top corresponding to pipe lengths of 6 to 8 ft. On the other hand, under forced convection conditions prevailing at a high Reynolds number of 10,000 and with pipe length of 12 ft, the temperature of the outgoing air is about 120 and 130 deg F respectively under the two sets of boundary conditions considered. With lowering in Reynolds number and for pipe length of 12 ft, the corresponding temperature of the outgoing air increases. At the intermediate stage of transition from free or natural to forced convection, pipe length greater than 12 ft may be required to ensure that the temperature of the outgoing air approaches the temperature of the incoming hot water at top. It is thus evident from the design of a shell-and-tube heat exchanger that under boundary conditions of natural or free convection, heat transfer would take place quickly with a possible reduction in the pipe length. Taking the viscosity of air to be 0.0182 centipoise, the values of pressure drop at various mass flow rates of air through tubes of different diameters and lengths have been calculated and are given in Table 1. It is possible to accommodate about 200 tubes of ½ in. internal diameter, with triangular pitch at a distance between the centers of the two tubes 1.5 in. in a shell 2 feet in diameter and 6 feet in height. However, in the present equipment operating at atmospheric pressure, about 100 such tubes are used.* Air blowers, generally available, have a delivery * To realize high efficiency of h e a t transfer, free and unres t r i c t e d flow of w a t e r into t h e shell at atmospheric pressure from t h e hot w a t e r inlet a t t o p is necessary and greatly depends on t h e a r r a n g e m e n t of tubes inside the shell. A model can be c o n s t r u c t e d from t r a n s p a r e n t plastic a n d the movem e n t s of water, u n d e r various working conditions, observed. This would greatly help in a r r i v i n g a t t h e final a r r a n g e m e n t of tubes inside t h e shell. 143
TABLE 1--PRESSURE DROP THROUGH TUBES OF DIFFERENT DIAMETERS AT VARIOUS RATES OF MASS AIR FLOW RATES* NRe
Tube dia., in. m, lb/hr Pressurein. water/ft.dr°p'
5000
½ 7.57 0.1
10,000
1 2 ½ 31.028 62.0 15.14 30.28 15.14 56 0.01 0.0015 0.2 0.04 0.006
* Data obtained from Figs. 5-26 page 5-23 in Perry's Chemical Engineers' Handbook McGraw-Hill Book Co. Inc., New York (1963).3 TABLE 2--MAXIMUM LIMIT OF PRESSURE DROP PERMISSIBLE IN PIPES OF DIFFERENT DIAMETERS* Tube diameter, Mass flow rate of in. / air, lb/hr/tube
1_
i /
3.5 2O 130
NRe (approx.)
Max. permissible limit of Ap/tube/ft., in. waler
.
2,400
7,000 20,000
/
0.02 0.02 0.02
* Data obtained from Fig. 21 page 379 in Perry's Chemical Engineers' Handbook, McGraw-Hill Book Co. Inc., New York (1950) Third Ed. TABLE 3--MASS FLOW RATE OF AIR FOR DIFFERENT PIPE DIAMETER AND REYNOLDS NUMBERS NRe
½
1
2
10,000
15.14
30.28
60.56
5,000 3,300
7.57
5.~
15.14 10.00
30.28 20.00
2,400 1,864
3.66 2.83
7.32 5.66 3.04
14.64 11.32 6.08
1,000
1.52
pressure of about 10 to 20 in. of water. Presently, a blower of only 10 in. of water pressure is considered. Ap/tube = 10/100 = 0.1 in. of water and A p / t u b e / f t = 0.1/6.0 = 0.02 in. of water.
(4)
The m a x i m u m permissible limits of pressure drop allowed in pipes of different diameters are given in Table 2. Similarly in Table 3 are given the mass flow rates of air in pipes of different diameters and the corresponding Reynolds numbers. The dotted line drawn in Table 3 corresponds to the m a x i m u m permissible flow rate in individual pipe with the m a x i m u m pressure drop of 0.02 in. of water per foot of the length. The mass flow rate figures below the dotted line have lower than 0.02 in. of water-pressure drop. The use of ½-in. pipe 6 feet long is restricted to mass flow rate of air of 1.52 and 2.33 l b / h r / t u b e corresponding to Reynolds numbers 1000 and 1864 respectively. The rest are ruled out being either close to or above the dotted line. As regards l-in. pipe, it would be advantageous to employ the mass flow rates of 3.04, 5.66 or 144
7.32 l b / h r / t u b e corresponding to Reynolds numbers, 1000, 1864 and 2400 respectively, although higher mass flow rates of 10.00 and 15.14 are also permissible. With respect to 2-in. pipe, the entire range of mass flow rates of air, considered in the present case, is permissible.
Discussion For efficient and uniform drying of materials, a strict control over temperature, relative humidity and rate of flow of air inside the dryers is essential. Two m a j o r factors are involved, namely, the temperature and the quantity of hot air to be circulated in a chamber of a given size. The ultimate use, to which the solar heated air is to be put, demands maintenance of predetermined constant temperature, which is the foremost criterion; while the quantity of hot air required comes next and is related to the dryer's capacity. The aim of this study is to select heat-exchange equipment that will give the temperature of the outgoing air to within 4 deg F of the temperature of the incoming water from the solar water heater. From Figs. 1 and 2, it is evident t h a t for a pipe length of 6 feet, the flow conditions corresponding to Reynolds number lower than 2000 for case I and 1800 for case I I are essential. F r o m Table 3 mass flow rate, corresponding to i in. pipe at Reynolds number 1000 is 1.52 l b / h r / t u b e and the rest are ruled out being either very close to or above the dotted line. For 1-in. pipe, it would be advantageous to adopt mass flow rate of 3.04 l b / h r / t u b e corresponding to Reynolds numbers 1000. With respect to the 2-in. pipe, mass flow rate is 6.08 l b / h r / t u b e for Reynolds numbers 1000. This type of reasoning will greatly help in arriving at the final design of the shelland-tube heat exchanger to be used in drying a particular material, as conditions of drying v a r y from material to material? Taking ½ as a safety factor, the Reynolds n u m b e r of 1000 has been considered for the actual design conditions. This gives about 1.5 l b / h r / t u b e mass flow rate of air in ½ in. i.d. tube. Taking it for granted t h a t the air outlet temperatures, as calculated here, are realized in actual practice, the utilization of the data in the design of the heat exchanger could be employed usefully in drying different materials and will be discussed in subsequent papers.
REFERENCES 1. Khanna, M. L., Solar Energy, I1, 87 (1967). 2. Khanna, M. L., Indian Jour. Tech., In press. 3. Perry, J. H., "Chemical Engineers' Handbook," McGrawHill Book Co. Inc., New York (1963) Fourth Edition. P. 10-30, Tables 10-8 and 10-9; Third Edition (1950) p. 379 Fig. 21. 4. B.S.--3274: 1960, Tubular heat exchangers for general purposes and B.S.--2041: 1953, Tubular heat exchangers for use in the petroleum industry. Solar Energy