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INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY,
TRIVANDRUM
HEAT TRANSFER PROJECT
MADE BY:
Sampathi Divyajyothi (SC09B038)
Maddala Deepthi (SC09B040)
Rupali Sahu (SC09B049)
Prachi Agrawal (SC09B071)
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1. Introduction 32.Specifications 43.Procedure 54.Observations 65.Results and Discussions 76. Inferences 77.References 7
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ABSTRACT
In this work the thermal diffusivity of potato was determined by numerical method
solution of Fouriers second law. The heat transfer model was solved using two
curves of temperature history. The two temperature profiles obtained in two
different positions in biological material under unsteady state heat transfer were
used. The experimental data were adjusted by using the explicit numerical method
of finite differences. The calculated thermal diffusivity for cylindrical and flat plate
geometry presented good results with the average relative deviation less than
0.78%.
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Determination of thermal diffusivities of complex shapes requires high
analytical skills. Here we have used finite difference numerical method
which greatly simplifies the problem. Fouriers second law for
unidirectional transient heat conduction in Cartesian and cylindrical
coordinates was employed. Thermal diffusivity has been assumed
constant over the range of temperatures used. Moisture content was
assumed to be 80%.
Equations used:
a) For cylindrical piece
(Ti+1
-Ti)/t = (Tm-1-2Tm+Tm+1 )/r
2
T(r=0) =T0
T(r=R) =Ts
b) For flat piece
(Ti+1
-Ti)/t=(Tm-1-2Tm+Tm+1)/x
2
T(r=0) =T0
T(r=R) =Ts
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SPECIFICATIONS:
Thermometer 1:
Digital thermometer with range -0 to 10C; least count: 0.1C
Thermometer 2:
Glass and mercury thermometer with range - to 110c; least count:
0.1C
Cylindrical specimen:
Height: 5cm
Radius: 15 mm
Cuboidal specimen:
Height: 5cm;
Width: 1cm;
Thickness: 3cm
Water bath temperature: 0C
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PROCEDURE
1)The specimen was put into a water-bath maintained at a constanttemperature, with its circular surfaces (cylindrical specimen) or
lateral surfaces (cuboidal specimen) insulated with thermocole to
ensure heat transfer in 1 direction.
2)Bores were made at the center and at a distance of R/2 from the centerand thermometers inserted.
3) Temperature readings were taken at equal intervals of time foraround 30 minutes.
4)Above mentioned equations and boundary conditions used tocalculate thermal diffusivity for each set of readings and average
taken.
a. Cuboidal b. Cylindrical
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b.OBSERVATIONSTEMPERATURE PROFILE:
A) For cylindrical specimen:
B) For cuboidal specimen:
X: time(s)
Y: temp(deg C)
X: time(s)
Y: temp(deg C)
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RESULTS AND DICUSSIONS:
For cylinder, the thermal diffusivity has been found out to be2.2x10
7
m
2
/sFor the cuboidal plate, the thermal diffusivity is 2.4 x107m2/s
INFERENCES:
The experiment yielded a greater value of thermal diffusivity for the flat
plate than the cylindrical specimen, but both were quite close to theactual value of 1.3x10
7m
2/s.
Errors might have arisen due to the following reasons:
1.Since the specimen is kept in water bath, its moisture contentincreases.
2.Error in reading temperature values from the thermometer3.The spacing used was too large to apply finite difference numerical
method without much loss in accuracy.
REFERENCES:
[1] Carciofi, B.A.M. et al. Determination of Thermal Diffusivity of MortadellaUsing Actual Cooking Process Data. J. Food Eng. v. 55(1), p. 89-94, 2002
[2] Yunus A. Cengel, Heat and Mass Transfer-a Practical Approach, third
edition, p.286-289, 2010.