Exp 3 absorption

8/10/2019 Exp 3 absorption

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UNSTEADY STATE HEAT TRANSFER CLB21003 2013

Objective

1. To determine the heat transfer coefficient of moving water to Aluminium

2. To determine the Biot Number of Aluminium

Summary

The purpose of this experiment is to determine the heat transfer coefficient of moving

water to Aluminium and also determine the Biot Number of Aluminium. Under Steady state

conditions the temperature within the system does not change with time. Conversely, under

unsteady state conditions the temperature within the system does vary with time. The SOLTEQ

Unsteady-state Heat Transfer Unit (HE 178) has been designed to run experiments on unsteady

state heat transfer. The temperature at the centre was determined by referring to Heisler Chart.

The temperature for Sphere is 48.7 C, for slab is 47.4 C and for cylinder is 50.0 C. When

compare the reading for time 70 seconds for both solid, aluminum and stainless steel,

shows that the aluminum is more efficient in heat conduction because the center

temperature is more high than stainless steel especially for cylinder where the center

temperature near to 55 C at 70s. Based from the theory, the higher the center

temperature, the efficiency in heat conduction of the material increased. Finally, the

temperature at the center of sphere by using Heisler Chart at time t = 95s is 51.8 C, for slab

is 49.8 C and for cylinder is 51.7 C. The N Bi is calculating to know the assumption is

reasonably accurate or not. The N Bi be less than 0.1 shows the experiment is successful.

After calculate, the result shows that the N Bi for sphere is 0.002165, for cylinder is

0.002434, and for slab is 0.003245. The N Bi for all the shapes are less than 0.1 identified

that the experiment is valid.


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Introduction

Heat transfer is the transfer of thermal energy from a body, at a high temperature, to another

at a lower temperature. This transfer of thermal energy may occur under steady or unsteady

state conditions. Under Steady state conditions the temperature within the system does not

change with time. Conversely, under unsteady state conditions the temperature within the

system does vary with time.

Unsteady state conditions are a precursor to steady state conditions. No system exists

initially under steady state conditions. Some time must pass, after heat transfer is initiated,

before the system reaches steady state. During that period of transition the system is under

unsteady state conditions.

Clearly, no system can remain under unsteady state conditions perpetually. The temperature

of the system will eventually reach the temperature of the heat source, and once this happens, the

system will be at steady state. Even if the amount of heat being transferred into the system is

increased, at some point the system reaches its critical temperature and the energy transferred

into it the starts causing phase changes within the system rather than temperatures increases.

The SOLTEQ Unsteady-state Heat Transfer Unit (HE 178) has been designed to runexperiments on unsteady state heat transfer. It supplied with a heated water bath and a set of

solid shapes with built-in temperature sensor to monitor the temperature at the centre of the

shape that allow analyze the heat flow using an appropriate transient temperature of heat flow

chart provided. Basically it consists of two sets of simple shape (solid sphere, rectangular slab

and long solid cylinder) made up of brass and stainless steel. Each of the shape has a built-in

temperature sensor to measure the temperature at the centre of the shape. Measurement taken can

be used to confirm the conductivity of a similar shape with different material.

The water bath has a capacity of 30L and is heated by 3.0kW. The large volume of water in

the bath ensures that change in the temperature of the water, as the measurements are taken is

negligible. The velocity of the water can be varied by adjusting the voltage supplied to the pump.


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The heat transfer characteristics and also the water temperature surround the shape remains

constant due to the upward flow of water at constant velocity past the shape.


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Results and Discussions

T Slab Sphere Cylinder

Time (s) T( oC) ln (T-T )/(T 0-T ) T(oC) ln (T-T )/(T 0-T ) T(

oC) ln (T-T )/(T 0-T )

0 26.4 0 23.0 0 25.1 0

5 26.4 0 23.0 0 25.1 -0.0116

10 30.9 0 26.2 -0.034 30.7 -0.054

15 34.7 -0.044 30.1 -0.132 34.9 -0.150

20 36.6 -0.078 32.5 -0.242 37.7 -0.264

25 38.8 -0.123 34.7 -0.336 40.4 -0.340

30 42.2 -0.160 37.1 -0.499 44.0 -0.57235 42.0 -0.182 39.2 -0.621 43.8 -0.563

40 42.9 -0.218 41.1 -0.809 45.2 -0.783

45 43.8 -0.258 43.3 -1.012 46.6 -0.877

50 44.6 -0.291 44.5 -1.193 47.6 -1.265

55 45.4 -0.525 45.6 -1.347 48.3 -1.465

60 46.2 -0.564 46.6 -1.558 49.0 -1.724

65 46.9 -0.739 47.7 -1.801 49.5 -1.958

70 47.4 -0.781 48.7 -2.065 50.0 -2.185

75 48.0 -0.831 49.5 -2.371 50.4 -2.436

80 48.5 -0.971 50.2 -2.742 51.0 -2.912

85 49.0 -1.058 50.9 -3.281 51.1 -3.202

90 49.3 -1.079 51.4 -3.992 51.6 -3.856

95 49.8 -1.147 51.8 -6.016 51.7 -5.590

100 50.2 -1.246 52.3 -4.155 51.9 -4.071

105 50.4 -1.376 52.7 -3.485 52.4 -3.162

110 50.6 -1.481 52.9 -3.253 52.5 -2.860

115 50.9 -1.253 53.2 -2.972 - -

120 51.2 -1.716 53.5 -2.797 - -

125 51.3 -1.855 53.7 -2.689 - -

130 51.6 -1.987 53.8 -2.639 - -


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Table 1: Table for Stainless Steel

Slab : T o=22.7 oC

Sphere : T o=23.0 oC

Cylinder : T o=26.5 oC

T o : Temperature at time 0

T : Temperature (water bath)



oC) ln (T-T )/(T 0-T )

135 51.7 -2.381 53.9 -2.587 - -

140 52.2 -2.437 54.2 -2.457 - -

145 52.4 -2.510 54.3 -2.417 - -

150 52.5 -2.721 - - - -

T ( oC) 50.5 51.7 50.6


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oC) ln (T-T )/(T 0-T )

0 24.0 0 22.8 0 28.2 0

5 27.0 -0.134 25.7 -0.1002 27.0 -0.122

10 30.7 -0.350 29.5 -0.2492 30.1 -0.235

15 34.2 -0.673 32.4 -0.3797 34.2 -0.247

20 36.4 -0.758 34.9 -0.5081 37.2 -0.545

25 38.8 -0.910 37.0 -0.6301 40.3 -0.798

30 40.8 -1.065 38.9 -0.7555 42.8 -0.816

35 42.4 -1.087 40.6 -0.8828 44.9 -0.951

40 43.8 -1.106 42.0 -1.0021 46.3 -1.13445 45.0 -1.230 43.3 -1.1273 47.6 -1.302

50 46.2 -1.379 44.6 -1.2704 48.7 -1.341

55 47.0 -1.601 45.4 -1.3711 49.5 -1.589

60 47.8 -1.799 46.3 -1.4965 50.3 -1.766

65 48.5 -1.995 47.0 -1.6045 50.9 -1.891

70 48.9 -2.147 47.9 -1.7675 51.5 -2.001

75 49.4 -2.342 48.6 -1.9161 52.0 -2.013

80 49.8 -2.550 49.2 -2.0617 52.5 -2.157

85 50.4 -2.674 49.7 -2.2016 52.9 -2.233

90 50.6 -2.734 50.0 -2.2993 53.0 -2.440

95 50.9 -3.465 50.4 -2.4452 53.4 -3.259

100 51.0 -3.743 50.9 -2.6578 53.5 -3.598

105 51.4 -3.987 51.0 -2.7164 53.7 -2.001

110 51.6 -4.901 51.0 -2.7214 53.8 -1.962

115 51.9 -5.675 51.2 -2.8274 - -

120 52.0 -3.224 51.4 -2.9534 - -

125 52.2 -3.012 51.7 -3.1734 - -

130 52.5 -2.344 51.6 -3.0970 - -


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Table 2: Table for Aluminium

Slab : T o=24.3 oC

Sphere : T o=25.0 oC

Cylinder : T o=24.8oC

T o : Temperature at time 0

T : Water bath temperature



oC) ln (T-T )/(T 0-T )

135 52.6 -1.463 51.7 -3.1814 - -

140 - - 51.8 -3.2735 - -

T 47.2 52.9 50.6


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Figure 1: Graph of ln (T- T)/(T0 -T) vs Time (s) for Stainless Steel

-7

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

00 50 100 150 200

l n (

T - T / T

- T )

Time (s)

ln (T- T/T -T) vs Time (s)

slab stainless steel

sphere stainlesssteel

cylinder stainlesssteel


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Figure 2: Graph of ln (T- T)/(T0 -T) vs Time (s) for Aluminiu m

Unsteady-state heat transfer is important because of the large number of heating

and cooling problems occurring industrially. Two experiments are conducted to meet the

objectives of each experiment respectively. In experiment one; we used aluminium to

determine the heat transfer coefficient of moving water and to determine the Biot Number

of aluminium whereas for experiment two, we used stainless steel to compare the

experimental and the theor etical center temperatures profile of stainless steel. Three

different shapes consists of sphere, cylinder and the slab are used in both experiments

which to identify good surface area to determine the center temperature of each shapes.

Measurement taken on a shape of a particular material can be used to confirm the

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

00 50 100 150

l n (

T - T

/ T - T )

Time (s)

ln (T- T/T -T) vs time (s)

slab aluminium

sphere aluminium

cylinder aluminium


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conductivity of a similar shape of different material. Monitoring of temperature at the

center of shape allows analysis of heat flow using the appropriate transient-

temperature/heat flow charts provided.

In experiment one, aluminum is used to determine the heat transfer coefficient ( h)

by using the formulaV C

hAm

p where the value for m is the dimensionless parameters for

use in Heisler Chart means the slope is get from the graph ln (T- T / T o- T ) versus t for

each shape. The value of h for sphere is 644.39 W/m 2 K, for cylinder is 4327.8 W/m 2 K and

for slab is 3568.4 W/m 2 K. For this experiment, the heat transfer coefficient of moving

water to aluminium is represented with the value of h. The value of h is determined to

describe the heat leaves a surface, as a function of the temperature difference between the

surface and the ambient. h is the function of the system geometry, fluid properties, and flow

velocity and temperature difference.

The value of h is used in the formula to identify the Biot Number (N Bi) by using the

formula N Bi =k

hx1 which is dimensionless. The N Bi compares the relative values of internal

conduction resistance and surface convective resistance to heat transfer. Theoretically, the

less the N Bi means the faster heat conduction inside the body than the heat conduction

away from its surface. The N Bi is calculating to know the assumption is reasonably accurate

or not. The N Bi be less than 0.1 shows the experiment is successful. After calculate, the

result shows that the N Bi for sphere is 0.002165, for cylinder is 0.002434, and for slab is

0.003245. The N Bi for all the shapes are less than 0.1 identified that the experiment is valid.

The Biot Number (N Bi) for sphere is the lowest among the other shapes. This shows

that the best surface area for aluminum is sphere where the entire surface is joining in the

water bath. So, the temperature is faster heat conduction inside the body than the heat

conduction away from its surface.

The stainless steel is used in experiment two to compare the different result in

experiment one by using aluminum. These experiment used different solution to identify


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the temperature at the center where is used Heisler Chart. Initial temperature (T o) for

sphere is 23.0 c, for slab is 22.7 c and for cylinder is 26.5 c. The water bath temperature

(T ) for sphere is 51.7 c, for slab is 50.5 c and for cylinder is 50.6 c.

After calculate the needed parameters and refer the Heisler Chart, the temperature

at the center was determined. The temperature for Sphere is 48.7 C, for slab is 47.4 C and

for cylinder is 50.0 C. When compare the reading for time 70 seconds for both solid,

aluminum and stainless steel, shows that the aluminum is more efficient in heat conduction

because the center temperature is more high than stainless steel especially for cylinder

where the center temperature near to 55 C at 70s. Based from the theory, the higher the

center temperature, the efficiency in heat conduction of the material increased. Finally, the

temperature at the center of sphere by using Heisler Chart at time t = 95s is 51.8 C, for slab

is 49.8 C and for cylinder is 51.7 C.


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Conclusion

In conclusion, for both experiment a different material were used. In experiment

one, the material used was aluminium. The heat transfer coefficient, h of moving water forshape of sphere was 644.39 W/m 2 K, cylinder 4327.8 W/m 2 K and slab 3568.4 W/m 2 K. The

value of h is determined to describe the heat leaves a surface, as a function of the

temperature difference between the surface and the ambient. h is the function of the

system geometry, fluid properties, and flow velocity and temperature difference. The Biot

Number (N Bi) was also calculated for both experiment. The N Bi for sphere was 0.002165,

cylinder 0.002434 and slab 0.003245. The N Bi for all the shapes are less than 0.1whereby it

showed that the experiment valid. A stainless steel was used in experiment two to compare

the result with aluminium. . The center temperature for sphere was 48.7 C, slab 47.4 C

and cylinder 50.0 C. When compare the reading for time 70 seconds for both solid,

aluminum and stainless steel, it clearly showed that the aluminum is more efficient in heat

conduction because the center temperature is higher than stainless steel.

References

1) Chopey, N. P Handbook of Chemical Engineering Calculations , 2 nd Edition, McGraw

Hill, 1994

2) Perry, R.H. Green D.W. and Maloney, J.O Perry`s Chemical Engineering Handbook ,

6th Edition, McGraw Hill, 1984

3) Christi J. Geankoplis, Transport Processes and Unit Operations, 3 rd Edition, Prentice

Hall International Edition, 1995, pp 217-219


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Appendix

A. Calcul ation Stainless Steel

1.0 Slab

1 =

=

= 0.01 m

X =

= (4.201 10 -6 ) (150 s) / (0.01m) 2

= 6.3015

m =

= 15.2 / (612 ) (0.01m)

= 2.4837

Graph: 0.13 Y 0

Y0 =

0.13 =


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T = 48.63 C

2.0 Sphere

X =

= (4.201 10 -6 ) (145 s) / (6.667 x 10 -3)2

= 13.7044

m =

= 15.2 / (473 ) (6.667 10 -3 m)

= 4.82

Graph: 0.0012 Y 0

Y0 =

0.0012 =

T = 54.20C

3.0 Cylinder

X1 =

=


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= 7.5 10 -3 m

X =

= (4.201 10 -6 ) (110 s) / (7.5 10 -3 m) 2

= 8.215

m =

= 15.2 / (502 ) (7.5 10 -3 m)

= 4.0371

Graph: 0.02 Y 0

Y0 =

0.02 =

T = 51.98 C


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B. Calculation for Al uminum

1.0 Slab

m =

-0.0041s = -h (0.0151m 2) / (896 2707 4 (0.02m) 3

h = 66.21

X1 = 0.01 m

X1 =

= (8.411 10 -5 ) (135 s) / (0.01m) 2

= 113.55

Bi =

Bi = (66.21 ) (0.01m) / 204

= 3.245 10 -3

Graph: 0.001 Y 0

Y0 =

0.001 =

T = 53.77 C


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2.0 Sphere

X1 = =

= 6.667 10 - 3 m

Bi =

Bi = (66.21 ) (6.667 10 - 3 m) / 204

= 2.165 10 -3

Graph: 0.001 3 Y 0

Y0 =

0.0013 =

T = 51.76 C

3.0 Cylinder

X1 = 7.5 10 -3 m

X1 =

= (8.411 10 -5 ) (110 s) / (7.5 10 -3 m) 2

= 164.48


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Bi =

Bi = (66.21 ) (7.5 10 -3 m) / 204

= 2.434 10 -3

Graph: 0.002 Y 0

Y0 =

0.002 =

T = 53.75 C

Exp 3 absorption

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