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Matakuliah : S0262-Analisis Numerik

Tahun : 2010

– Heat Transfer

** Heat Transfer**

Lakes in temperature zone can be thermally stratified especially in tropical area such as Indonesia. Such stratification can divide lake vertically in to 2 layers: epilimnion and hypolimnion seperated by thermocline layer. The hard task is to locate the thermocline. The location of thermocline is at deplection point.

** Heat Transfer**

A set of data of temperature as a function of depth (z) was collected and given below.

**T o C 22.8 22.8**

**22.8**

**20.6**

**13.9**

**11.7**

**11.1**

**11.1**

Z (m) 0 2.3

4.9

9.1

13.7

18.3

22.9

27.2

Locate the thermocline!

** Heat Transfer**

**T o C 22.8 22.8**

**22.8**

**20.6**

**13.9**

**11.7**

**11.1**

**11.1**

Z (m) 0 2.3

4.9

9.1

13.7

18.3

22.9

27.2

The location of thermocline at inflection point

d 2 T/dz 2 =0. Several steps needs to be performed

1. Smoothing the data: use 3 rd order lagrange interpolation to interpolate the data such that the values of T are available for z: 0 - 28 for any values of Z

2. Use the function found from step-1 to find dT/dz for z:0 - 28

** Heat Transfer**

The location of thermocline at inflection point

d 2 T/dz 2 =0. Several steps needs to be performed.

3. The inflection point will be the maximum of dT/dz

**T o C 22.8 22.8**

**22.8**

**20.6**

**13.9**

**11.7**

**11.1**

**11.1**

Z (m) 0 2.3

4.9

9.1

13.7

18.3

22.9

27.2

f

3

*(z) f*

3

( z )

*L i*

( z )

* j i*

3

1

*L i*

( z )

0

3

*, j i z z i*

* f ( z i*

) z j z j f

3

(z)

** Heat Transfer**

**T o C 22.8 22.8**

**22.8**

**20.6**

**13.9**

**11.7**

**11.1**

**11.1**

Z (m) 0 2.3

4.9

9.1

13.7

18.3

22.9

27.2

Find the the lagrange interpolation f

3

(z) using the first

4 data and the last 4 data and use them to find dT/dz, etc……………………..