# Homework Help: Interactive Heat Transfer 4.0 "number of unknowns exceeds number of knowns" Matlab code?

1. Nov 16, 2014

### Matthecat

1. The problem statement, all variables and given/known data
I have to come up with a program that calculates the nodal temperatures of a sheet with a slot with 2D conduction. Due to symmetry the shape can be reduced to an L shape. Matlab and loops have always given me trouble, so I tried the Interactive Heat Transfer 4.0. Unfortunately the code that I came up with doesn't work, the program says I have too many unknowns. I know that if I could write a few loops in Matlab I would be able to compute all of it so much easier. If someone could look over my original code and point out what I'm doing wrong or give me a starting place for matlab I'd really appreciate it.

2. Relevant equations

3. The attempt at a solution

Similar Nodes 13-21, 24-32, 35-43, 46-48, 57-59

Nodes 1, 11, 55, 65
Nodes 2-10, 50-54, 60
Nodes 12, 23, 34, 45, 56, 22, 33, 44, 62 63, 64
Nodes 61 and 49 are unique

This is the code that I wrote in IHT

//Properties
k = 25 //Turbine blade thermal conductivity, W/mK

//Thermal Conditions
Tinfo = 1700 //Combustion gas temperature, K
ho = 1000 //Convection coefficient for combustion gases, W/m^2K
Tinfi = 400 //Air temperature, K
hi = 200 //Convection coefficient for air, W/m^2K

//Dimensions
delx = 0.0005 //Delta x value, m (same as delta y value)

//Constants
Co = ho*delx/k
Ci = hi*delx/k

//Nodal Equations

T2 + T7 - (2 + Co)*T1 = -Co*Tinfo //Node 1

T1 + T3 + 2*T13 - 2*(2 + Co)*T2 = -2*Co*Tinfo //Node 2

T2 + T4 + 2*T14 - 2*(2 + Co)*T3 = -2*Co*Tinfo //Node 3

T3 + T5 + 2*T15 - 2*(2 + Co)*T4 = -2*Co*Tinfo //Node 4

T4 + T6 + 2*T16 - 2*(2 + Co)*T5 = -2*Co*Tinfo //Node 5

T5 + T7 + 2*T17 - 2*(2 + Co)*T6 = -2*Co*Tinfo //Node 6

T6 + T8 + 2*T18 - 2*(2 + Co)*T7 = -2*Co*Tinfo //Node 7

T7 + T9 + 2*T19 - 2*(2 + Co)*T8 = -2*Co*Tinfo //Node 8

T8 + T10 + 2*T20 - 2*(2 + Co)*T9 = -2*Co*Tinfo //Node 9

T9 + T11 + 2*T21 - 2*(2 + Co)*T10 = -2*Co*Tinfo //Node 10

T10 + T22 - (2 + Co)*T11 = -Co*Tinfo //Node 11

T1 + 2*T13 + T23 - 4*T12 = 0 //Node 12

T2 + T12 + T14 + T24 - 4*T13 = 0 //Node 13

T3 + T13 + T15 + T125 - 4*T14 = 0 //Node 14

T4 + T14 + T16 + T26 - 4*T15 = 0 //Node 15

T5 + T15 + T17 + T27 - 4*T16 = 0 //Node 16

T6 + T17 + T18 + T28 - 4*T17 = 0 //Node 17

T7 + T16 + T18 + T29 - 4*T18 = 0 //Node 18

T8 + T17 + T19 + T30 - 4*T19 = 0 //Node 19

T9 + T18 + T20 + T31 - 4*T20 = 0 //Node 20

T10 + T19 + T21 + T32 - 4*T21 = 0 //Node 21

T11 + 2* T21 + T33 - 4*T22 = 0 //Node 22

T12 + 2*T24 + T34 - 4*T23 = 0 //Node 23

T13 + T23 + T25 + T35 - 4*T24 = 0 //Node 24

T14 + T24 + T26 + T35 - 4*T25 = 0 //Node 25

T15 + T25 + T27 + T36 - 4*T26 = 0 //Node 26

T16+ T26 + T28 + T37 - 4*T27 = 0 //Node 27

T17 + T27 + T29 + T38 - 4*T28 = 0 //Node 28

T18 + T28 + T30 + T39 - 4*T29 = 0 //Node 29

T19 + T29 + T31 + T40 - 4*T30 = 0 //Node 30

T20 + T30 + T32 + T41 - 4*T31 = 0 //Node 31

T21 + T31 + T33 + T42 - 4*T32 = 0 //Node 32

T22 + 2* T32 + T44 - 4*T33 = 0 //Node 33

T23 + 2*T35 + T45 - 4*T34 = 0 //Node 34

T24 + T34 + T36 + T46 - 4*T35 = 0 //Node 35

T25 + T35 + T37 + T47 - 4*T36 = 0 //Node 36

T26 + T36 + T38 + T48 - 4*T37 = 0 //Node 37

T27 + T37+ T39 + T49 - 4*T38 = 0 //Node 38

T28 + T38 + T40 + T50 - 4*T39 = 0 //Node 39

T29 + T39 + T41 + T51 - 4*T40 = 0 //Node 40

T30 + T40 + T42 + T52 - 4*T41 = 0 //Node 41

T31 + T41 + T43 + T53 - 4*T42 = 0 //Node 42

T32 + T42 + T44 + T54 - 4*T43 = 0 //Node 43

T33 + 2* T43 + T55 - 4*T44 = 0 //Node 44

T34 + 2*T46 + T56 - 4*T45 = 0 //Node 45

T35 + T45 + T47 + T57 - 4*T46 = 0 //Node 46

T36 + T46 + T48 + T58 - 4*T47 = 0 //Node 47

T37 + T47 + T49 + T59 - 4*T48 = 0 //Node 48

2*T38 + 2*T48 + T50 + T60 - 2*(3 + Ci)*T49 = -2*Ci*Tinfi //Node 49

2*T39 + T49 + T51 - 2*(2 + Ci)*T50 = -2*Ci*Tinfi //Node 50

2*T40 + T50 + T52 - 2*(2 + Ci)*T51 = -2*Ci*Tinfi //Node 51

2*T41 + T51 + T53 - 2*(2 + Ci)*T52 = -2*Ci*Tinfi //Node 52

2*T42 + T52 + T54 - 2*(2 + Ci)*T53 = -2*Ci*Tinfi //Node 53

2*T43 + T53 + T55 - 2*(2 + Ci)*T54 = -2*Ci*Tinfi //Node 54

T44 + T54 - (2 + Co)*T55 = -Ci*Tinfo //Node 55

T45 + 2*T57 + T61 - 4*T56 = 0 //Node 56

T46 + T56 + T58 + T62 - 4*T57 = 0 //Node 57

T47 + T57 + T59 + T63 - 4*T58 = 0 //Node 58

T48 + T58 + T60 + T64 - 4*T59 = 0 //Node 59

2*T59 + T49 + T65 - 2*(2 + Ci)*T60 = -2*Ci*Tinfi //Node 60

T56 + T62 - 2*T61 = 0 //Node 61

T61 + 2* T57 + T63 - 4*T62 = 0 //Node 62

T62 + 2* T58 + T64 - 4*T63 = 0 //Node 63

T63 + 2* T59 + T65 - 4*T64 = 0 //Node 64

T60 + T64 - (2 + Co)*T65 = -Ci*Tinfo //Node 65

Thanks,
Matt

2. Nov 21, 2014