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Interactive Heat Transfer 4.0 "number of unknowns exceeds number of knowns" Matlab code?

  1. Nov 16, 2014 #1
    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. jcsd
  3. Nov 21, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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