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This is a section of cooling channels in injection moulding tools.

enter image description here enter image description here

I have tried to calculate the thermal resistance in this section with 2 methods, one analytical and one numerical.

  1. analytical solution:

I have calculated the thermal resistance by this equation

enter image description here

  1. numerical there I have the difficulties, I vary the T1 and T2 and I read out the heat flows from ANSYS. What I can't understand is, which heat flow should I take (on the wall? or on the channel? in the middle?), because the heat flow is not constant in the part.

enter image description here

Many thanks

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    $\begingroup$ What is painted in color? $\endgroup$
    – Alex Trounev
    Commented Jan 14, 2020 at 0:17
  • $\begingroup$ This is a transient problem, right? $\endgroup$
    – Chet Miller
    Commented Jan 14, 2020 at 0:49
  • $\begingroup$ @ChetMiller Yes, it's a transit analysis. $\endgroup$
    – Zouhir Bensebban
    Commented Jan 14, 2020 at 10:28
  • $\begingroup$ @AlexTrounev do you mean the last painting? $\endgroup$
    – Zouhir Bensebban
    Commented Jan 14, 2020 at 10:29
  • $\begingroup$ @ZouhirBensebban There is one color drawing - something with many holes. Is this a tool section? $\endgroup$
    – Alex Trounev
    Commented Jan 14, 2020 at 10:50

1 Answer 1

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A numerical solution to the problem $\nabla ^2 T=0$ with boundary conditions $T=T1=200C$ at the upper boundary and $T=T2=40C$ at the boundary of the hole is shown in Figure 1 on the left, and the heat flux at the upper boundary $\dot {q}=-\vec {n}.\lambda \nabla T$ at $\lambda = 1$ on the right. To find the thermal resistance, we calculate the integral $$\dot {Q}=\int_0^b \dot {q}dx$$ Figure 1

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  • $\begingroup$ Thank you very much for your helpful answer. how did you get this curve? through Matlab? i first have to simplify dot {q} to calculate this integral $\endgroup$
    – Zouhir Bensebban
    Commented Jan 15, 2020 at 10:03
  • $\begingroup$ I used FEM and Mathematica 12. $\endgroup$
    – Alex Trounev
    Commented Jan 15, 2020 at 11:39
  • $\begingroup$ Hello, Alex, is the integral with the separation of the variable solvable? I have followed the steps in the book "Fundamentals of Heat and Mass Transfer by Theodore L. Bergman" on pages 211-214, but I am confused when it comes to inserting constants. $\endgroup$
    – Zouhir Bensebban
    Commented Jun 11, 2020 at 8:33

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