Hi Everyone,
I am trying to do the heat balance in my microwave heating system.
The system consist of Zeolite Y fixed-bed (L:8mm,200mg) in a quartz tube (Din:7mm,Dout:9mm ), which is introduced inside the TE10 mode waveguide cavity vertically. N2 is flowing through the bed (up->down). The experimental data has been obtained after drying the zeolite sample. We have fixed-bed temperature (Ts), quartz wall temperature (Tw) and outlet N2 gas temperature.
So, is this correlation correct or not?
𝑄𝑑𝑖𝑠𝑠.𝑑𝑡 −ℎ𝑔.𝐴𝑠.∆𝑇𝑠𝑔.𝑑𝑡=𝑚𝑠.𝐶𝑝𝑠.𝑑𝑇𝑠
(i) Heat dissipated in the adsorbent bed due to MWs (ii) Heat exchanged between the adsorbent (s) and the inert gas (g) flowing through the bed -sg (iii) Heat accumulated by the adsorbent bed.
I am quite confused about the calculation using my experimental data due to the unsteady state condition.
I would appreciate if someone could help me.
Powerpoint slide has been also attached to clarify.
This is most often done using a generation term. You can start with uniform generation and then get more precise, as the actual heating won't be uniform.
The o.d.e. (𝑄𝑑𝑖𝑠𝑠.𝑑𝑡 −ℎ𝑔.𝐴𝑠.∆𝑇𝑠𝑔.𝑑𝑡=𝑚𝑠.𝐶𝑝𝑠.𝑑𝑇𝑠) corresponds to a "lumped system" (i.e., zero-dimensional) transient model. It may be adequate, but I don't have enough information to determine this. You are measuring "Qdiss", "T", and "t". "Cp" and "ms" are properties. "As" is the total surface area (calculated). The only unknown is "hg". This is a separable ordinary differential equation whose solution is T=c1+c2*exp(-hg*As*t/ms/Cps). As you have the data in Excel, you can use the "Solver" to find the value of "hg" that best fits the data. In a column next to the data, calculate the temperature at each time based on an assumed value of "hg" (guess something and put in a cell, for instance, $C$2). In another column calculate the error (calculated-measured) then use $D$15=sumsq(errors) to get the total residual. Use the Solver to determine "hg" so that sumsq(errors) is minimized. The result is your experimental "hg." Select "assume non-negative" and "use automatic scaling" when you set up the Solver. I have attached a spreadsheet that illustrates this.
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