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Natural convection between parallel isothermal plates at different temperatures

  1. Jan 2, 2012 #1
    I was searching this forum for a post like mine but couldn't find anything suitable. The problem is as follows:

    There is an electronics cabinet with a double wall, and between the walls there is an air-flow that cools down the cabinet. The walls are isothermal and at different temperatures, both temperatures being higher than the ambient one. What I had to do first was to find the heat flow to the fluid when the temperatures were given, and I was able to do that quite easily with a few correlations that I found in a book called "Handbook of heat transfer fundamentals".

    Nu=[itex]\frac{qs}{2HW(T_{w}-T_{∞})k}[/itex]

    where T[itex]_{w}[/itex] = [itex]\frac{1}{2}(T_{1}+T_{2})[/itex], s the distance between the plates, H the hight of the plates and W their width. q is the heat thransfer to the fluid from both plates.

    Nu[itex]_{fd}[/itex]=[itex]\frac{4T*^{2}+7T*+4}{90(1+T*)^{2}}[/itex]Ra

    where Ra=[itex]\frac{gβ(T_{w}-T_{∞})s^{3}}{\nu \alpha}[/itex][itex]\frac{s}{H}[/itex] and T*= [itex]\frac{T_{2}-T_{∞}}{T_{1}-T_{∞}}[/itex], [itex]T_{1}≥T_{2}[/itex]

    Nu= [itex][(Nu_{fd})^{m}+(cRa^{1/4})^{m}]^{1/m}[/itex]

    I know all the constant values and can thus find q. Now to the problem itself:
    After having found q I should find how much energy flows through wall no 2, if there is a constant heat flux from the environment toward wall 1, called [itex]q_{1}[/itex].
    This I need to know in order to find the wall temperatures in another phase of the problem. I know I will have to iterate the temperatures but I am having trouble understanding the physics of this whole problem.

    So, What I know is the Nusselt number and the h (from h=[itex]\frac{k}{s}[/itex]Nu) but how can I find the temperatures? What I don't understand is whether the h I already found is only the convection heat transfer from both walls to the fluid or if I can use it in the expression q=hA([itex]T_1-T_2[/itex]), or the heat flow from wall 1 to wall 2, as well. If this is so, I guess I should only find suitable energy balances for both points and then iterate woth some initial temperatures.

    Could someone please help me with this? I am a bit stuck as I don't understand the physics of what I am doing quite clearly. Cheers.
     
  2. jcsd
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