I have some confusion regarding the effect of axial conduction at micro-scale heat transfer in micro-channels. Consider a conjugate heat transfer problem wherein micro channels are used for cooling some electronic device. The boundary conditions are as follows: heat flux applied to one of the face while other faces are generally treated as adiabatic. Now here solving the problem of heat carried away by coolant and temperature distribution in solid substrate, are we accounting the effect of adiabatic conduction. As per what I understand is, the effect of axial conduction will only be observed when some surfaces are not given as adiabatic thereby permitting some heat to flow out of the system. This may be achieved by modelling the channels using plenum or manifolds and applying heat flux only below the micro channels. Consequently owing to axial conduction of the solid substrate, there will be redistribution of heat with significant heat entering the fluid region near the entrance. However some portion of heat will also be transmitted to regions outside the channels.
My confusion is that if we are giving all surfaces (except heat flux) an adiabatic, do we then also encounter effect of axial conduction if form of heat loss to be carried away by cooling medium? My understating suggests that though heat flow may be redistributed owing to lower convective resistance near channel inlet, but amount of heat into the system will be same as total heat carried away by cooling medium (under steady stare conditions).(i.e. heat flux x surface area where flux is applied = mass flow rate x specific heat x difference of bulk temp. of fluid at outlet and inlet).
I am not answering the question but i failed to understand what exactly your problem is? Can you rephrase the question in a quite simple manner. If possible i will try to answer.
Hi Balkrishna,
I have rephrased the question and edited it. In very simple terms, my question is, how do we account for effect of axial conduction in micro channel cooling during simulation.
I came across a literature wherein it was mentioned that Total heat into the system= heat carried by water+heat carried by axial conduction+heat losses. My concern is the part of heat lost by axial conduction where is this part going. Does this mean that while doing numerical studies I have to model not only the micro channel but also the plenum etc to account for the same.
Kindly let me know if this is clear else I will post the relevant paper for further exemplification.
As far as my knowledge, when you want to simulate convection in microchannel, you have to solve energy equation for both solid domain as well as fluid domain.
You have asked about different heat. One point is fixed that energy will always be conserved, i.e., whatever heat is given will be taken out by fluid+ losses. The only difference in case of axial conduction is that the axial variation of temperature will be different than the conventional case.
I answered, What I have understood from your question. If you have further query please communicate
Hi Balkrishna,
Seeking further clarification reg your answer, I understand the temperature profile will not be linear (as in case of simple heat transfer for uniform heat flux).
Is this the only effect of axial conduction.??
Suppose I simulate the same problem with inlet manifold/plenum attached to the micro channel, then will axial conduction affect heat carried away by fluid?? putting in simpler terms, the confusion is where does axial conduction affect apart from temperature profile of surface where heat is applied.
I hope I am making clear this time. In case not, kindly tell
d'kar
Here I am assuming that you are talking about axial conduction in solid only, i.e., for high Pe. When you are considering axial conduction in solid, in that case, if your plenum's domain is significant then the total heat input given by you will also conduct to the plenum. Thus your heat input in microchannel domain is less than your input but at the same time, heat diffused in plenum will heat the fluid inside. So when you do the energy balance for plenum + microchannel, it should be equals to heat carried by the fluid plus losses.
The effect of axial conduction is that it may modify the thermal boundary condition at liquid-solid interface thus the heat transfer characteristics.
Hi,
You have mentioned that axial conduction may modify thermal boundary condition at liquid-solid interface. Isn't it vice-versa?
I mean the flow conditions in micro-channel (developing or developed) will govern convective resistance which in turn will affect the heat carried away by water. Where this resistance is less (as in developing region) heat flow due to axial conduction may be significant towards inlet.
Also in case of solid, you have mentioned high Pe.How do we define Pe for solid. (In case your are not talking about the one used in CFD-FVM i.e diffusion coeff./diffusion length(area))
If Flow Re is less effect of axila conduction is more dominating.
Energy balance will always hold.
Pe is defined for fluid flow only. I meant to say that for high Pe you neglect axial conduction in fluid, you are only concerned about axial conduction in solid.
Hi there,
Fisrt of all you have to sparate between the effect of the manifold and axial conduction throogh micorchannel wall. If you consider a single microchannel with its walls (sides and bottom walls), if these walls are thick you have to consider the effect of conduction and you can neglect conduction effect if these walls are thin. Please, see the attached article. You can measure the effect of conduction through the walls by considering Biot number
http://en.wikipedia.org/wiki/Biot_number
As you mentioned, the amount of heat is the same regardless the assumption of heat conduction or not (First Law of Thermodynamics). In micro and may in macro channels the heat conduction through the solid conduit is important. The mechanism of heat conduction is to distribute the heat and alter temperature at the boundary compared with ideal system (the conduction through the solid conduit is negligible).
The neglect of axial conduction and adiabatic BC imposition are all in error in addressing conjugate heat transfer. Suggest you look at Optimal Modified Continuous Galerkin CFD text, recently from Wiley, Figure 8.11 for correct BCs and Figure 8.12 for an illustration on structure axial conduction influence.
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