I have been assigned to work out how much air flow is needed through each partition of our servers in order to keep our processors at (or below) 60C (333K).
I have worked out the current mass flow rate going through each partition, and the heat flow rate, and I know the temperature of each processor from the system logs.
However I don't know how to calculate the required mass flow rate to bring down the temperature of the CPU's to a certain value.
For example, let's assume on one partition I have found:
air mass flow rate = 0.01 kg/s heat flow rate = 150 J/s temperature of inlet air = 298K temperature of outlet air = 308K temperature of CPU = 353K Goal CPU temperature = 333K.
So I need to reduce the CPU temperature by approximately 6% (1 - 333/353).
Does this mean I simply need to increase the airflow by 6%? I originally figured this could be true because a decrease in temperature of the CPU would be a linear decrease in the heat flow. So according to the heat capacity formula (q=mc$\Delta$T), where q is the heat flow, m is the mass flow, c is the heat capacity at constant pressure, and $\Delta$T is the change in temperature:
1.06 * 150 J/s = 1.06 * 0.01kg/s * 1000J/kgK * (308K - 298K) Therefore the mass flow rate needs to be 0.0106m/s.
The problem with this is I am assuming the outlet temperature remains the same, which I don't expect would happen. And the mass flow increases by such a marginal amount. I just don't feel like an increase in mass flow by 6% would decrease the CPU temperature by 20C.
Could someone please show me how I should be doing this? (Please note the goal is simply to find how much I need to increase the airflow)