Cooling a 5cm x 5cm Chip with Water: Temperature vs Time

[Frandy]

Homework Statement

An electronic chip of 5cm x 5cm surface is to be cooled by a water cooling method (see drawing)

Homework Equations

If 500W of heat is to be removed from the chip, what is the temperature of water from the time of operation until 5 hours if the fan is not operational (assuming the water quantity is 20 liters, and initial temperature is 15°C). (Plot temperature vs time) (water flows 50 cc/s).

The Attempt at a Solution

If you turn on the fan of 12 cm in diameter with 100 cfm flow, what do you expect the temperature will be in the next one hour (plot temperature vs time in every 5 minutes) (assuming the air temperature is 15°C).
What do you expect the die temperature for the above two cases (fan on and off)? Plot temperature vs time. The Chip has a die initial temperature of 100°C.

 

[LawrenceC]

Where is the drawing?

 

[Frandy]

Here it is in the attached file

 

[LawrenceC]

Hint:
The power is 500 watts. If the temperature is to remain at 100 C, that much power must be removed from the chip. The heat removed from the chip goes into the water. A watt is a unit of power meaning energy per unit time - calories per second.

 

[rezeew]

As a scientist, it is important to consider all factors and variables in a cooling system in order to accurately predict and understand the temperature changes over time. In this scenario, the size and surface area of the chip, the quantity and initial temperature of water, the rate of water flow, and the fan size and air flow all play a role in the cooling process.

To calculate the temperature of the water over time, we can use the equation Q = mcΔT, where Q is the heat removed, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. In this case, Q = 500W, m = 20kg (20 liters of water), and c = 4.186 J/g°C. Assuming the water is initially at 15°C, we can solve for ΔT.

ΔT = Q/mc = (500 W)/(20 kg x 4.186 J/g°C) = 5.99°C

This means that the temperature of the water will increase by approximately 6°C over the course of 5 hours, assuming no other factors affect the cooling process. This can be plotted as a linear increase in temperature over time.

If we turn on the fan with a flow rate of 100 cfm, we can expect the air temperature to decrease as it passes over the chip and absorbs heat. However, the exact temperature change will depend on the efficiency of the fan and the surrounding air temperature. This can also be plotted as a linear decrease in temperature over time.

The die temperature of the chip will also be affected by these cooling methods. With the fan off, the chip will likely reach a steady state temperature that is higher than the initial 100°C due to the heat being generated by the chip and the limited cooling capacity of the water. With the fan on, the chip temperature will decrease as the fan helps to remove heat from the chip. This can be plotted as a exponential decrease in temperature over time.

Overall, the temperature changes over time will depend on the specific conditions and variables of the cooling system. As a scientist, it is important to consider all factors and carefully analyze the data to make accurate predictions and conclusions.