- #1

RiccardoVen

- 118

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Hello,

I'm trying to build a custom made fridge made by a cube by 120cm on each side.

The material used to isolate the cube will be some polystyrene panels, with thickness s=4cm.

Let's imagine to cool the dry air inside in order to reach the internal temperature of 8 degree Celsius, while the outside air

is 18 degree Celsius.

From a given time t

The aim is to estimate the time needed by the internal air to reach 18 degrees.

This is how I reasoned:

Q = Deltat x P, where:

Q = heat needed to heat the air from 8 to 18 degrees

P = heat power sucked into the fridge in the Deltat time

Q could be estimated like this:

Q = cp x phoair x V x DeltaT = 1005 x 1.225 x (1.2)

Keeping K = 0.04 W/mK the polystyrene thermal conductivity, we can get the heat power using Fourier's law over the the overall

total cube area, i.e.:

P = (KxAxDeltaT) / s = (0.04x(1.44x6)/0.04)x(18-8)) = 86.4W

So the final Deltat will be:

Deltat = Q / P = 246.225s = 4.1m

Some assumptions done: cp and K have been considered constant during the whole temperature transition.

The fridge does not touch the floor, but it's kept detached from it through some small blocks or so.

Is the reasoning I'm doing correct, please?

Thanks in advance

I'm trying to build a custom made fridge made by a cube by 120cm on each side.

The material used to isolate the cube will be some polystyrene panels, with thickness s=4cm.

Let's imagine to cool the dry air inside in order to reach the internal temperature of 8 degree Celsius, while the outside air

is 18 degree Celsius.

From a given time t

_{0}we stop the cooling, leaving the internal air to reach the thermal equilibrium with the outside.The aim is to estimate the time needed by the internal air to reach 18 degrees.

This is how I reasoned:

Q = Deltat x P, where:

Q = heat needed to heat the air from 8 to 18 degrees

P = heat power sucked into the fridge in the Deltat time

Q could be estimated like this:

Q = cp x phoair x V x DeltaT = 1005 x 1.225 x (1.2)

^{3}x(18-8) = 21273.84 JouleKeeping K = 0.04 W/mK the polystyrene thermal conductivity, we can get the heat power using Fourier's law over the the overall

total cube area, i.e.:

P = (KxAxDeltaT) / s = (0.04x(1.44x6)/0.04)x(18-8)) = 86.4W

So the final Deltat will be:

Deltat = Q / P = 246.225s = 4.1m

Some assumptions done: cp and K have been considered constant during the whole temperature transition.

The fridge does not touch the floor, but it's kept detached from it through some small blocks or so.

Is the reasoning I'm doing correct, please?

Thanks in advance

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