Question

A blower fan is blowing external ambient air to cool an aluminum box 19" x 3.45" x 14.25". The box has air holes that will allow some of the air flow through (I’m supposed to pick these fans off of the internet so no information has been given for them). There is an exhaust fan pulling the air through the system. I need to write a matlab code that shows how the temperature of the aluminum box will change over time and at different ambient temperatures. Please give me the formulas (and some explanation of why) that I would use to do this.

Answer 1

The blower which is blowing the air through the duct

So consider the volume of box ,because the volume flow from the box will

Net volume flow from the box = (surface area of box-(n x area of holes))x length

Let a,b,c be the major dimentions (L,W,D Respectively) and d be the dia of holes

let n be the no of holes

net volume = (((2x (bxa))+(2 x(cxa))- (n x3.14x d²/4))xa  

So from this above formula you will get the loss in air flow.

It is convective heat transfer

So formula to calculate the time dependent Temperatures at different points is given by

(T-T_A)/(T_I-T_A)= e^{((-hAt)/(dVC))}

Where T=temperature at any point at any time

T_A= Ambient temperature

T_I= Initial temperature

h= coefficient of thermal convection

A =area through which the heat transfer

t= time

d= density

v= volume

c=specific heat

All units to be in KGS system (metric).