6 replies to this topic

[ss3]

I'm a 1st year chem. Eng. student and I need help with this heat transfer question I'm doing.

How do you calculate the time taken for ice to melt completely in a box comprising a 0.01m thick layer of polystyrene (thermal conductivity = 0.04 W/m K) sandwiched between two 0.004m Al sheets (thermal conductivity = 202 w/m K) provided the ice completely fills the cubical box of dimensions 0.6m? The box is placed at room temp of 26oC with convective heat transfer coefficient of 10 W/m2 K to all the walls of the box. Then, find the temp of the outer walls of the box.

Am I right to find Q using Q=UA(T1-T2) and the heat required to melt the ice = mass x latent heat of ice? Such that time taken to melt the ice = Heat required/Q? But in which part of my calculations then do I take into account thermal conductivity?

Pls correct me if I'm wrong.

[tejasbhatelia]

Hey,
Its understandable but a bit confusing problem, first you need to draw a block diagram on how the heat is going to be transfered from oustide room to ice, I will tell u the steps,
1) heat will be transfered by convection from thin boundary layer outside the outermost aluminium plate on to aliminium plate. this is where convective heat transfer comes into picture.
2) heat transfer by conduction through the outer aliminium plate.
3) heat transfer by conduction through polystyrene layer.
4) heat transfer by conduction through inner Al layer.
5) heat transfer to Ice through convection.
this will give you q1q2 ...... and so on
the you will have over all heat transfer Q, which u use to in your normal Q= m x latent heat and Q= UA (dT)
one thing u gotto remember is you have to find over all heat transfer coefficient U from individual heat transfer coefficient.
but if u get your Q i.e. your rate of heat transfer your time required will be wrong and hence your outside temp will be wrong.
Hope this helps,
You might wanna look into Heat transfer text book. its all in there with solved examples
Cheers
Tejas

[abhi_agrawa]

Just an addition to all that has been said: the controlling heat transfer will be through polystyrene. In fact the other heat transfer resistances can be neglected.

-abhishek

[tejasbhatelia]

You are right Abhi in practical approach, but may be when the problem has stated the heat transfer coefficients and thckness for Al i guess his prof. would like to have them included as he has asked for the outside temp as welll.
Cheers
Tejas

[ss3]

Thank u all for ur help.

I'd like to clarify one more thing though. I understand that as mentioned, heat is transferred to the ice by convective heat transfer. So does that mean I'd have to find the local convection coefficient 'h' (for heat trasnfer to the ice) to be able to calculate q = hAdT? Because if I'm not mistaken, the heat transfer coefficient of 10W/m2 K only applies to the external convection to the box (from the air) and not within it.

ss3

Hey,
Its understandable but a bit confusing problem, first you need to draw a block diagram on how the heat is going to be transfered from oustide room to ice, I will tell u the steps,
1) heat will be transfered by convection from thin boundary layer outside the outermost aluminium plate on to aliminium plate. this is where convective heat transfer comes into picture.
2) heat transfer by conduction through the outer aliminium plate.
3) heat transfer by conduction through polystyrene layer.
4) heat transfer by conduction through inner Al layer.
5) heat transfer to Ice through convection.
this will give you q1q2 ...... and so on
the you will have over all heat transfer Q, which u use to in your normal Q= m x latent heat and Q= UA (dT)
one thing u gotto remember is you have to find over all heat transfer coefficient U from individual heat transfer coefficient.
but if u get your Q i.e. your rate of heat transfer your time required will be wrong and hence your outside temp will be wrong.
Hope this helps,
You might wanna look into Heat transfer text book. its all in there with solved examples
Cheers
Tejas

[ss3]

It's alright. Finally got round it all =)