Solving Heat Transfer Rate for 10 mm Ice Layer at -5°C

[debwaldy]

Homework Statement

hi,i was wondering if someone could tell me if the following solution makes sense,ithink it does but not sure why?


cool air blowing across the surface of a frozen lake keeps the top surface of the ice at a temperature of -5degrees celsius.what is the rate of increase in the thickness of the ice layer when the ice is 10 mm thick?

Homework Equations

the density,thermal conductivity and specific latent heat of fusion of ice are 920 kg m^-3, 1.7 J m^-1 K^-1 s^-1 and 3.3*10^5 J kg^-1 respectively

The Attempt at a Solution

so i said that:

the heat transfer coefficient = thermal conductivity/thickness of material
i.e heat transfer coefficient= 1.7/0.01= 1.7*10^2 J K^-1 s^-1

then i said :
heat flux=(1.7*10^2) *5 = 8.5*10^2

then:
8.5*10^2/920 = 9.23913*10^-1

and so:
9.23913*10^-1/3.3*10^5= 2.799* 10^-6 ms^-1

i know the answer is right but i don't quite understand the thinking behind it.could anyone explain it to me?
any help would be much appreciated

 

[AlephZero]

You seem to have done the right sums, but not in a logical order.
Your heat transfer coeff. and heat flux are OK.

Now think about what happens to 1 square meter of lake surface in 1 second.

850 J of heat flows out of the lake. That freezes 850/3.3*10^5 = 2.575*10^-3 Kg of ice.

The volume of the ice is 2.575*10^-3/920 = 2.799*10^-6 m^3.

We were considering 1 square meter of area, so 2.799*10^-6 m^3 is a block of size 1m * 1m * 2.799*10^-6 m.

The time was 1 second, so the thickness changes at 2.799*10^-6 ms-1.

 

[debwaldy]

thanks a million,that makes sense to me now alright...wasnt really thinking bout it in a logical manner
thanks for clearing that up!