Ice melting in water over time?

[gillwoman]

Homework Statement

Hi, I need some help with a homework assignment I have, the scenario is as follows:

The Saudi Arabian government has decicded to look into towing a large iceberg from Antarctica to solve problems with low water supply. As their top physics advisor, you are to explore the plausability of such a proposal.

Homework Equations

Not Sure, Q=MC∆Tand MLf?

The Attempt at a Solution

I have researched into tugboats, and found a tugboat capable of pulling a 250 000 ton ship at 7.4km/h (4 knots). I have decided for simplicity's sake to ignore the extra drag an iceberg would produce. For the same reason, I have ignored the lightning of the mass as the iceberg melts. This is because I do not understand the physics required to find the pulling force or the tugboat given the HP, and I don't believe I am expected to for the purposes of this task.

I have constructed a path based on water currents and water temperature, and have split it into 11 sections, calculating the water temperature of each section, and the time taken to complete each section.
Section A: 200 hours @2°C
Section B: 88 hours @5°C
etc.
I just need help applying time into the equation. The initial temperature of the ice is -30°C, so I will need something along the lines of:
Q=MC∆T(ice)+MLf(Ice/Water)
I assume perhaps the solution will have something to do with Watts (J/s), as have previous questions I've Had to do, I am just not sure how to apply this.

Any Help Would Be greatly appreciated
Thankyou, Ashley Gillman

 

[gillwoman]

ok, so i understand from further reading this will require some pretty heavy maths, like calculus, using furface area, convection, radiation, conduction and such, does anyone know the formula so I can perhaps try to simplify it?

 

[Ry122]

Use this equation to find the gradient.

$$q = h*a \Delta T$$

q = rate of heat transfer (watts usually)
h = heat transfer coefficient (in w/m^2*K)
a = effective area (m^2)
Delta T = temperature difference (K)

 

[gillwoman]

Thanks, I don't suppose you have a reference though?

Is h the transfer coefficient of water or ice?

 

[Ry122]

The formula came from Newton's law of cooling.
I'd assume the heat transfer coefficient would be for water to ice.

 

[gillwoman]

Ok, i looked into that a bit, but I can't find the convective heat coefficient of ice anywhere, any idea where I can find it, I need to be able to reference it though

 

[gillwoman]

Don't worry, I ended up just using 12, most likely unreliable, but it will do the job, thanks for the help
Do I have to mark this as solved? I am not sure how