Heat Transfer Coefficient for Ice Melting Time

[Point Conception]

Homework Statement

One liter of water at 30 C ( 30000 calories )
100 gram (100 cc ) sphere of ice at 0 C is in center of water volume.
The ice will absorb 8000 cal melting and final water temp = 22000 cal/ 1100 g = 20 C
Assuming mixing and uniform water temp during melting ,and vessel is insulated from
surroundings , how long for ice to melt ?

Homework Equations

Heat Transfer Coefficient: for phase changes between a fluid and solid
h = q/A delta T

q = cal/sec
h = cal/sec/M² C for ice .523
A= surface area sphere = .01034 M²
delta T = 30 C

The Attempt at a Solution

This is difficult since delta T and A are both going to 0
For initial conditions only q = (.523 cal/sec/M² C) (.01034 M²)30 C
q= .162 cal/sec , 8000 cal/.162 cal/sec = 13.7 hrs

 

[Point Conception]

Homework Statement

One liter of water at 30 C ( 30000 calories )
100 gram (100 cc ) sphere of ice at 0 C is in center of water volume.
The ice will absorb 8000 cal melting and final water temp = 22000 cal/ 1100 g = 20 C
Assuming mixing and uniform water temp during melting ,and vessel is insulated from
surroundings , how long for ice to melt ?

Homework Equations

Heat Transfer Coefficient: for phase changes between a fluid and solid
h = q/A delta T

q = cal/sec
h = cal/sec/M² C for ice .523
A= surface area sphere = .01034 M²
delta T = 30 C

The Attempt at a Solution

This is difficult since delta T and A are both going to 0
For initial conditions only q = (.523 cal/sec/M² C) (.01034 M²)30 C
q= .162 cal/sec , 8000 cal/.162 cal/sec = 13.7 hrs

Attn Moderator: Since the physicists are not able to answer this , would you please
move it to the Other Sciences section so the Chemists and Engineers can look at it.
Thank you.