# Integral Calculus help for Heat Transfer Problem

• Apr 17th 2011, 01:40 AM
morrobay
Integral Calculus help for Heat Transfer Problem
The Heat Transfer Coefficient : h = q / A * delta T
q = heat flow , cal/sec
h = heat transfer coefficient , cal/sec / M^2 Centigrade
A = heat transfer surface area M^2
delta T = difference in temp between solid surface and surrounding fluid
Consider a 100 cc sphere of ice at 0 C in 1 liter of water at 30 C insulated from
surroundings. The water contains 30 000 cal and the ice will absorb 8000 cal
melting so final temp is 22000 cal/1100 g water = 20 C
The initial surface area of ice = .01034 M^2 radius = 2.87 cm
For water in free convection ,h = 14.3 cal/sec/ M^2 * C
delta T = 30 C
Just using initial conditions , q = h * A * delta T
q = 4.5 cal/sec
8000 cal/ 4.5 cal/ sec = .5 hour for melting time
But in this problem the surface area, A is going from .01034 M^2 --> 0
and delta T is going from 30 C --> 20 C
So in the calculation would A = integral A initial - A final ?
And how would you calculate delta T ?