Conduction & Convection

Enjoying an ice cream cone on a summer day often becomes a race between the rate of

ice cream consumption and the rate of ice cream melt. But does ice cream melt faster on a

windy day or when the air is still? Will it melt more slowly if you walk, or if you stand still?

This is the question that you will answer in this assignment. And you will do so by means

of a controlled experiment that you will design, perform, and interpret.

You may be tempted to immediately look up the answer to this question on the Internet.

Please don't do so... at least not yet. You will get much more out of this assignment if

you \discover" the answer for yourself instead of short-circuiting the intended learning

process. It may reassure you to know that the answer to the question isn't the important

part of this exercise.

Context, Background, & Theory

A solid object melts when its temperature rises above the melting point of the material

from which it is made. Recalling that temperature is a measure of the average thermal energy

per molecule, melting occurs when that average thermal energy per molecule is sucient to

overcome the chemical bonds that otherwise prevent molecules from moving very much

relative to one another. So, to melt, a solid must rst absorb enough thermal energy.

As explained in your textbook, heat (thermal energy) can be transported via three mech-

anisms: conduction of heat within a material or across the boundary between two materials

in physical contact with each other; convection that moves a mass of uid and so carries

away the thermal energy contained in it (often driven by density dierences - so-called natu-

ral convection), and electromagnetic (EM) radiation emitted from the surface of an object

because of its temperature. The radiation mechanism will be the subject of a future assign-

ment. For the present task, it is the mechanisms of conduction and convection which require

closer examination.

NOTE: In the discussion that follows a small amount of math-like notation is used to

precisely describe conduction. Don't worry about that math and instead focus on the

qualitative description of which factors govern the scale of heat

a) Heat Transfer - Conduction

Conduction occurs when heat ows from higher temperature regions to lower temperature

regions, both inside a single material and across boundaries. Suppose a cold frying pan is

placed on a hot surface. Heat rst ows across the boundary from hot to cold, increasing

the temperature of the bottom side of the pan (see Fig. 1). And, as soon as the temperature

of the bottom of the pan increases compared to the top surface, heat ow begins within the

pan itself, eventually increasing the temperature of the top surface (see Fig. 2).

However, the ow of heat in a material isn't instantaneous. The time rate at which

heat ows between two regions is proportional to the dierence in temperature. It is also

Ttop T1 bottom = T top