Heat Transfer

Conductive heat transfer is the movement of heat through solids or between two solids that are touching. An example of conductive heat transfer is common when cooking on the stovetop. We set the pan on top of the stove. The stove heats the pan at the bottom of the pan, but it is not just the bottom of the pan that gets hot. The handle of the pan often gets hot also. This is because conduction occurs within the pan that transfers the heat from the bottom of the pan, throughout the pan to the handle. In the potato example, heat is conducted from the oven rack that the potato is sitting on, to the potato skin, and again from the outside of the potato to the inner potato. When hot food is placed on a cold plate, heat is transferred via conduction from the hot food that is touching the plate to the plate. Conductive heat transfer can be represented by a basic equation. Our task is to introduce this equation and dissect it into understandable parts.

Q = -kA(D T)/(D x)

Each symbol stands for a different quantity.

• - : negative sign

• Explains the direction of heat transfer. If Q is calculated to be negative, then heat is leaving, if Q is calculated to be positive, then heat is entering the object.

• Q: heat transferred (See heat definition)

• Units: units of energy

• k: Thermal conductivity: a constant that describes the ability of the object to move heat through the object. It changes depending on what object it is relating to and what temperature and pressure the object is at.

• Units: units of energy / (time*length*temperature)

• A: Area: The space an object takes up in two dimensions.

• The area of a square or rectangle can be found by multiplying the lengths of the two sides of the box together. If we call the length of one side b and the other side c, then the area is represented by multiplying the two together.

A = b * c

• The area of a circular object can be found by multiplying the constant P (3.14) times the length across half of the circle (the radius, r) squared.

A = P r²

• Units: units of length * length (or length²)

• D : Greek letter called "delta" that represents the words "change in."

• When the symbol D is used, it refers to subtracting the beginning value from the final value of the symbol following the D .
• For example: D T = T₂ – T₁ = the last T – the first T, where T represents temperature.

• T: Temperature (See temperature definition)

• Units: ^oC, ^oF, K, R

• X: distance

• The D x referred to in the equation represents the change in distance. According to the Cooking a Potato example, it refers to the length of the potato.
• Units: m, ft, cm, in

Therefore, returning to the equation,

Q = -kA(D T)/(D x)

It was shown that the equation above describes that the heat of the system is equal to the negative thermal conductivity times the area, times the change in temperature across the length of the object divided by the length of the object.

© 2007 Arizona Board of Regents for The University of Arizona