I told you homeboy u can't touch this
Yeah that's how we're livin' and you know u can't touch this.

("Can't Touch This," by M.C. Hammer, 1990)

 

OUCHEE WA-WA!

Factually speaking, a person CAN touch the hot handle of a pan that has been on a hot burner for several minutes.

The lesson NOT TO TOUCH the hot handle is usually  learned by burning oneself.

Afterall, the heat source is the orange electric burner in the graphic. The handle of the pan appears safe enough to touch being so distant from the heat source.

The same lesson is learned by the overly anxious child that licks the spoon that stirred a delicious hot cup of cocoa.

For smart children once is enough to learn that sufficient heat has been transferred into the metal spoon to enable burning of the interior of the mouth.

And yet this lesson must be learned because it is the liquid cocoa that appears steaming hot and (in this case) the handle of the spoon can be held comfortably.

How does heat transfer so far away from the heat source and what can be done to stop  unwanted heat transfer that burns unsuspecting hands and mouths?

 

 

 

 

 

HEAT TRANSFER VIA CONDUCTION

Heat Transfer via Conduction will happen wherever there is a physical barrier separating a hot area from a colder area. 

A physical barrier is any barrier that can be seen and touched.

Conducted heat will transfer through the barrier from the hot side to the cold side. 

 

Examples of Physical Barriers

In the above diagram the barrier is a rectangle that has a thickness denoted as the length "L."

(In the process industries, the above graphic could be illustrating how the heat generated by combustion comes in contact with the refractory that lines the walls of the firebox.)

In the hot-pot example, two examples of Heat Transfer by Conduction can be identified.

The heat generated at the electric burner is just like the flame in the above diagram; heat from the electric burner is conducted through the bottom of the cold metal pan that has just been placed upon the burner.

The above graphic is drawn to show that the heat conducted through a substance (like a metal pan) excites the molecules that the substance is made out of.

Of course the pan does not move or jump about, but at the atomic level the molecules get excited and bump into each other and that is how they spread the heat.

The pan is hottest where it interfaces with the burner but still quite hot at the handle.

The heat is conducted through the thickness of the metal pan and continues to migrate through the entire pan in an attempt to equalize temperatures and extinguish the Delta T.

Secondly, conducted heat is transferred from the surface of the hot handle (the Hot Temperature) into the skin of the now burning hand that is in equilibrium with the 98.6 °F body temperature  (the Cold Temperature).

Note that the heat is being transferred through the entire exposed area of the pot handle; thus the unfortunate person picking up the pot would be burned with the same intensity if they touched the top, sides, or bottom of the pot handle.

Likewise, the metal spoon illustrates two types of Conduction Heat Transfer.

The hot liquid cocoa is the heat source.

Heat is transferred from the hot cocoa (the Hot Temperature) through the spoon which was originally at room temperature (the Cold Temperature).

Afterward, placing the hot spoon into the mouth (the Hot Temperature) burns all parts of the colder mouth that come into contact with the surface area of the spoon .... the roof, the sides, and tongue.

The heat in the spoon is transferred through the metal spoon into the mouth tissue while equalizing the hot and cold temperatures.

So the "L" in the Conduction Heat Transfer graphic to the right is the thickness of a barrier and could also be a symbol representing:

• the thickness of the bottom of the pot being heated up.
• the thickness of the skin being burned by the hot handle.
• the thickness of the spoon being heated up by hot cocoa.
• the thickness of the tongue and roof of mouth being burned by the hot spoon.

 

HEAT TRANSFER VIA CONDUCTION
MATHEMATICAL EXPRESSION

The below expression is mankind's best attempt to understand Conduction Heat Transfer...and it works pretty well!

NOTE: To view the equation more clearly click on it and it will appear in another window. THEN LEFT ARROW BACK (the arrow near your browser window) to return to your place in this PTOA Segment.

 

The Left Side of the Expression Defines Heat and Heat Rate

Q  = Heat  and is expressed in BTUs or Joules

t = Time and is typically expressed in hours

When both sides of the expression are divided by t, the t disappears from the right side of the equation and Q/t appears on the left side.

Q/t = Conduction Heat Transfer Rate expressed in BTU/hr or J/hr

Hey!

PTOA Readers and Students recognize that BTU/hr or J/hr is a heat rate. In this case the rate of Heat Transfer via Conduction, meaning heat transferred through a physical barrier that separates a hot area from a colder area.

 

The Right Side of the Expression Reveals the Components that contribute to Conduction Heat Transfer  

PTOA Readers and Students recently reviewed that the commonly used concept of Velocity is defined by a relationship between d = Distance and t = Time.

Likewise, the rate of Conduction Heat Transfer (Q/t) is defined by a relationship of variables as shown on the right side of the expression. Use the trick you learned above to see the equation more clearly.

PTOA Readers and Students recognize Delta T as the driving force required for Conduction Heat Transfer to occur; without a Delta T heat cannot exist!

Delta T = (Hot Temp - Cold Temp) = (T_Hot - T_Cold) in °F or °C

PTOA Readers and Students also already know that the greater the difference between the hot and cold temperatures, the more heat (Q) will be transferred over a given time (Q/t).

Hey, the math model seems to jive with the Universe:

Bigger Delta T will yield a bigger Conduction Heat Transfer Rate (Q/t)!

A = the surface Area of the physical barrier that is exposed to heat transfer.
A might be expressed in square feet (ft²) or square inches (in²) or square meters (m²) or square centimeters (cm²).

Aha!

Increasing the surface area of the barrier that lies between the Hot and Cold temperatures will increase the rate of Conduction  Heat Transfer!

Increasing A increases Q/t!

That must be why the tube side flow through a shell and tube heat exchanger is divided up in a tube sheet and made to flow through the multiple tubes of a tubebundle! Dividing up the flow into separate tubes creates a lot more surface area exposed for Conduction Heat Transfer to take place.

The "d" in the denominator is the thickness of the barrier through which the Conduction Heat Transfer is occurring.

d = thickness of barrier and might be expressed in inches, feet, centimeters, or meters.

In the above expression "d" is the same as "L" in the drawing on the right.

PTOA Readers and Students can easily visualize that the rate of Conduction Heat Transfer (Q/t) will decrease as the length (aka thickness) of the barrier between the hot and cold areas increases.

Likewise, the rate of Conduction Heat Transfer (Q/t) will increase as the length (aka thickness) of the barrier between the hot and cold areas decreases.

What is this interesting thing called "k"?

K is the thermal conductivity capability of the material that the barrier is made of.

k = Thermal Conductivity Factor and is expressed in
[Watt/(meters-°K)] = 0.5779 [ BTU / (foot hr °F)]

The weird units of k cancel out all others in the expression so that the definition of Conduction Heat Transfer Rate ends up being expressed in BTU/hr and J/hr.

K is sufficiently interesting to warrant exploration in the next PTOA Segment so do not stress about it now.

 

TAKE HOME MESSAGES:

The mathematical expression for the rate of Conduction Heat Transfer (Q/t, expressed BTU or Joules per unit of time) seems to accurately describe how heat is transferred through a physical barrier that separates a hot region from a colder region.

The Conduction Heat Transfer Rate Q/t will increase when using:

• a higher conductivity material with a big "k" factor.
• a greater surface area A is exposed to the heat source.
• a greater Delta T between the hot and cold temperatures separated by the barrier.

The Conduction Heat Transfer Rate Q/t will: 

• decrease as d, the thickness of the barrier, increases.
• increase as d, the thickness of the barrier, decreases.

 

©2015 PTOA Segment 00062
PTOA Heat Transfer Focus Study Area

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