(All together now) All together now!
(All together now) All together now!
(All together now) All together now!
(All together now) All together now!

("All Together Now," by the Beatles, 1967)

 

THIS HOT LUNCH IS BROUGHT TO YOU BY ... 

As far as PTOA Readers and Students are concerned, they are just heating up a can of soup for lunch.

In reality, heat transfer is making a hot soup lunch possible!

The below schematic does not clarify the correct order of the three heat transfer methods that work together to heat up the soup;  otherwise the schematic is worthy of being included in the PTOA.

The correct order of heat transfer methods that heat up the soup are:

1. Radiation
2. Conduction
3. Convection

1. RADIATION

The above schematic clearly shows that Radiation transfers heat in (squiggly) beams that shoot out in all directions from the electric burner.

Of course in real life the beams of radiated heat are invisible.

A gas burner more clearly shows an open flame as the radiating point source.

Whichever device is used,  both the electric and gas burners radiate invisible electromagnetic beams.

The mathematical expression to the left defines Radiated Heat (Q, in BTUs) as a relationship with:

 

• Delta T, the (T⁴_Hot - T⁴_Cold) phrase in the expression.
• The surface area available to radiate heat (A).
• Yet another Greek symbol that in this case represents how proficient the material that the burner is made out of can reflect irradiated beams (σ).

 

The mathematical expression is hard to see! So click on it and it should show up in a window that is easier to see! Then use the ARROW BACK button near the website address so you don't lose your place!  Sorry for the confusion.

 

The materials of fabrication for the  burners are selected by the designers of the kitchen range and installed at the manufacturing plant that built the appliance.

The materials of fabrication chosen for the range determine how well the burners will irradiate heat (represented as the Greek symbol σ in the Radiation expression below).

The style of the burners are likewise determined during the design-phase of the kitchen range.

The selection of burner type and style determines how much surface area is available for irradiation, A.

Therefore, the only way to change the amount of heat available for Radiation is to change the T_Hot .

T_Cold cannot be changed because it is the ambient temperature in the kitchen where the range is installed. The temperature of the pan before it is heated up on the stove top will have also equalized to the ambient temperature of the room.

Ergo, adjusting T_Hot upward or downward determines how much Radiation Heat (Q, in BTUs) will be available for Radiation Heat Transfer.

 

2. CONDUCTION

PTOA Readers and Students have already figured out that heat is conducted through the physical barrier created by the saucepan's bottom which separates the hot exterior bottom of the pan (exposed to irradiate heat) from the cooler interior side of the pan.

Q/t in The Real World: 

The  rate of Heat Transfer via Conduction (Q/t, in BTU/hr or Joules/hr)  through the pan bottom is expressed:

Conduction Heat Transfer is defined:

         Q/t = [k* A* (Delta T)] / d

A and d in the Real World:

The diameter of the pan's bottom determines the surface area (A) available for Conduction Heat Transfer.

A larger diameter pan has more surface area (A) exposed to Conduction Heat Transfer.

The thickness of the saucepan's bottom (d) is also decided when the pan is designed.

The sky blue balls in the picture to the left represent the atoms that the pan bottom is made out of.

The thickness of the saucepan influences how quickly heat will be conducted from the hot side (the side exposed to the flame) through the atoms to the cold side where the soup is contained.

A thicker pan than the one shown in the above graphic would have more rows of sky blue atoms. The heat would have to be conducted through more atoms to heat up the soup.

A thinner pan than the one shown in the graphic would have fewer rows of sky blue atoms. The heat would be conducted through fewer atoms to heat up the soup.

Ergo, the rate of Conduction Heat Transfer (Q/t) would be slower if the bottom of the saucepan is thicker and faster if the bottom of the saucepan is thinner.

When PTOA Readers and Students choose the size and style of saucepan for heating up soup, they are simultaneously choosing the surface area that will be available for Conduction Heat Transfer (A) and the thickness of the barrier through which the heat will be conducted (d).

k in the Real World:

PTOA Readers and Students chose the material of manufacture for the saucepan on the day that the saucepan was purchased.

How quickly the atoms become excited and vibrate has a big impact on how fast conduction heat transfer will spread through the bottom, sides, and handle of the saucepan.

The material of manufacture is a major factor that determines the rate of Conduction Heat Transfer (Q/t) because the material that the saucepan is made of determines the thermal conductivity factor (k).

 

Material	Thermal conductivity
Copper	401 W/m*deg K
Aluminum	237 W/m*deg K
Cast Iron	80 W/m*deg K
Carbon steel	51 W/m*deg K
Stainless steel	16 W/m*deg K

 

The above table shows that a copper pan will conduct heat much more intensely than a stainless steel pan because the thermal conductivity factor (k)  for copper is much larger than the thermal conductivity factor for stainless steel.

The picture to the left shows heat transferred through a pan made of stainless steel.

The above table states that k for stainless steel = 16 W/(m*deg K) which is also  2.9 BTU/(hr*ft²*deg F).

The picture to the above right shows heat transferred through a pan made of copper (k = 401 W/m*K = 70.7 BTU/(hr*ft²*degF).

In all other respects, the two pans compared above were identical.

The compared pictures illustrate how much more intensely heat is transferred throughout the copper pan.

Conclusion: Copper is a better conductor than stainless steel.

Manipulating Delta T in the Real World:

One more time, recall the expression for Conduction Heat Transfer:

Conduction Heat Transfer is defined:

         Q/t = [k* A* (Delta T)] / d

PTOA Readers and Students have just learned that k, A, and d are decided way before that saucepan was put on the stove top.

The only control PTOA Readers and Students have regarding heating up the soup is adjusting the Delta T between the bottom exterior of the pan and the bottom interior of the pan.

Likewise, PTOA Readers and Students already know that the intensity of the Radiant Heat Transfer establishes the hot side temperature experienced at the exterior bottom of the saucepan.

Adjusting the amount of Radiant Heat Transfer is accomplished by dialing up or down on the electrical/gas range temperature control knob or interface.

Increasing the Hot Temperature increases Delta T, the main driving force for Conduction Heat Transfer.

 

3. CONVECTION

Eventually the conducted heat has transferred through the bottom of the saucepan that is initially filled with cold soup.

The  liquid at the bottom of the pan starts to heat up. At the molecular level, the increase in temperature agitates the particles of soup and they begin to bump into and bounce away from each other.

The now-hotter, now-less-dense liquid starts to rise up in the saucepan.

The colder, heavier liquid at the top liquid level in the pan drops to the bottom of the pan to fill in the void left by a rising mass of liquid.

The cyclic rising and falling of waves of convected heat has started and will continue to heat up the mass of soup in the saucepan.

PTOA Readers and Students already know that the total thermal energy (q, expressed in BTUs or Joules)  transferred in the soup via Convection  depends upon:

• The heat capacity of the soup, Cp, expressed in BTU/lb-°F or Joules/grams-°C or perhaps Joules/kg-°C.
• The amount of soup in the saucepan, m, expressed in pounds or grams or kilograms.
• Delta T between the hottest temperature at the bottom interior of the pan and the coldest temperature of the soup, expressed in °F or °C.

 

Otherwise stated, the total amount of thermal energy transferred via Convection into the soup is defined:

q (in Joules or BTUs) =

                      C_p            *     m      *  (Delta T)

The Delta T will get smaller and smaller while the constantly churning soup eventually comes to a roiling boil and the overall average temperature of the liquid soup becomes 212 °F (100 °C).

Time to eat!

 

 

 

 

TAKE HOME MESSAGES:  Heat Transfer via Radiation, Conduction, and Convection are all required to make a hot bowl of soup.

The next PTOA Segment will demonstrate how the three methods of heat transfer work together in temperature-changing process industry equipment.

 

©2015 PTOA Segment 00067
PTOA Heat Transfer Focus Study Area

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