It's like a heat wave burnin' in my heart.
I can't keep from cryin', it's tearin' me apart.
Yeah yeah yeah yeah ooh ooh oh ...  heat wave!

("Heat Wave," by E. and B. Holland & L. Dozier, 1963)

 

CONVECTION HEAT TRANSFER MAKES WAVES

PTOA Readers and Students already know that heat transfer by conduction is accomplished through a physical barrier which separates a hot area from a cold area.

In contrast, Heat Transfer via Convection is thermal energy (aka: heat) transferred from waves of flowing fluids. 

PTOA Readers and Students learned way back in PTOA Segment 3 that a fluid can be a gas, vapor, or liquid and/or a mixture of the three.

Actually, during an earthquake even solids like the ground of the earth can be "fluidized"; but PTOA will just stick with the common definitions of gas, vapor, or liquid as "fluids."

PTOA Readers and Students learned about natural draft in PTOA Segment 41 that featured hyperbolic cooling towers.

Natural draft is also Convection!

Natural draft and Convection are fluid movement caused by temperature changes that impact the density of a fluid:

• getting warmer → becoming less dense → becoming lighter and rising.
• getting colder → becoming more dense → becoming heavier and sinking.

"Waves of fluid" are frankly hard to see when the flowing fluid is a gas, like air.

The sand shown flowing in the top photo of an Australian  sandstorm helps define the shape of Convection waves.

Another photo that captures Heat Transfer via Convection is shown below.

Waves of heat are convected from the surface of a hot tarmac and distort this photo of a jet plane.

The waves of heat from the very hot tarmac can easily be imagined to be the red waves that flow vertically upward in the illustration to the left.

 

DEJA VU ALL OVER AGAIN

PTOA Readers and Students were unknowingly introduced to Heat Transfer via Convection while simultaneously learning about the the driving force for heat transfer, Delta T, in PTOA Segment 58.

The hot cup of coffee that helped define Delta T had a visible wave of hot vapor wafting from it.

That wave of heat wafting into the atmosphere was another glimpse of Heat Transfer via Convection.

How much thermal energy was transferred into the atmosphere?

That question is the perfect segue to introduce the mathematical expression that defines Heat Transfer via Convection.

 

DEFINITION AND MATHEMATICAL EXPRESSION
FOR HEAT TRANSFER VIA CONVECTION

The below expression defines the Heat of Convection (q) that a hot fluid contains:

The Heat of Convection contained in a hot fluid is a product of:

m = the mass of the hot fluid, measured in kilograms.

ΔT = the Temperature Differential between a hot fluid and the colder temperature, both measured in degrees Celsius/Centigrade.

Sometimes the colder temperature is the surrounding ambient temperature and sometimes the colder temperature is a colder fluid.

C_p = the specific heat of one kilogram of fluid from which the heat is being transferred, measured in Joules/kilogram-deg C.

Say, what? What's this C_p thing?

Basically, like "k" in the Conduction Heat Transfer expression ...

C_p was determined by dedicated nerds who spent their lives determining the heat capacities of various substances.

Thanks to those dedicated researchers, the rest of us can just look up C_p in tables like the one provided below by Engineering Toolbox:

Table of Specific Heats

 

USES OF THE HEAT OF CONVECTION EXPRESSION

So...

How much heat did the cup of coffee transfer into the atmosphere while its temperature equalized with the ambient temperature as shown in the below graph?

The first step is to take a few things for granted:

1. The above graph illustrates that the hot coffee is at 200 °F (93 °C) in the beginning and then cools down over time to the room temperature of 65 °F (18 °C).

2. The coffee is left sitting in the cup long enough to transfer all of its heat into the atmosphere.

According to the graph, about 600 minutes (10 hours) is required for the coffee to line out to room temperature (65 °F = 18 °C).

3. The cup of coffee contains 230 grams of coffee = 0.230 kilograms (because a kilogram is 1000 grams!).

4. The C_p (specific heat) of the coffee is the same as water (because liquid coffee is 99% water).

Thus...

The Heat Capacity for water listed in the Table of Specific Heats link above can be used to represent the C_p for coffee.

C_p for Water/Coffee  =  4182 J/(kg deg C).

Fantastico!

Now it is possible to determine how much heat the hot coffee transferred into the atmosphere using the below expression that defines Convection Heat Transfer:

q (in Joules) =

                      C_p            *     m      *  (Delta T)

= 4182 J/(kg Deg C) * .230 kg * (93 - 18) deg C

= 4182 * 0.230 * 75 = 72,140 J =  72.1 kJ

and since those of us in the good ole USA use British units:

72.1 kJ * 1 BTU/1.055 kJ = 68.3 BTU

Aha!

q = 68.3 BTU

The wafting hot vapors from the cup of coffee transfer a total of 68.3 BTU by convection into the surrounding room atmosphere.

Over the total 10 hours, the heat rate of Convective Heat Transfer (q/t) averaged 68.3 BTU/10 hours = 6.83 Btu/hr.

However .... as the graph shows, most of the heat was actually transferred within the first three hours.

PTOA Readers and Students already know that the heat transfer rate (q/t) decreased as rapidly as the Delta T between the coffee and room temperature decreased.

Delta T is the driving for all types of heat transfer.

 

Hey! What about Fred? 

PTOA Readers and Students read about the unfortunate drowning of Fred the Stick Man while learning the differences between "heat" and "temperature" in PTOA Segment 59.

How much heat did Fred's body transfer into the 50 °F ocean water?

As usual, the determination of total heat transferred requires taking some things for granted:

1. The Heat Capacity of the human body is listed in the below link.

Heat Capacity of Human Body

C_p Human Body = 3470 J/(kg Deg C)

2. Hey! The heat capacity of the human body uses Degrees C so the two Delta T temperatures must be converted to that temperature scale.

The below link to Google's temperature scale conversion tool will be helpful:

Google Deg C and Deg F Conversion Tool

3. The Hot Temperature is the normal temperature of a human, 98.6 °F which converts to 37 deg  °C.

4. The Cold Temperature is the temperature of the ocean water where Fred drowned, 50 °F  which converts to 10 °C.

5. Fred weighs 196 pounds which is the same as stating he has a mass of 196 pounds.

The conversion between pounds mass and kilograms is easy given the equivalency that 454 grams is equal to one pound:

196 pounds * 454 grams/pound * 1 kg/1000 grams =

 (196 * 454) / 1000 = 89 kg (kilograms)

Therefore Fred's mass m = 89 kg.

Now there is enough real information to shove into the expression that defines Convective Heat:

q = 3470 J/kg-deg C * 89 kg * (37-10) deg C =

3470 * 89 * 27 = 8,338,410 J = 8338 kJ

Convert to English Units more understandable in the USA:

8338 kJ * 1 BTU /1.055 kJ = 7903 BTU

q = 7903 BTU

Wow!

Fred's body heated up the ocean by transferring 7903 BTUs into the water!

¡Que lastima!

Fred's sacrifice went unnoticed.

The mass of water (water has an m, too!) was too great of a heat sink  to cause an increase in temperature!

TAKE HOME MESSAGES: Heat Transfer via Convection is heat that is transferred from a flowing mass of fluid into a colder environment.

The mathematical expression that defines the Heat of Convection (q, in Joules or BTUs) is below.

The Heat of Convection contained in a fluid is a product of the Heat Capacity of the fluid, the fluid's mass, and the Delta T between the hot fluid and the colder surroundings:

q (in Joules) = C_p * m * (Delta T)

Heat Capacity (C_p) for a variety of materials are found in "Look Up" tables that have been developed by scientists who dedicated their lives to better understanding heat transfer via Convection.

©2015 PTOA Segment 00064
PTOA Heat Transfer Focus Study Area

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