Do you do, do you remember
You were the song stuck in my head
Every song that I’ve ever loved
Played again and again and again.

("Favorite Record," by Fall Out Boy, 2015)

PTOA Segment 62: CAN'T TOUCH THIS

The common learning experiences of burning a hand by touching the handle of a hot pan and burning the inside of a mouth by licking a hot metal spoon were used as examples to illustrate Heat Transfer via Conduction to PTOA Readers and Students.

PTOA Readers and Students learned that Conductive Heat Transfer requires heat to be transferred through a physical barrier that separates a hot area from a colder area.

The greater the temperature difference between the hot and cold areas, the greater the Delta T and thus the greater the  Conductive Heat Transfer Rate (q/t, measured in BTUs or Joules per unit time .... typically an hour).

Even though the naked eye does not perceive any heat-induced barrier movement, at the molecular level the atoms that make up the barrier become excited by the heat and bang into each other which is how the heat is spread through the barrier. This process of heating up barrier atoms by banging into each other is called "conduction."

PTOA Readers and Students deduced from the above statements that the ability of the barrier to conduct heat would greatly impact the rate of Conductive Heat Transfer as would the thickness of the barrier.

The "Conductivity Factor" of the barrier is given the symbol "k" and is measured in BTU/(ft hr °F) or in the SI units of Watts/(meter °K). The larger the Conductivity Factor, the faster the heat transfer rate and vice versa.

PTOA Readers and Students learned that the thickness of the barrier, "d" (and sometimes "L", measured in inches or centimeters)  inversely impacts the rate of heat transfer.

Inversely means that the thicker the barrier (more inches or centimeters) the lower the rate of conductive heat transfer. The thinner the barrier thickness "d" of "L," the faster the rate of conductive heat transfer.

The larger the surface area exposed to the heat source in conductive heat transfer, the faster the rate of conductive heat transfer. Surface Area is given the symbol  "A" and is measured in inches or feet, or centimeters or meters.

All of the above information has resulted in human beings defining Conductive Heat Transfer Rate (Q/t) as a direct relationship between multiplying Delta T with the surface area exposed to heat (A) and the  conductivity capability of the barrier (k).

The Conductivity Heat Transfer Rate has an inverse relationship with the thickness of the barrier (d, and sometimes L) which means it appears in the denominator and is divided into the other conductivity parameters.

In summary, the mathematical relationship human beings used to define Conductive Heat Transfer is:

Q/t = [k* A* (Delta T)] / d

 

PTOA Segment 63: A-OK!

PTOA Readers and Students focussed on "k," the thermal conductivity factor that is part of the mathematical expression that defines Heat Transfer via Conduction.

Scientific engineers of yore dedicated their lives to determining the conductivity factors for materials which makes it easy for the rest of us to look-up  "k" factors

A link to a Conductivity Factor look-up table was included in this PTOA Segment.

The thermal Conductivity Factor is a big number for good conductors; the look-up table accessed via the link indicated the conductivity of copper is 400 W/(meter-°K) at 25 °C (77 °F) and decreases to 398 W/(meter-°K) at a temperature of 225 °C (437 °F).

The thermal Conductivity Factor is a small number for good insulators; the look-up table accessed via the link indicated that the conductivity of plastic is 0.03 W/(meter-deg K) at 25 °C (77 °F).

The common English units for "k" are BTU/(foot-hr-°F).

The SI units for "k" are typically  Watt/(meter-°K).

The conversion factor between the two is:

1 Watt/(meter-°K) = 0.5779 BTU/(foot-hr-°F).

The weird units of "k" make the units of the expression for Conductive Heat Transfer Rate match on both the left side and the right side of the expression.

Verifying the "consistency of units" between the left side (the term being defined) and the right side of a mathematical expressions (the relationship of terms used in the definition) is an important last step of understanding definitions defined by mathematical expressions.

An example of using the "factor-labelling method" to verify units appeared at the conclusion of this PTOA Segment; specifically, the factor-labelling method was used to verify that Btu/hr = Btu/hr.

PTOA Readers and Students should study this example of factor-labelling and understand the process of unit verification.

The process of factor labelling requires lining up the units used to express both sides of the equation. Then conversion factors are used to reduce the units of the expression to equivalency.

In the event the units cannot match on both sides of the expression, an error is present in the calculation.

 

PTOA Segment 64: LIKE A HEAT WAVE .... YEAH YEAH YEAH YEAH!

PTOA Readers and Students learned that Convective Heat Transfer is defined by waves of flowing thermal energy.

PTOA Readers and Students were already familiar with the concept of naturally flowing thermal energy; air flow through a hyperbolic cooling tower and the circulating flow of bfw and steam in a package boiler are examples of flow caused by the temperature differentials that occur in the flowing fluid.

PTOA Readers and Students realized that the amount of Convective Heat Transfer greatly depends upon a Delta T (in °F, but usually °C) between a hot temperature and a cold temperature.

The amount of Convective Heat Transfer also depends upon the mass of fluid (in pounds, grams, or kilograms) from which heat is being transferred into or out of.  The mass term in the definition of Conductive Heat Transfer is assigned the letter "m."

The Heat Capacity of the fluid also impacts Convective Heat Transfer.

A look-up table listing the "Specific Heat" of many substances appeared in this PTOA Segment. "Specific Heat" means "Heat Capacity per unit mass" of the fluid and is symbolized by "C_p."

The look up table indicated that water (at 20 °C which is 68 °F)  is assigned a Specific Heat of 1.0.

Ergo, a fluid with a Specific Heat exceeding "1" has the capacity to hold more thermal energy than water (per pound). Likewise, a fluid with a Specific Heat below "1" has less capacity than water to hold thermal energy (per pound).

The look-up tables used for Specific Heat use the following SI units.

cal/(gram-°C)
J/(kg-°C)

The weird units of Specific Heat Capacity,  "C_p," help achieve unit consistency between the definition of Conductive Heat (q, in BTUs or Joules) and the factors used to define Conductive Heat.

Summarizing all of the above,  PTOA Readers and Students learned that human beings decided the mathematical expression which  defines Convective Heat Transfer (q, in BTUs or Joules) is:

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

Since Cp is expressed in SI units, determining the magnitude of Convective Heat (q) is first performed using SI units for mass (gram or kilogram) and Delta T (deg C).  The result is expressed in Joules which is easily converted to BTUs by the few of us left in the world that still use the British system to determine the magnitude of heat transferred.

PTOA Readers and Students learned how to use the above mathematical expression for Convective Heat Transfer to quantify the amount of thermal energy (aka heat) that wafted in to the ambient air from a hot cup of coffee in PTOA Segment 58.

PTOA Readers and Students learned how to quantify the amount of heat that transferred out of Fred The Stickman's body and into the ocean in PTOA Segment 59.

The convective heat transferred from the mass of coffee in the cup and Fred's body illustrated what a heat sink is.

Neither the heat transferred from the limited mass of coffee nor Fred's body contained sufficient heat to change the temperature of their respective colder and much more vast surrounding ambient environments (air for the coffee and water for Fred's body).

©2015 PTOA Segment 00081
PTOA Deja Vu Review 3-2

You need to login or register to bookmark/favorite this content.