What are the three modes of heat transfer?

Thermal conduction

Heat conduction depends on the temperature gradient, cross section, path length, and the properties of materials. The expression is very similar to Ohm's Law for electric conduction. The analog of the voltage difference is the temperature difference, the analog of electric current is the heat flow rate, and the analog of electric resistance is thermal resistance (inverse of thermal conductance).

Substance  
k (W/mK)  
 
Metals  
  
Stainless steel  
14  
Lead  
35  
Aluminum  
235  
Copper  
401  
Silver  
428  
Gases  
  
Air (dry)  
0.026  
Helium  
0.15  
Hydrogen  
0.18  
Building Materials  
  
Polyurethane form  
0.024  
Rock wool  
0.043  
Fiberglass  
0.048  
White pine  
0.11  
Window glass  
1.0  
 
aConductivities change somewhat with temperature. The given values are at room temperature.

 

Sample problem: Two rods, one lead and the other copper, are connected in series between metal plates held at 2 C and 106 C. Both rods have a length of 2 m and a diameter of 10 cm. Neglecting any heat flow through the sides, what is the temperature at the lead-copper junction? What is the rate of heat flow through the rods?
Solution: In this example, the two rods are in series and their thermal "resistances" therefore add as electrical resistances do in series.


 

Sample problem: Two rods, one lead and the other copper, are connected between metal plates held at 2 C and 106 C. If the rods have a diameter of 10 cm and are 2 m long, what is the rate of heat flow through the rods? Neglect any heat flow through the sides.
Solution: In this example, the rods are in parallel and their thermal "resistances" therefore add as electrical resistances do in parallel.


 

Sample problem: The wall of a house is composed of a solid 3.5 m x 5 m concrete block (15 cm thick) with outside brick veneer (7 cm thick) and is faced on the inside with fiberboard (2 cm thick). If the outside temperature on a cold day is -10C and the inside temperature is 20C, what is the daily cost of replacing the heat leakage?
Solution:
 

Phase transitions for water

 

Sample problem: A 42-g ice cube at -10.0C is placed in a Styrofoam cup containing 350 g of water at 0C. How much ice is in the water at equilibrium?
Solution: In this problem, before setting up the equations, we need to decide if the final system is at 0C or lower. The wrong guess is not lethal. It simply produces a temperature which falls outside the assumed range.

 

Sample problem: A 0.090-kg ice cube at 0 C is dropped into a Styrofoam cup holding 0.35 kg of water at 15 C. Find the final temperature of the system and the amount of ice (if any) remaining.
Solution: Once again, before setting up the equations, we need to decide if the final system is at 0C or lower. The wrong guess is not lethal. It simply produces a temperature which falls outside the assumed range.

 

Radiation

Sample problem: The filament of a light bulb has a temperature of 3000 C and radiates 60 watts of power. The emissivity of the filament is 0.36. Find the surface area of the filament.
Solution:

 

Sample problem: Suppose a person is unclothed and energy is being lost via radiation from a body surface area of 1.40 m2, which has a temperature of 34 C and an emissivity of 0.7. Suppose also that metabolic processes are producing energy at a rate of 115 W. What is the temperature of the coldest room in which this person could stand and not experience a drop in body temperature?
Solution:


Sample problem: The supergiant star Betelgeuse has a surface temperature of about 2900 K and emits a radiant power (in joules per second or watts) of approximately P=41030 W, which is about 10,000 greater than that of our Sun. Assuming that Betelgeuse is a perfect emitter (e = 1) and spherical, find its radius.
Solution: The radius of Betelgeuse is twice the distance of the Earth from the Sun, which is even greater than the distance of Mars to the Sun.

 


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