Why do cars heat up so quickly in the summer and get so cold in the winter?
Why does tile feel colder than carpet?
Why do large bodies of water take so long to heat up?
Why do computers have fins embedded in their circuitry?
Let’s learn some concepts first so we can answer these questions. There isn’t a moment when heat transfer is not taking place. A bead of sweat evaporating from a warm brow, a refrigerator extracting heat from various foods and beverages and expelling it out the backside, a pot of water boiling in preparation for a delicious meal, and the sun warming a remote alpine lake to name a few.
First, heat and temperature are NOT the same thing. Heat is the flow of energy due to a temperature difference. It always flows from hot to cold. How amazing would it be if when touching a hot stove, heat transferred out of a hand into the already hot stove? Instead heat predictably dissipates from the hot temperature body to the cooler one it’s in contact with. As humans we crave nothing more than comfortable temperatures. We yearn for warmth to escape the cold of winter and the refreshing coolness from air conditioning on a brutal summer day. Our preferences are so strong that men and women stereo-typically never seem to agree on the optimal temperature. Better understanding the principles of heat transfer can help us better enjoy and understand the world around us.
The three modes of heat transfer are:
- Conduction
- Convection
- Radiation
Conduction
Conduction is the physical contact of two substances at different temperatures. Collisions at the atomic level transfer heat through the length of the material and eventually to the material(s) it is in contact with. The governing equation is:
where Q = the amount of heat transferred, k = the object’s thermal conductivity. A = Surface area, ΔT = the temperature difference, t = the object’s thickness
It is an intuitive equation, if surface area increases the number of molecular interactions increases and therefore the quantity of heat transfer increases. Increasing the thickness of the metal makes it tougher to transfer heat. The most interesting quantity is thermal conductivity, k. Thermal conductivity is a material property. Copper metal pots transfer heat to food much more efficiently than ceramic pots do due to their higher thermal conductivity. Metal, due to their abundance of free electrons, have high thermal conductivity values. This is why cars heat up in the summer and get frigid in the winter. The metal that makes up the car transfers heat very efficiently; it quickly reaches the temperature of its environment. This is why we don’t insulate our homes with metal. The entire purpose of insulation is to pick a material that has low thermal conductivity to minimize the heat flow into or out of a home.
The answer to the above question, “why tile feels colder than carpet?” is also answered by thermal conductivity. Assume that the temperature in a home is at a constant 70 °F. The tile somehow feels colder than carpet or even hardwood though they are all at the same bulk temperature of 70 °F. The Surface area and thickness remain constant between the surfaces. The internal temperature of a human is about 98.6 °F so the temperature difference is 98.6 °F – 70 °F = 28.6 °F. It feels colder to a person touching the tile so the heat transferred, Q must be greater compared to carpet and hardwood. Thermal conductivity is the difference maker not temperature. The Engineering Toolbox has tabulated values of thermal conductivity for a variety of materials. The thermal conductivity of tile is 172 times better than wool carpet at transferring heat. The data for the calculations is found below:
| k, tile (W/m*K) | k, hardwood (W/m*K) | k, carpet (W/m*K) | Q, tile (W) | Q, hardwood (W) | Q, carpet (W) |
| 5 | 0.16 | 0.029 | 79.44 | 2.54 | 0.461 |
Water has a thermal conductivity of 0.58 compared to air which has a much lower value of 0.024. Based on thermal conductivity alone water should heat up faster than air. However, from experience we all know that is not the case. There is another thermodynamic property that causes large bodies of water to take longer to heat up compared to air, heat capacity. Heat capacity is the amount of energy it takes to cause one gram of substance to rise one degree Celsius. A calorie by definition is the amount of energy to cause 1 gram of water to rise by 1 degree Celsius. The equation for heat capacity is found below:
where c = specific heat capacity (J/g°C), Q = heat (J), m = mass of substance (grams), ΔT = the temperature difference (°C)
Water’s inter-molecular hydrogen bonding allows more energy to be stored in those bonds before a temperature change is manifest. Water’s heat capacity is 10x greater than iron’s and 4x greater than air’s. This explains the disparity in temperature rise as the air heats up and the lake water remains cold throughout the spring. A lake requires 4x the energy transferred that the air does to see a 1 degree temperature rise.
Convection
Convection is the transfer of heat by a fluid via bulk flow. Getting cooled down by the wind and cooking pasta with boiling water are two examples.
As particles heat up they rise due to their lower density and by so doing transfer heat and allow other particles to heat up and so on. Boiling is the best example of this. Nucleate bubbles rise as they are heated until they collapse at the surface transferring heat throughout the pot. The equation for convection is found below:
where Q = heat (J), h = the convection coefficient (W/m^2*K), T∞ = the temperature of the bulk fluid (K), Ts = the temperature of the surface being heated (K).
The convection coefficient is a function of the fluid and the speed of that fluid among other factors. Water has higher h values than air which should makes sense because water is more dense and would transfer more heat due to the increased amount of molecules a given surface is in contact with. Convective coefficient values also increase as the velocity of the fluid increases. This is why fans are used to cool electronics; air is more efficient in convective heat transfer when the hotter air is blown away. This is called forced convection. The Engineering Toolbox created the plot below that shows the relationship between the speed of air and its convection coefficient.
Computers have fans in their cicuitry to increase the convection coefficient, but they also use fins. Heat leaves the computer and travels up the long thin fins before the air cools it via forced convection. The fins don’t affect the heat transfer coefficient. Instead they increase the surface area which also increases heat transfer and prevents the computer from overheating. A picture of this type of heat transfer optimization is found below.
Radiation
Radiation is the emission of electromagnetic energy by a substance and the absorption of that energy by another substance. Simply put, any time you see something that is bright/red hot like a coal or the sun it is transferring heat via radiation. The math behind radiation is complex, but the bottom line is the closer an object is to a black body the better the heat transfer. As we all know wearing dark colored shirts is not a good way to stay cool in the summertime!
Now most of the time, there are multiple methods of heat transfer simultaneously occurring for a given situation. However, one method usually predominates. I hope this post was instructive and you will look for instances of heat transfer in your own life.
*How Things Work Now is an excellent book with basic explanations covering an array of technical subjects including heat transfer. A link to buy the book is found here
where P = principal, FV = Future Value, r = interest rate, n = compounding period, and t = time
