Convective and Radiant Heat Transfer Equations

Heat transfer can be represented by numerous different equations. Convective heat transfer is the movement of heat due to fluid movement. If you were to fill a bathtub full of water and then realize that it was too hot, you would add more cold water. If you can relate to such an instance, you know that the cold water is often at the faucet end of the tub, while the hot water stays at the other end. If you swirl the water around though, it mixes. The hot water transfers heat to the cold water by heat convection due to the swirling. Heat convection is also demonstrated in an example discussed for this project. In the example discussing baking a potato in the oven, heat convection is due to the natural movement of the air in the oven. The air in the oven is naturally moving slightly, so it is able to transfer heat from the oven air to the potato through convection.

Radiant heat transfer is the transfer of heat from a heated surface. The most common form of radiant heat transfer is the transfer of heat from the sun to the earth. This is what keeps us warm. We can also see radiant heat transfer while baking a potato in the oven. The oven is heated up and then the heat is transferred radiantly from the walls of the oven to the potato in the oven. Radiant and convective heat transfer are represented by a similar equation. Our task is to introduce the equation and dissect it into understandable parts. The equation below represents both radiant and convective heat transfer.

Q = -hA(T_s – T)

Each symbol stands for a different quantity.

Q: heat transferred (See heat definition)

Units: units of energy

Example: Joules (J), kilojoules (kJ), ergs, calories (cal), kilocalories (kcal), Newton-meters (Nm), or BTU’s

h: heat transfer coefficient: A constant that represents how easily heat can move. When discussing convective heat transfer, h_c is used, whereas when discussing radiant heat transfer, h_r is used. Both values can be found in the literature. They vary depending on what the heat is transferring through.

Units: units of energy / (time*area*temperature)

(Note: area = length * length)

Example: Btu / (h * ft² * ^oF)

A: Area: The space an object takes up in two dimensions.

The area of a square or rectangle can be found by multiplying the lengths of the two sides of the box together. If the length of one side is represented by b, and the length of other is represented by c, then the area can be found by multiplying the two together.

A = b * c

The area of a circular object can be found by multiplying the constant P (3.14) times the length across half of the circle (the radius, r) squared.

A = P r²

Units: units of length * length (or length²)

Example: m², cm², ft², miles²

T_s: temperature at the surface of the object (See temperature definition)

Units: ^oC, ^oF, K, R

T: temperature of the surrounding medium such as the temperature of the air

Units: ^oC, ^oF, K, R

Therefore, returning to the equation,

Q = -hA(T_s – T)

It was shown that the equation describes the heat of the system is equal to the negative heat transfer coefficient times the area, times the change in temperature from the surface to the point at which you are taking the measurement.

Proceed to Convection Example
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This project was funded in part by the National Science Foundation and is advised by Dr. Masel and Dr. Blowers at the University of Illinois.