 
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.
Example: Joules (J), kilojoules (kJ), ergs, calories (cal),
kilocalories (kcal), Newtonmeters (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 * ft^{2} * ^{o}F)
 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
r^{2}
 Units: units of length * length (or
length^{2})
Example: m^{2}, cm^{2}, ft^{2}, miles^{2}
 Units: ^{o}C, ^{o}F,
K, R
 T: temperature of the surrounding medium such as the
temperature of the air
 Units: ^{o}C, ^{o}F, 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
Return to Heat Transfer
[Introduction 
Kinetics 
Heat Transfer 
Mass Transfer 
Bibliography]
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.
