# Heat Transfer

Heat transfer is a discipline in engineering that is used to predict the energy transfer between two objects due to temperature differences. More specifically heat transfer predicts the rate that the energy moves between the two objects. Looking back at thermodynamics the energy that will be transferred between the two objects is heat.

Even though heat transfer and thermodynamics are closely related there are some key differences. For one, thermodynamics looks at systems that are already in equilibrium. Thermodynamics can be used to predict the amount of energy that would be required to change the system from one equilibrium state to another, but it does not predict how quickly this change could occur. Heat transfer on the other hand supplements the first and second laws of thermodynamics so that the energy transfer rates can be determined.

For example what if you have a part that is currently at a temperature of 100 degrees C. You put this part into a volume of water that is currently at 20 degrees C. Now using thermodynamics you can determine the final temperature of the two objects once they reach thermal equilibrium. However, thermodynamics cannot be used to determine how long it would take to reach equilibrium. Heat transfer on the other hand can be used to predict the temperature of both items as a function of time.

## Forms of Heat Transfer

There are three basic forms of heat transfer. They are conduction, convection, and radiation. Conduction is the rate of heat transfer due to the direct conduct between bodies. Conduction can occur in all three phases of mater; solid, liquid, and gas. Convection is the rate of heat transfer caused by a fluid (gas or liquid) moving over another object. Radiation is the rate of heat transfer between two objects of different temperature through space, for example the heat felt from the sun is due to radiation.

## General Equations

### Conduction

(Eq 1) $q_x = -kA\frac{ΔT}{Δx}$

(Eq 2) $R = \frac{Δx}{kA}$

Equation 1 is used to calculate conductive heat transfer. Equation 2 is used to calculate conductive resistance to heat transfer.

### Convection

Equation 3 is used to calculate the convective heat transfer. Equation 4 is used to calculate the resistance to convective heat transfer. Equation 5 is used to find the average convective heat transfer coefficient across a flat plate. Equation 6 is used to find the convective heat transfer rate for fluid flowing through a tube.

(Eq 3) $q = hA(T_w – T_∞)$

(Eq 4) $R = \frac{1}{hA}$

(Eq 5) $\overline{h}_L = \frac{Nu_L k}{L}$

(Eq 6) $h = \frac{Nu_d k}{d}$

(Eq 7) $q_{emitted} = εF_GσAT^4$
(Eq 8) $R = \frac{1 – ε}{ εA}$
(Eq 9) $R = \frac{1}{A_1F_{1-2}}$