Heat transfer involves the movement of thermal energy due to temperature differences. It occurs through conduction, convection, and radiation. Below are the key formulas for each mode of heat transfer:
1. Conduction
Heat transfer through a solid material due to temperature difference.
Formula:
\[
Q = \frac{k \cdot A \cdot (T_1 – T_2) \cdot t}{d}
\]
Where:
\( Q \) = Heat transferred (Joules or \( \text{J} \))
\( k \) = Thermal conductivity of the material (\( \text{W/m·K} \))
\( A \) = Cross-sectional area (\( \text{m}^2 \))
\( T_1, T_2 \) = Temperatures on either side (\( \text{K} \) or \( \degree \text{C} \))
\( d \) = Thickness of the material (\( \text{m} \))
\( t \) = Time (\( \text{s} \))
2. Convection
Heat transfer between a surface and a fluid in motion.
Formula:
\[
Q = h \cdot A \cdot (T_s – T_\infty)
\]
Where:
\( Q \) = Heat transferred (\( \text{J} \) or \( \text{W} \))
\( h \) = Convective heat transfer coefficient (\( \text{W/m}^2\cdot\text{K} \))
\( A \) = Surface area (\( \text{m}^2 \))
\( T_s \) = Surface temperature (\( \text{K} \) or \( \degree \text{C} \))
\( T_\infty \) = Fluid temperature (\( \text{K} \) or \( \degree \text{C} \))
3. Radiation
Heat transfer through electromagnetic waves.
Formula:
\[
Q = \sigma \cdot \epsilon \cdot A \cdot (T_1^4 – T_2^4) \cdot t
\]
Where:
\( Q \) = Heat transferred (\( \text{J} \))
\( \sigma \) = Stefan-Boltzmann constant (\( 5.67 \times 10^{-8} \, \text{W/m}^2\cdot\text{K}^4 \))
\( \epsilon \) = Emissivity of the surface (unitless, \( 0 \leq \epsilon \leq 1 \))
\( A \) = Surface area (\( \text{m}^2 \))
\( T_1, T_2 \) = Temperatures of the radiating bodies (\( \text{K} \))
\( t \) = Time (\( \text{s} \))
4. Heat Energy (General Formula)
The general formula to calculate heat energy is:
Formula:
\[
Q = m \cdot c \cdot \Delta T
\]
Where:
\( Q \) = Heat energy (\( \text{J} \))
\( m \) = Mass (\( \text{kg} \))
\( c \) = Specific heat capacity (\( \text{J/kg·K} \))
\( \Delta T \) = Change in temperature (\( \text{K} \) or \( \degree \text{C} \))
5. Latent Heat
For phase changes without temperature change.
Formula:
\[
Q = m \cdot L
\]
Where:
\( Q \) = Heat energy (\( \text{J} \))
\( m \) = Mass (\( \text{kg} \))
\( L \) = Latent heat (\( \text{J/kg} \))
6. Rate of Heat Transfer
If calculating the rate of heat transfer:
Formula:
\[
\dot{Q} = \frac{Q}{t}
\]
Where:
\( \dot{Q} \) = Heat transfer rate (\( \text{W} \))
\( Q \) = Heat energy (\( \text{J} \))
\( t \) = Time (\( \text{s} \))
These formulas provide a foundation for understanding and solving heat transfer problems.
