Heat Emission Radiators

Overview

Engineering reference data for Heat Emission Radiators in heat transfer.

Key Formulas

Fourier's Law

$q = -k \nabla T$

Heat flux proportional to temperature gradient.

Convective Heat Transfer

$Q = hA(T_s - T_\infty)$

Heat transfer between surface and fluid.

Stefan-Boltzmann Law

$q = \varepsilon \sigma T^4$

Radiative heat flux from a surface.

Thermal Resistance

$R_{th} = \frac{L}{kA}$

Resistance to heat conduction.

Variables

Radiator Type Constants

The exponent n characterizes the convective behavior of different radiator types:

Higher n values indicate greater reliance on convection rather than radiation for heat transfer.

Log Mean Temperature Difference (LMTD)

The formula employs the logarithmic mean temperature difference between the water and air. For a radiator with inlet temperature $t_i$, outlet temperature $t_r$, and air temperature $t_a$:

$\Delta T_{ln} = \frac{t_i - t_r}{\ln\left(\frac{t_i - t_a}{t_r - t_a}\right)}$

This represents the effective average temperature difference driving heat transfer across the radiator surface.

Nominal Design Conditions

Radiators are typically rated at standard nominal conditions:

• Inlet water temperature $t_i = 80°C$ (or $75°C$ per EN442)
• Outlet water temperature $t_r = 60°C$ (or $65°C$ per EN442)
• Room air temperature $t_a = 20°C$
• Temperature difference $\Delta T = 50°C$

The $P_{50}$ value represents heat output at this 50°C difference and serves as the baseline for performance calculations.

Testing Standards

Different standards specify different test conditions, affecting published heat output ratings:

Switching from BS 3528 to BS EN442 conditions reduces measured heat output by approximately 11%.

Oversized Radiator Considerations

Oversized radiators are common since standard sizes rarely match exact room heat loss. When a radiator is oversized:

• Return water temperature $t_r$ increases above design values
• Water volume flow can be reduced
• The average temperature difference $\Delta T_{ln}$ decreases
• Actual heat emission remains matched to room loss (not exceeding $P_{50}$)

Use the return temperature calculator to determine the resulting $t_r$ and flow rate when operating at partial load.

References

• Original Source