Convective Heat Transfer in Heating Furnaces

Introduction to Convective Heat Transfer Inside Industrial Furnaces

In earlier discussions, natural convection under free-flow conditions was used to explain heat exchange mechanisms such as heat loss through furnace walls, air ducts, gas ducts, and steam pipes. These principles are useful when estimating external thermal losses, but they cannot be directly applied to the heat transfer that occurs inside a furnace chamber.

The main limitation is that the flow and temperature conditions inside a furnace often fall outside the range of traditional experimental data. Additionally, the surrounding refractory structure influences gas movement and temperature distribution in ways that do not exist in open-air convection studies.

Because of these factors, classical equations for natural convection are not recommended for furnace interior heat-transfer analysis.

Why Free-Convection Formulas Do Not Apply Inside a Furnace

Several fundamental issues prevent direct application:

1. Flow conditions exceed tested ranges

The temperature inside a heating furnace is significantly higher than the experimental conditions used to derive natural convection equations. Gas velocity and turbulence also differ substantially.

2. Wall influence on gas flow

Furnace walls create strong thermal gradients and complex interaction patterns, altering flow velocity and direction.

3. Gas mixture properties differ from pure air

Natural convection formulas are based on the physical constants of air, such as:

• Thermal conductivity (λ)

• Viscosity (μ)

However, the furnace atmosphere is a combustion-gas mixture. Even when applying mixture rules, calculated values cannot accurately represent the real variations occurring inside the furnace.

Because of this, a different approach is required.

Forced Convection Dominates in Furnace Chambers

In most industrial heating furnaces, the motion of combustion gases is driven by burners, jets, and momentum forces. This means:

Gas movement inside the chamber is considered forced convection, not free convection.

Forced convection leads to a different heat transfer mechanism, different temperature distributions, and a different method for calculating heat-transfer coefficients.

Heat Transfer Correlations for Forced Convection

Theoretical analysis and experimental studies indicate that for forced convection:

Nu = φ (Re, Pe)

Where:

• Nu = Nusselt number

• Re = Reynolds number

• Pe = Peclet number

This relationship has been studied most extensively in straight cylindrical tubes under turbulent conditions (Re > 2320). These formulas are valid only when:

• The heat-transfer coefficient is constant

• Wall surface temperature does not change with time

• Fluid temperature profile does not vary along the heating surface

These assumptions rarely hold inside a heating furnace, which is why specialized furnace-specific approaches are needed.

Heat Transfer with Variable Surface and Fluid Temperatures

In earlier chapters, conditions were examined where either wall temperature or fluid temperature changes over time following a defined pattern.

However, in furnace operations, a more common engineering scenario occurs:

Both the fluid temperature and the wall temperature vary along the heating surface.

This condition represents heat exchange between two flowing fluids separated by a wall.

• For the hotter fluid, the wall acts as a cooling surface.

• For the cooler fluid, the wall acts as a heating surface.

Understanding this bidirectional heat-transfer path is essential for accurate furnace design, combustion control, energy efficiency optimization, and product heating uniformity.

Conclusion

Inside a heating furnace, heat transfer cannot be treated using natural convection principles. Forced convection dominates, and temperatures vary continuously along heating surfaces. Modern furnace design relies on advanced convective heat-transfer correlations, turbulence modeling, and real-time measurement to achieve accurate temperature control and high thermal efficiency.