Modeling Transient Heat Conduction across Clay Coated Folding Cartonboards
Clay coating orientation and core pulp density govern transient thermal lag across cartonboards, dictating minimum dwell times for heat seal activation.
Biot Number
Thermal Resistance Ratio
Thermal conduction resistance within a solid body divided by the thermal convection resistance at its surface provides a dimensionless ratio that determines temperature uniformity during heating or cooling. When assessing paperboard drying or polymer extrusion, the biot number dictates whether temperature gradients within the sheet can be ignored during thermal processing. A value below zero point one indicates that internal heat conduction is fast enough to keep the temperature of the material nearly uniform throughout its volume.
Convective Heat Transfer
High-speed forced air dryers or hot metal drums alter the boundary conditions on the paper web, causing the dimensionless ratio to rise and generating temperature differences between the surface and the core of the sheet. In these scenarios, the biot number rises above the threshold of uniform temperature, meaning that the thermal resistance of the paper board itself governs the rate of heat penetration. This condition requires operators to lower the heating rate to prevent surface thermal degradation while waiting for the core to reach the necessary temperature.
Process Drying Dynamic
Moisture evaporation from the paper web during multi-cylinder drying shifts the local thermal balance and alters the effective heat transfer coefficient. Because of this dynamic shift, the biot number changes throughout the length of the dryer section, requiring precise zone temperature profiles to maintain dry-line stability and prevent curl.