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.
Fourier Number
Dimensionless Time Ratio
The ratio of the rate of heat conduction through a body to the rate of thermal energy storage within that body acts as a non-dimensional measure of transient heat transfer. For paper machine drying sections and heat seal operations, the fourier number represents the dimensionless time elapsed during a thermal process. A higher value indicates faster heat penetration through the thickness of the paperboard sheet, which determines the required duration of heating contact.
Thermal Penetration Rate
Thin paper sheets dry almost instantly because their small thickness yields a high value for this non-dimensional parameter, allowing rapid equilibration with the drying cylinder temperature. Conversely, thick folding boxboards require much more time to reach thermal equilibrium, as the fourier number is inversely proportional to the square of the material thickness. This relationship implies that doubling the sheet thickness increases the heating time required to achieve the same core temperature by a factor of four.
Process Cycle Influence
High-speed rotary sealing jaws on packaging lines operate with contact times as short as twenty milliseconds, limiting the available heat transfer. Under these conditions, the fourier number must be calculated to verify if the seal interface will reach the activation temperature during the brief jaw contact.