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1 2011

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Arctangent Approximation of the Thermal Diffusivity Coefficient in Wood Hot Rolling Process

Malujda I., Marlewski A.

Machine Dynamics Research

2011

Vol. 35, No. 2

20-28

Basing on the measurements of the thermal conductivity A. of beech wood in the temperature λ varying in the range 40-160°C we worked out the arctangent approximation of λ = λ(υ). In this paper we combine it with some formulae for the specific heat capacity cp = cp(υ) and this way we get AK and AS (K as Kirillov, S as Simpson-TenWolde) descriptions of the thermal diffusivity α = λ/(ρ-cp), where the density p remains constant. We provide these functions in all three anatomical directions of wood and this way we have the approximate formulae for the diffusivity α staying in the almost general onedimensional free heat conduction equation. Having this formula we are able to solve numerically this differential equation and, in consequence, we can optimize the hot rolling process to plasticize beech wood layer or sawdust briquettes.