Inverse thermal problems in computational modelling of the paper vacuum drying process

Figures & data

Table 1. Values of parameters in modified Henderson sorption isotherm model.

n	A (1/K)	B
1.9126	1.3792	1555.6

Figure 1. Relative sensitivity coefficients of temperature field after 100 s after beginning of the vacuum period with respect to heat conduction coefficient (a), evaporation constant (b), lumped diffusion coefficient of water in paper (c) and specific heat capacity (d).

Figure 2. Parts of the paper vacuum drying experimental stand: (a) vacuum chamber and (b) paper coil with thermocouples.

Figure 3. Thermocouples arrangement within (a) the paper coil and (b) initial temperature field. Dimensions are in millimetres and temperatures are in degrees Celsius.

Table 2. Results of the inverse analysis.

Quantity	First approach	Second approach	Third approach
Evaporation	0.5493	0.0391	0.2979
constant, 1 m^−1
α1/X2	6.2858E+00	0.0583	0.0547
α2/X3	5.6129E+00	0.1550	0.1549
α3/X4	−1.1762E+01	0.0848	−0.0758
α4/X5	−1.1433E+01	0.0427	0.0736
α5/X5	−1.0183E+01	0.1220	−0.0623
α6/X6	2.1365E+01	0.0784	0.1062
α7/X7	5.9675E+00	0.0662	−0.0449
α8/X8	5.3273E+00	0.1048	0.0621
α9/X9	−1.1166E+01	0.0795	0.1037
Initial moisture	0.0193	0.0551	0.0204
content (kg)
Objective	1.399E+03	3.187E+02	3.755E+02
function value

Figure 4. Initial moisture distribution obtained with: (a) the first approximation approach, (b) the second approximation approach and (c) the third approximation approach.

Figure 5. Comparison of temperature histories obtained for the first, the second and the third approximation approach with the measurements at points no 2: (a) the best fitting and 3 (b) the worst fitting.