MODEL OF A PROCESS FOR DRYING Eucalyptus spp AT HIGH TEMPERATURES

A mathematical model of a process for drying of Eucalyptus spp is presented. This model was based on fundamental heat and mass transfer equations and it was numerically solved using a segregated finite volume method. Software in the FORTRAN language was developed to solve the mathematical model. The kinetic parameters of drying for Eucalyptus spp were experimentally obtained by isothermal thermogravimetry (TG). The theoretical results generated using the mathematical model were validated by experimental data.

Diffusion mechanism; heat transfer; kinetic; mathematical model; numerical method; porous media; thermogravimetry; wood

Authorship

P. C. C. PINHEIRO

UFMG, Departamento de Engenharia MecânicaUFMGUFMG, Departamento de Engenharia Mecânica

T. J. RAAD

UFMG, Departamento de Engenharia MecânicaUFMGUFMG, Departamento de Engenharia Mecânica

M. I. YOSHIDA

UFMG, Departamento de Química, IcexUFMGUFMG, Departamento de Química, Icex

SCIMAGO INSTITUTIONS RANKINGS

UFMG, Departamento de Química, IcexUFMGUFMG, Departamento de Química, Icex

UFMG, Departamento de Engenharia MecânicaUFMGUFMG, Departamento de Engenharia Mecânica

Figures | Tables

Figures (7)
Tables (8)

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Figure 1:
Physical Domain - Control volume and boundary conditions.

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Figure 3:
Numerical mesh and variable locations.

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Table 1:
Transport property equations [Pakowski et al (1991)]

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Table 2:
Boundary conditions equations

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Table 3:
Model constant parameters

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Table 4:
General equation parameters

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TREF D(mm) L(mm) mi(g) mf(g) U0(%) r S TSUR h DAV.PG a F[x] a F[r] 75 8.65 13.30 0.6881 0.5795 18.74 742.4 50.4 14.0 3.36 0.80 0.20 100 8.80 13.30 0.7177 0.6000 19.62 742.4 60.2 15.2 3.80 0.80 0.20 125 8.93 13.70 0.7604 0.6365 19.46 742.4 68.0 16.4 4.25 0.80 0.20 150 8.40 12.93 0.6342 0.5318 19.26 742.4 76.0 15.2 4.73 0.80 0.20 175 8.70 13.00 0.6903 0.5743 20.20 742.4 78.4 17.0 5.23 0.80 0.20 200 8.52 13.45 0.6910 0.5688 21.48 742.4 81.9 16.9 5.75 0.80 0.20 225 8.60 13.05 0.6848 0.5636 21.50 742.4 84.9 17.4 6.30 0.80 0.20

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TREF D(mm) L(mm) mi(g) mf(g) U0(%) r S TSUR h DAV.PG a F[x] a F[r] 75 8.98 12.30 0.9526 0.5417 75.86 694.7 49.0 15.1 3.36 0.85 0.85 100 9.33 12.75 1.0739 0.6051 77.47 694.7 54.9 17.4 3.80 0.85 0.85 125 9.02 12.50 0.9947 0.5545 79.38 694.7 60.8 16.8 4.25 0.85 0.85 150 9.42 12.60 1.0992 0.6100 80.21 694.7 64.9 19.5 4.73 0.85 0.85 175 9.19 12.43 1.0463 0.5727 82.69 694.7 68.5 19.1 5.23 0.85 0.85 200 9.53 12.65 1.1312 0.6264 80.59 694.7 71.2 21.8 5.75 0.85 0.85 225 8.89 13.34 1.0131 0.5756 82.05 694.7 73.3 19.1 6.30 0.85 0.85

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TREF D(mm) L(mm) mi(g) mf(g) U0(%) r S TSUR h DAV.PG a F[x] a F[r] *115 10.82 9.63 0.9768 0.4697 108.0 530.9 73.0 - - - - *140 10.32 8.30 0.7768 0.3687 110.7 530.9 80.0 - - - - 115 10.46 9.20 0.8629 0.4197 105.6 530.9 72.5 25.8 4.07 0.75 0.10 140 10.44 7.55 0.6791 0.3430 98.0 530.9 79.2 26.7 4.54 0.75 0.10

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Table 8: Kinetic parameters of 1

Figure 1: Physical Domain - Control volume and boundary conditions.

Figure 3: Numerical mesh and variable locations.

Table 1: Transport property equations [Pakowski et al (1991)]

Equation	Coefficient						Temp rang	Eq N⁰.
Equation	a₀	a₁	a₂	a₃	a₄	a₅	Temp rang	Eq N⁰.
	2.8223	1.1828 x10^-2	-3.5047 x10^-5	3.6010 x10^-8			0 to 350⁰C	(37)
	1.8830	-0.1674 x10^-3	0.8439 x10^-6	-0.2697 x10^-9			20 to 1200⁰C	(38)
	1.0093	-4.0403 x10^-5	6.1760 x10^-7	-4.0972 x10^-10			-40 to 1000⁰C	(39)
	0.3838	5.2533 x10^-3	-6.3689 x10^-6				0.01 to 350⁰C	(40)
	1.7153 x10^-2	1.9569 x10^-4	-3.3839 x10^-6	3.1203 x10^-8	-1.1539 x10^-10	1.6104 x10^-13	0.01 to 300⁰C	(41)
	2.4250 x10^-2	7.8891 x10^-5	-1.7903 x10^-8	-8.5705 x10^-12			-40 to 1000⁰C	(42)
	267.155	374.2	0.38				0.01 to 350⁰C	(43)
	133.322	18.3036	-3816.4	-46.13			0.01 to 350⁰C	(44)

Table 2: Boundary conditions equations

For t = 0, " r, " x

For r = 0, " t

For r= R, x = 0, x = L , t > 0

Table 3: Model constant parameters

Notation	Parameter	Unit	Value	Reference
a _G	gas permeability - x direction	(m²)	1.0x10^-10	Alves and Figueiredo (1989)
a _G	gas permeability - r direction	(m²)	1.0x10^-13	Alves and Figueiredo (1989)
m _G	dynamic viscosity of the gas	(N.s/m²)	2.81x10^-4	Gieck and Gieck (1990)
k_S	thermal conductivity of the solids	(kW/m.K)	1.59x10^-4	Gieck and Gieck (1990)
R_V	vapor equivalent constant	(kJ/kg.K)	0.462	Gieck and Gieck (1990)
R_A	air equivalent constant	(kJ/kg.K)	0.287	Gieck and Gieck (1990)
e	solids porosity	(m³ air/m³sol)	0.64	Gieck and Gieck (1990)
l	solids emissivity	-	0.95	Gieck and Gieck (1990)
s	Stefan-Boltzman constant	(kW/m².K⁴)	5.673x10^-11	Perry and Green (1984)

Table 4: General equation parameters

Eq n⁰

Mathematical Model
Physical Equations

General Equation Parameters

T_REF	D(mm)	L(mm)	m_i(g)	m_f(g)	U₀(%)	r _S	T_SUR	h	D_AV.P_G	a _F[x]	a _F[r]
75	8.65	13.30	0.6881	0.5795	18.74	742.4	50.4	14.0	3.36	0.80	0.20
100	8.80	13.30	0.7177	0.6000	19.62	742.4	60.2	15.2	3.80	0.80	0.20
125	8.93	13.70	0.7604	0.6365	19.46	742.4	68.0	16.4	4.25	0.80	0.20
150	8.40	12.93	0.6342	0.5318	19.26	742.4	76.0	15.2	4.73	0.80	0.20
175	8.70	13.00	0.6903	0.5743	20.20	742.4	78.4	17.0	5.23	0.80	0.20
200	8.52	13.45	0.6910	0.5688	21.48	742.4	81.9	16.9	5.75	0.80	0.20
225	8.60	13.05	0.6848	0.5636	21.50	742.4	84.9	17.4	6.30	0.80	0.20

T_REF	D(mm)	L(mm)	m_i(g)	m_f(g)	U₀(%)	r _S	T_SUR	h	D_AV.P_G	a _F[x]	a _F[r]
75	8.98	12.30	0.9526	0.5417	75.86	694.7	49.0	15.1	3.36	0.85	0.85
100	9.33	12.75	1.0739	0.6051	77.47	694.7	54.9	17.4	3.80	0.85	0.85
125	9.02	12.50	0.9947	0.5545	79.38	694.7	60.8	16.8	4.25	0.85	0.85
150	9.42	12.60	1.0992	0.6100	80.21	694.7	64.9	19.5	4.73	0.85	0.85
175	9.19	12.43	1.0463	0.5727	82.69	694.7	68.5	19.1	5.23	0.85	0.85
200	9.53	12.65	1.1312	0.6264	80.59	694.7	71.2	21.8	5.75	0.85	0.85
225	8.89	13.34	1.0131	0.5756	82.05	694.7	73.3	19.1	6.30	0.85	0.85

T_REF	D(mm)	L(mm)	m_i(g)	m_f(g)	U₀(%)	r _S	T_SUR	h	D_AV.P_G	a _F[x]	a _F[r]
*115	10.82	9.63	0.9768	0.4697	108.0	530.9	73.0	-	-	-	-
*140	10.32	8.30	0.7768	0.3687	110.7	530.9	80.0	-	-	-	-
115	10.46	9.20	0.8629	0.4197	105.6	530.9	72.5	25.8	4.07	0.75	0.10
140	10.44	7.55	0.6791	0.3430	98.0	530.9	79.2	26.7	4.54	0.75	0.10

Table 8: Kinetic parameters of 1

Sample Group	Drying Temperature (⁰C)	Evaporation Temperature (⁰C)	Drying Rate k (s^-1) x 10³	Activation Energy E (kJ/mol)	Pre-exponential factor A (s^-1)
1	100	60.2	1.412	53.78	3.776 x 10⁵
1	125	68.0	2.205	53.78	3.776 x 10⁵
2	100	55.0	1.786	56.44	1.742 x 10⁶
2	125	60.7	2.805	56.44	1.742 x 10⁶
3	115	72.5	1.748	61.70	3.485 x 10⁶
3	140	79.2	2.672	61.70	3.485 x 10⁶

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MODEL OF A PROCESS FOR DRYING Eucalyptus spp AT HIGH TEMPERATURES

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