Academic Open Internet Journal

Volume 11, 2004

A PREDICTION OF THE THERMAL CONDUCTIVITY OF SAPELLI

Joseph Albert Mukam Fotsing

Senior Lecturer

Email: mukam_fotsing_j_a@fulbrightweb.org

And

Mbatene Takam

Graduate Student

University of Yaounde I

Ecole Normale Supérieure

P. O. Box 3482

Yaounde CAMEROON

Abstract

The measurement of the thermal conductivity of Sapelli is carried out. A comparison of the experimental and theoretical results is made from some calculation models available in the literature. Equations predicting the thermal conductivity according to the moisture content are proposed in the longitudinal, radial, and tangential directions.

Keywords: Sapelli, thermal conductivity, moisture content.

Introduction

Thermal conductivity is one of the physical properties of wood essential to drying. Within the framework of this paper, we will study it using a local wood of Cameroon: Sapelli (Entrandrophragma cylindricum). Wood is a heterogeneous and porous material. The phenomena of heat transfer in wood depends on the geometry of the wood, as well as porosity. Thermal conductivity is different in solids, gases and liquids. As wood is a heterogeneous medium containing the three phases, its thermal conductivity is only an apparent conductivity because it results from complex exchanges concerning simultaneously: conduction in gases, conduction in the liquids, conduction in the solid (constitutive matter). Wood cannot be considered completely dried, so we can classify it among the mediums with three phases: a solid phase of thermal conductivity l_s occupying a fraction of volume (1 - e); a gas phase (air in our case) occupying the voluminal fraction q_a= e - q₁ and of thermal conductivity l_g; a liquid phase occupying the voluminal fraction q₁ and of thermal conductivity l_l.

Materials and method

The experimental principle lies in the determination of the quantity of heat which is transferred through a sample in steady operation. The material we want to measure the conductivity is placed between an isothermal capacity and a box (of parallelepipedic form) surrounded by a framework (figure 1). By imposing on the faces of the sample the temperatures T1 and T2 with T1 > T2, the one-way flow Q crossing surface S of the sample thickness e is given by:

(1)

It comes

(2)

Figure 1: Longitudinal section of the device used for the experiments.

Heat exchange between the box and outside is never null. It is thus difficult to obtain in a uniform way a temperature T_i inside the box equal to that of outside T_e. There is thus a loss Q_osuch as:

Q_t = Q_o + Q (3)

With

Q_o = K(T_e – T_i) (4)

Where K is a factor dependent on the box (in W.°K^-1).

The experimental study was undertaken on Sapelli which is a very abundant wood in the cameroonian forest. This study uses a technique of steady operation and emphasizes the influence on the thermal conductivity of the planes of cuts in wood and the moisture content. We will propose a linear model of conductivity according to moisture according to the three plans of wood.

The experimental device is made up:

- of an isothermal enclosure A of dimension 181 cm X 76 cm x26 cm. A system of cooling of environment: it consists of a heat exchanger supplied with a temperature regulator of fluid.

- of one (or two) box (es) B made of plywood isolated from the interior. One places the wood sample to be tested in this box equipped with a transmitter of heat C.

- temperature gauges on the two faces of the sample

- of a transformer which feeds heating resistance in tension

- of a multimeter which is used to measure the voltage at the boundaries of E like its impedance.

Once the sample is inserted in the box trough the open face, a tension V is applied at the boundary of the transmitter C. Then a liquid flows in the system and a gradient of temperature is produced in the sample. Temperatures T_C and T_F are produced on the hot and cold faces. At the stabilisation of these temperatures the steady state is reached, and we can write the following equations:

- the Joule effect produced by the heater C:

(5)

- thermal losses through box B:

(6)

- conductive flow through the sample

(7)

Where

E is the thickness of the sample (m)

S normal surface with the heat flow (m²)

T_C the temperature of its face higher (hot)

T_F the temperature of its cold face

V the terminal voltage of the transmitter of heat (v)

C₁ the total loss coefficient through the box

R the resistance of transmitter

T_A the ambient temperature of the room

T_B the ambient temperature of the interior of the box.

Then the energy balance is given by:

(8)

what leads finally to:

(9)

In this last equation, some data are measured at the beginning of handling. They are:

the thickness and the sample surface (length multiplied by width). Resistance R is measured after handling. As for the total loss coefficient of the box, it is fixed at 0,16 W.°K-1.

T_A, T_B, T_C, T_F and V. At the beginning of each handling, the sample is weighed and at the end, one obtains a mass M_o which does not vary practically any more. One deduces from the masses initial and finale moisture for each handling.

Experimental Results

L and l are respectively the length and the width of the sample. Equivalent conductivity is given by equation (9) with

S = l x L (10)

After the weighing of a 27x27x3 cm sample, we introduced it into a climatic chamber with the temperatures T_C and T_F ranging between 15°C and 25°C. At the end of a series of measurements, the sample is placed for 48 hours in a drying oven at 105°C in order to obtain the value of the real dry mass. The water content is calculated thereafter and the results are recorded in the tables below.

Table 1: Thermal conductivity in the axial direction according to

Moisture content

H (%)	16,7	21,3	27,3	36,7	42	52,7	60,7	68,7
l (W.m^-1.°K^-1)	0,375	0,4	0,438	0,475	0,463	0,513	0,55	0,54

H (%): Water content of wood

l (W.m-1.°K-1): Conductivity thermal

Table 2: Thermal conductivity in the tangential direction according

to moisture content

H (%)	3,3	8	14	22	25,3	29,3	34	37,3	50	55,3	66,7
l (W.m^-1.°K^-1)	0,16	0,17	0,18	0,20	0,21	0,22	0,23	0,24	0,26	0,29	0,31

Table 3: Thermal conductivity in the radial direction according to moisture content

H (%)	3,3	10	12,7	20,7	24,7	32	36,7	47,3	51,3	61,3	65,3
l (W.m^-1.°K^-1)	0,16	0,19	0,19	0,21	0,23	0,24	0,25	0,29	0,31	0,31	0,32

According to the graphs, we note that l = uH + v where u is the slope of the right-hand side and v the ordinate for a null moisture content in each case. Thermal conductivity thus varies practically in a linear way with moisture content in the material used (Sapelli). We note that this thermal conductivity decreases with moisture content. This remains in conformity with the theory. During drying, water is replaced by gaz, and we know that thermal conductivity of water is higher than that of gas. A meticulous observation leads us to note that the plan of cut has an influence on conductivity, this is explained by the difference between the three equations of right-hand side. By extrapolating the line obtained to the dry state, we have:

(11)

This result is close to that obtained by Maclean (5).

Figure 3: Thermal conductivity as a function of moisture content (axial).

Figure 4 : Thermal conductivity as a function of moisture content (tangential).

Figure 5 : Thermal conductivity as a function of moisture content (radial).

Discussion

We expose here a model of calculation if the space of the pores is saturated by a thermal gas of conductivity l_g and the conductivity of the solid being l_s. The model consists in calculating the limits of the values of the thermal conductivity of wood in a dry state. It is shown that apparent thermal conductivity, for a porosity e of porous and heterogeneous mediums, always lies between conductivities of two mediums (gas /solid) made of parallel layers.

Series model (lower Limit): the mediums consist of solid layers and gases perpendicular to the heat flow.

Figure 6: Perpendicular disposition of the phases solid and gas with the heat flow.

In this case

(12)

Parallel model

The porous environment consists of layers of solid and gases parallel with the heat flow.

Figure 7: Disposition in the direction parallel with the heat flow of the solid and gas phases.

We have

(13)

Application of the models series and parallel to wood

In wood, the solid phase is the substance of the cellular wall (lignin) and the gas phase is the air. The wood saturated with the air is wood in a dry state. For the calculation of l_max and l_min, we will use the tabular values (given by Siau) of l_g = 0,024 W.°K-1.m-1, l_s= 0,44 W.°K-1.m-1, l_{s/ /}=0,88 W.°K-1.m-1 and the physical characteristics (e= e_g) of the sample of Sapelli given by NGOHE-EKAM (2). Then, it will be checked if l_max < L <l_min (experimental values).