Heat transfer in the sample is assumed to be one-dimensional because temperatures are measure at centre of surfaces. A differential element in the centre of the sample is taken as volume of control. Equation 1 describes heat transfer in this volume of control.

d2T (x, t) _ 1 dT (x, t)

dx2 a dt (Ec.1)

Where,

X 2

a _ thermal difussivity _ [m / s]

P-cp

X _ thermal conductivity [W /(m — K)]

p _ density [kg / m3 ]

cp _ heat capacity [ J /(kg — K)]

In the experimental setup boundary conditions are:

. at ^ t* = —- = Fo L2

dx*2 dFo

= — Bi в*(1,Fo)

Solution for infinite plane wall is: ад в = X Cn exp(^n2 • Fo) • cos(^n • x*) n=1 C = 4 • sen(L) n 2 •£, + sen (2 •£,) In cases that Fo>0.2: в* = C1 exp(<^2 • Fo) • cos(^1 • x*) = в0* cos(^1 • x*) в0* = в*(x* = 0, Fo) = C1 • exp(<^2 • Fo)

(Ec.2)

(Ec.3)

(Ec.4)

dT_ dx

x=0

= 0

-A

dT_ dx

h [T (T, t) — Tf ]

x=L

The problem can be expressed using non dimensional variables:

* x x = — L

(Ec.5) (Ec.6) (Ec.7)

(Ec.8) (Ec.9)

(Ec.10) (Ec.11)

в T — Tf

в T — Tf

д в дв

дв

dx двв

= 0

x =0

dx

x =1

Bi =

hL T:

where h = forced heat convection coefficient

T (x = 0, t = 0) = T

For each instant measured, Biot and Fourier number are obtained, and then thermal diffusivity is estimated.