Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

Heat flows across the boundaries of each segment along the z-axis by conduction. Fourie r’s law of

heat conduction states that the conductive heat flow per unit area is negatively proportional to the

temperature gradient in the direction of flow. The heat flow from the constant temperature source at

the bott om to the first segment with temperature T

1

is

Q

0

¼kA

T

i

 T

Dz=2



¼

T  T

1

R

1

(6:278)

The term in parenthesis is the temperature gradient, and k is the thermal conductivity of the material.

R

1

represents the thermal resistance at the lower boundary and is computed from

R

1

¼

Dz

2kA

(6:279)

The internal heat flows are described by

Q

i

¼kA

T

iþ1

 T

i

Dz



¼

T

i

 T

iþ1

R

iþ1

,