|
|
|
THERMAL PARAMETERS |
|
Heat generated
by Linear Disc Resistors is dissipated mainly by radiation and convection
from the exposed surface areas. Within restricted domains, mathematical
models may be employed to permit heat transfer estimations. |
|
Symbols |
|
|
∆T |
= Temperature
Rise (°C) |
|
|
Wa |
= Watts / Unit Exposed Surface Area (W.cm
-2) |
|
|
v |
= Volume / Disc
(cm
3) |
|
|
cm |
= Specific Heat Capacity of Active Material = 2J. cm
-3. °C
-1 |
|
|
Do |
= Disc Outside
Diameter (cm) |
|
|
t |
= Resistor Thermal Time Constant (s) |
|
|
Radiation
and Convection
Wa
= 0.00026 (∆T) 1.4
(∆T
= 50 °C to 175 °C, Do = 1.9
cm to 15.1
cm, Ambient 25 °C) |
|
Dynamic Energy
Since the
active material has a negative Temperature Coefficient of Resistance,
estimated energies based on Bridge Resistance will be lower than the
actual. If the Temperature Coefficient is considered then a true Dynamic
Energy will result. |
|
If |
EB
= Energy in Joules based on a Bridge Resistance |
|
|
ED = True Dynamic Energy |
|
|
α = Temperature Coefficient of Resistance (TCR) |
|
Then |
ED
= (2/α).(1 - √(1- αEB)) Joules |
|
|
In this
relationship, α is the fractional (not %) value and the
negative sign has been included in the equation. |
|
Thermal
Conductivity
0.04 W / cm2. °C / cm |
|
Maximum
Insertion Energy Ratings
Disc diameters ≤ 11.2
cm
: ≤ 600 Joules / cm3
(Infrequently)
Disc diameters > 11.2
cm
: ≤ 500 Joules / cm3
(Infrequently) |
|
Recommended
Operating Temperatures
Disc diameters ≤ 11.2 cm :
≤ 300
°C
(Infrequent Operation)
Disc diameters > 11.2
cm
: ≤ 250
°C
(Infrequent Operation)
All Disc diameters:
≤ 150
°C
(Continuous Operation) |
|
Temperature
Rise from Energy Injection
∆T (°C) = Joules (per
disc) / (v x cm)
(Free Air) |
|
Thermal Time
Constant
t
(s) = Max Joules @ 25
°C / Max Watts @ 25
°C |
|
Full Cooling
≥ 4
t |
|
De-rating for other ambient
Temperatures (Ta
°C)
Multiply
Max Joules @ 25
°C & Max Watts @ 25
°C by the ratio (150 - Ta) / 125 |
|
Repetitive
Thermal Impulsing
Assuming that
the Heat Transfer Coefficient α (W / cm 2 .
°C / cm) is constant over the operating temperature range, then the Peak
temperature Rise (∆Tp) associated with repetitive impulsing can be
estimated by way of reference to a classical geometric progression: |
|
If |
∆Tp (°C) = ∆T x (
1 - (e - (
t
/
t
)
)n
) / (
1 - e - ( t
/
t
)
) ...............
1 |
|
Where |
∆T is the Temperature Rise
associated with each electrical impulse (°C)
t
is the Resistor Thermal Time Constant (s)
t is the
Repetition Rate (s)
n is the
number of impulses |
|
If the number of impulses (n)
→
∞ (i.e. continuous duty), then equation 1
can be simplified thus: |
|
|
∆Tp (°C) = ∆T / (
1 - e
- (
t
/
t
)
)
............... 2 |
|
