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

 
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
                     
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