Fourier’s Law
∆T
∆T
Q′ = A κ
=
L
(L / κ A)
Jx =
dQ
dT
=− κ
dt
dx
Jx ≡
1 dQx
A dt
Q′ = rate of heat flow or the heat current, A = cross-sectional area, κ
= thermal conductivity (material-dependent constant of
proportionality), ∆T = temperature difference between ends of
component, L = length of component
Ohm’s Law
∆V
∆V
I=
=
R
(L / σ A)
I = electric current, ∆V = voltage difference across the conductor, R =
resistance, L = length, σ = conductivity, A = cross-sectional area
Fourier’s Law
∆T
∆T
Q′ = A κ
=
L
(L / κ A) = θ
Q′ = rate of heat flow or the heat current, A = cross-sectional area, κ
= thermal conductivity (material-dependent constant of
proportionality), ∆T = temperature difference between ends of
component, L = length of component
Ohm’s Law
∆V
∆V
I=
=
R
(L / σ A)
=R
I = electric current, ∆V = voltage difference across the conductor, R =
resistance, L = length, σ = conductivity, A = cross-sectional area
Definition of Thermal Resistance
Q′ =
∆T
θ
Q′ = rate of heat flow, ∆T = temperature difference, θ = thermal
resistance
Thermal Resistance
L
θ=
Aκ
θ = thermal resistance, L = length, A = cross-sectional area, κ =
thermal conductivity
Analogy between thermal and electrical phenomena
THERMAL PHENOMENA ELECTRICAL PHENOMENA
Q = rate of heat flow
I = Current
∆T = temperature difference
∆V = bias (voltage)
Θ = thermal resistance
R = resistance
Q′ = ∆T/θ Force)
EMF (Electromotive
Heat reservoir ∆T
Absolute
Hot zero
Q′ =
∆T
θ
Cold
Heat generator
Q′
Q′
A
∆T
Current supply
Ground
Q′
θ
L
(a)
(b)
Fig. 2.23: Conduction of heat through a component in (a) can be
modeled as a thermal resistance θ shown in (b) where Q′ = ∆T/θ.
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
I=
∆V
R
Analogy between thermal and electrical phenomena
THERMAL PHENOMENA ELECTRICAL PHENOMENA
Q = rate of heat flow
I = Current
∆T = temperature difference
∆V = bias (voltage)
Θ = thermal resistance
R = resistance
Heat reservoir
EMF (Electromotive Force)
Absolute zero
Ground
Heat generator
Current supply
Essential Heat Transfer for Electrical Engineers (© S.O. Kasap, 2003: v.2.02) An e-Booklet
Analogy between thermal and electrical phenomena
THERMAL PHENOMENA ELECTRICAL PHENOMENA
Q = rate of heat flow
I = Current
∆T = temperature difference
∆V = bias (voltage)
Θ = thermal resistance
R = resistance
Heat reservoir
EMF (Electromotive Force)
Absolute zero
Ground
Heat generator
Current supply
Ti
T0
Q’=(Ti-T0)/Θ
IR2
Essential Heat Transfer for Electrical Engineers (© S.O. Kasap, 2003: v.2.02) An e-Booklet
Analogy between thermal and electrical phenomena
THERMAL PHENOMENA ELECTRICAL PHENOMENA
Q = rate of heat flow
I = Current
∆T = temperature difference
∆V = bias (voltage)
Θ = thermal resistance
R = resistance
Heat reservoir
EMF (Electromotive Force)
Absolute zero
Ground
Heat generator
Current supply
C = thermal capacitance
C = capacitance
δQ = C δT
Q′ = C
δT
δt
δQ = C δV
I =C
δV
δt
Analogy between thermal and electrical phenomena
and equivalent circuit of transistor
THERMAL PHENOMENA ELECTRICAL PHENOMENA
Q = rate of heat flow
I = Current
∆T = temperature difference
∆V = bias (voltage)
Θ = thermal resistance
R = resistance
C = thermal capacitance
C = capacitance
Heat reservoir
EMF (Electromotive Force)
Absolute zero
Ground
Heat generator
Current supply
Essential Heat Transfer for Electrical Engineers (© S.O. Kasap, 2003: v.2.02) An e-Booklet