Power Plant Engineering

84 POWER PLANT ENGINEERING

The heat Q 1 will flow into hot junction and conducted into the two legs, Qk. The Peltier heat Qp
will be produced at the junction due to current flowing through the circuit.

Joule heat Q 1 /2 will flow into the junction. It is assumed that half Joulean heat appears at each
junction. Heat balance at the junction will give,

Q 1 =

1

2 j

Q& = Q&p + Q&k

where Q&p = πp, n I = αp, n = I.T 1

Q&j =I^2 R = l^2 (Rp + Rn)

= I^2

pp nn

pn

L L

AA

ρ ρ

+



Q&k = k∆T = (kp + kn) (T 1 – T 0 )

=

pp nn

pn

kA kA

LL



+



(T 1 – T 0 )

Substituting the values into above equation

Q& 1 = αp, nIT 1 –

1

2

pp nn

pn

L L

AA

ρ ρ

+



I^2 +



+



pp nn

pn

kA kA

LL

(T 1 – T 2 )

The useful power generated,

WL = I^2 RL =

2

L

L

V

R

The voltage across the load,

VL = αp, n (T 1 = T 0 ) – I(Rp – Rn)

By Kirchhoff’s Law

I =

α−,1 0()

++

pn

Lpn

TT

RRR

Let m = L

pn

R

RR+

= Resistance ratio

∴ m + 1 =

pnL

pn

RRR

RR

++

+

Now I =

,10()

()(1)

pn

pn

TT

RR m

α−

++