Unformatted text preview: Review problems 659 The Coutte ﬂow of a ﬂuid between two parallel plates is considered. The temperature distribution is
to be sketched and determined, and the maximum temperature of the ﬂuid, as well as the temperature of the
fluid at the contact surfaces with the lower and upper plates are to be determined. Assumptions Steady operating conditions exist. Properties The viscosity and thermal conductivity of the ﬂuid are given to be p = 08 Ns/m2 and kf= 0.145
W/mK. The thermal conductivity of lower plate is given to be kp = 15 W/mK. Analysis: (a) Insulation ‘ v9 fee. 9". ova’0 9‘2'7'9'0 9 7‘0. vvv .‘Q'
202020:¢I¢$2€OI§OX¢I029202631020102033301020202.10‘ r, = 40°C k,, The sketch of temperature distribution is given in the ﬁgure. We observe from this ﬁgure that there are
different slopes at the interface (y = 0) because of different conductivities (k,, > kf). The slope is zero at the
upper plate 02 = L) because of adiabatic condition. (b) The general solution of the relevant differential equation is obtained as follows: u=lV———)iu—=lf—
L dy L
2 2 _ 2
a; if? iLJLwCI
dy kf L dy kf L2
—/l V2 2 a
T:———— +C +C
Zkf L2 y 1y 2
Applying the boundary conditions:
. . dT T(0)—T
””17“”? 7:7
y=0 y o p
kp
kal =T(C2 ‘TJ (1)
2
y=L.adiabatic dT =0————)Cl:iZ——
dy L kf L
k 2
FromEq. (1), C2 :b—fC] +Tv =b—g—V—+Tx
kp ' kp L Substituting the coefﬁcients, the temperature distribution becomes ...
View
Full Document
 Spring '06
 Rajadas

Click to edit the document details