24.53 For fluid flow over a surface, the heat flux to the surface can be computed as dT J = -k- dy where J = heat flux (W/m), k = thermal conductivity (W/m K), T = temperature (K), and y distance normal to the surface (m). The following measurements are made for air flowing over a flat plate that is 200 cm long and 50 cm wide: У, ст 1 T, K 900 480 270 200 If k = 0.028 J/s m K, (a) determine the flux at the surface and (b) the heat transfer in watts. Note that 1 J = 1 W s.

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Chapter8: Natural Convection
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Problem 8.47P
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24.53 For fluid flow over a surface, the heat flux to the surface can
be computed as
IP
J = -k-
dy
where J = heat flux (W/m), k = thermal conductivity (W/m · K),
T = temperature (K), and y = distance normal to the surface (m).
The following measurements are made for air flowing over a flat
plate that is 200 cm long and 50 cm wide:
Y, cm
1
5
Т, К
If k = 0.028 J/s·m· K, (a) determine the flux at the surface and
(b) the heat transfer in watts. Note that 1 J = 1 W s.
24.54 The pressure gradient for laminar flow through a constant
radius tube is given by
900
480
270
200
%3!
dp
8µ Q
dx
where p = pressure (N/m), x = distance along the tube's centerline
(m), u = dynamic viscosity (N · s/m3), Q = flow (m/s), and r =
radius (m).
(a) Determine the pressure drop for a 10-cm length tube for a vis-
cous liquid (u = 0.005 N s/m, density = p = 1 x 10' kg/m)
with a flow of 10 x 10-6 m'/s and the following varying radii
along its length,
%3D
х, ст
2
4
10
T, mm
1.35
1.34
1.6
1.58
1.42
(b) Compare your result with the pressure drop that would have
occurred if the tube had a constant radius equal to the average
radius.
(c) Determine the average Reynolds number for the tube to verify
that flow is truly laminar (Re = pvD/µ < 2100 where v =
velocity).
Transcribed Image Text:24.53 For fluid flow over a surface, the heat flux to the surface can be computed as IP J = -k- dy where J = heat flux (W/m), k = thermal conductivity (W/m · K), T = temperature (K), and y = distance normal to the surface (m). The following measurements are made for air flowing over a flat plate that is 200 cm long and 50 cm wide: Y, cm 1 5 Т, К If k = 0.028 J/s·m· K, (a) determine the flux at the surface and (b) the heat transfer in watts. Note that 1 J = 1 W s. 24.54 The pressure gradient for laminar flow through a constant radius tube is given by 900 480 270 200 %3! dp 8µ Q dx where p = pressure (N/m), x = distance along the tube's centerline (m), u = dynamic viscosity (N · s/m3), Q = flow (m/s), and r = radius (m). (a) Determine the pressure drop for a 10-cm length tube for a vis- cous liquid (u = 0.005 N s/m, density = p = 1 x 10' kg/m) with a flow of 10 x 10-6 m'/s and the following varying radii along its length, %3D х, ст 2 4 10 T, mm 1.35 1.34 1.6 1.58 1.42 (b) Compare your result with the pressure drop that would have occurred if the tube had a constant radius equal to the average radius. (c) Determine the average Reynolds number for the tube to verify that flow is truly laminar (Re = pvD/µ < 2100 where v = velocity).
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