A heat exchanger wall consists of a copper plate 2 cm thick. The heat transfer coefficients on the two sides of the plate are 2700 and 7000 W/( m2 K), corresponding to fluid temperatures of 92 and 32°C, respectively. Assuming that the thermal conductivity of the wall is 375 W/ ( m K), (a) compute the surface temperatures in °C, and (b) calculate the heat flux in W/ m2.
GIVEN
• Heat exchanger wall, thickness (L) = 2 cm = 0.02 m
• Heat transfer coefficients
? hc1 = 2700 W/(m2 K)
? hc2 = 7000 W/(m2 K)
• Fluid temperatures
? Tf1 = 92°C
? Tf2 = 32°C
• Thermal conductivity of the wall (k) = 375 W/( m K) FIND (a) Surface temperatures (Tw1, Tw1) in °F (b) The heat flux (q/A) in W/m2. ASSUMPTIONS
• One dimensional heat transfer prevails
• The system has reached steady state
• Radiative heat transfer is negligible
SKETCH
The thermal circuit for the wall is shown below
The surface temperatures can only be calculated after the heat flux has been established, therefore part
(b) will be solved before part (a).
(b) The resistances are in series, therefore the total resistance is
The total rate of heat transfer is given by
Therefore the heat flux (q/A) is
(a) Equation (1.10) can be applied to the convective heat transfer on the fluid 1 side
Similarly, on the fluid 2 side
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