Respuesta :
Given Information:
Velocity of water flow = 2 m/s
Temperature of water = 17° C
Heat dissipation = 2500 W
Area of copper plate = 0.04 m²
Required Information:
Temperature of copper plate = ?
Answer:
[tex]T_{p} = 27[/tex]° [tex]C[/tex]
Explanation:
Each chip dissipates 25 W so 100 chips will dissipate 25*100 = 2500 W
Area of copper plate = 0.2*0.2 = 0.04 m²
According to the convection rate equation
[tex]T_{p}= T_{w} + \frac{q}{hA}[/tex]
Where Tp is the temperature of copper plate, Tw is the temperature of water, q is the the heat dissipation of chips, A is the area of copper plate and h is the convection coefficient
The convection coefficient is given by turbulent flow correlation
[tex]h = Nu_{L}(k/L) =0.037Re_{L}^{4/5}P_{r}^{1/3}(k/L)[/tex]
Where Nu is Nusselt number, Re is Reynolds number, Pr = 5.2 is Prandtl number and k = 0.620 W/m.K
[tex]Re_{L}= uL/v[/tex]
Where u = 2 m/s and L = 0.2 m and v = 0.96x10⁻⁶m² /s
[tex]Re_{L}= 2*0.2/0.96x10^{-6}[/tex]
[tex]Re_{L}= 416666.66[/tex]
[tex]h = 0.037(416666.66)^{4/5}(5.2)^{1/3}(0.620/0.2)[/tex]
[tex]h = 6223.89[/tex] [tex]W/m^{2}K[/tex]
[tex]T_{p}= 17 + \frac{2500}{(6223.89)0.04}[/tex]
[tex]T_{p} = 27[/tex]° [tex]C[/tex]
Therefore, the temperature of the copper plate is 27° C
