Two metal plates with the same dimension are soldered together face to face. The face of plate 1 that is not touching plate two is keep at T1 = 106 0C. Similarly, plate 2 “open face” is keep at T2 = 0 0C. Assume the thickness of each plate is 3.0 mm and their areas are 82 cm2. For plate 1, K1 = 48.1 W/m-k and for plate 2, k2 = 68.2 W/m-k. Find the heat flow through the plates.
To find the heat flow through the plates, we need to calculate the thermal resistance and the temperature difference across the plates. By applying Fourier's law of heat conduction, we can determine the heat flow using the formula:
Q = (T1 - T2) / (R1 + R2)
where Q is the heat flow, T1 is the temperature of plate 1, T2 is the temperature of plate 2, R1 is the thermal resistance of plate 1, and R2 is the thermal resistance of plate 2.
To find R1 and R2, we can use the formula:
R = (thickness) / (k * area)
where R is the thermal resistance, thickness is the thickness of the plate, k is the thermal conductivity of the plate, and area is the area of the plate.
Let's calculate the thermal resistance of plate 1 (R1):
R1 = (3.0 mm) / (48.1 W/m-K * 0.82 m^2)
To convert the thickness to meters, we divide it by 1000:
R1 = (0.003 m) / (48.1 W/m-K * 0.82 m^2)
R1 = 0.0688 K/W
Similarly, we can calculate the thermal resistance of plate 2 (R2):
R2 = (3.0 mm) / (68.2 W/m-K * 0.82 m^2)
R2 = (0.003 m) / (68.2 W/m-K * 0.82 m^2)
R2 = 0.0589 K/W
Now that we have the thermal resistance, we can calculate the temperature difference (T1 - T2):
(T1 - T2) = 106 °C - 0 °C
(T1 - T2) = 106 °C
Finally, we can substitute the values into the heat flow formula:
Q = (T1 - T2) / (R1 + R2)
Q = 106 °C / (0.0688 K/W + 0.0589 K/W)
Q = 106 °C / 0.1278 K/W
Q ≈ 829.96 W
Therefore, the heat flow through the plates is approximately 829.96 W.