Question

The upper surface of an ASME SB-96 coppersilicon plate is subjected to convection with hot air flowing at \(7.5 \mathrm{~m} / \mathrm{s}\) parallel over the plate surface. The length of the plate is \(1 \mathrm{~m}\), and the temperature of the hot air is \(200^{\circ} \mathrm{C}\). The ASME Boiler and Pressure Vessel Code (ASME BPVC.IV-2015, HF-300) limits equipment constructed with ASME SB-96 plate to be operated at a temperature not exceeding \(93^{\circ} \mathrm{C}\). In the interest of designing a cooling mechanism to keep the plate surface temperature from exceeding \(93^{\circ} \mathrm{C}\), determine the variation of the local heat flux on the plate surface for $0

Short answer

The formula used to calculate the local heat flux on the ASME SB-96 coppersilicon plate in terms of the local heat transfer coefficient is: $$q_x = h_x (T_{air} - T_{plate})$$ where \(q_x\) is the local heat flux, \(h_x\) is the local heat transfer coefficient, \(T_{air}\) is the temperature of the hot air, and \(T_{plate}\) is the temperature of the plate, which must not exceed 93°C.

Step-by-step solution

Calculate Reynolds number

To calculate the Reynolds number, we can use the formula: $$Re_x = \frac{\rho v x}{\mu}$$ where Re_x is the local Reynolds number, \(\rho\) is the air density, v is the air velocity, x is the distance along the plate, and \(\mu\) is the air dynamic viscosity. #Step 2: Calculate Prandtl number#

Calculate Prandtl number

To calculate the Prandtl number, we can use the formula: $$Pr = \frac{c_p \mu}{k}$$ where Pr is the Prandtl number, \(c_p\) is the specific heat capacity at constant pressure, \(\mu\) is the air dynamic viscosity, and k is the air thermal conductivity. #Step 3: Calculate local Nusselt number using correlation for a flat plate#

Calculate local Nusselt number

We can use the following correlation for the local Nusselt number for a flat plate: $$Nu_x = (0.037Re_x^{4/5} - 871) Pr^{1/3}$$ #Step 4: Calculate local heat transfer coefficient#

Calculate local heat transfer coefficient

We can now find the local heat transfer coefficient using the formula: $$h_x = \frac{Nu_x k}{x}$$ where \(h_x\) is the local heat transfer coefficient and \(Nu_x\) is the local Nusselt number. #Step 5: Calculate local heat flux using the local heat transfer coefficient#

Calculate local heat flux

We can calculate the local heat flux using the formula: $$q_x = h_x (T_{air} - T_{plate})$$ where \(q_x\) is the local heat flux, \(h_x\) is the local heat transfer coefficient, \(T_{air}\) is the temperature of the hot air, and \(T_{plate}\) is the temperature of the plate, which must not exceed 93°C. #Step 6: Plot the local heat flux on the plate surface#

Plot the local heat flux

Now we will plot the local heat flux on the plate surface for \(0 \leq x \leq 1 \mathrm{~m}\). Using the formulas discussed in the previous steps, we can calculate the local heat flux values for different x values and plot these on a graph.