Hydrogen gas at \(1 \mathrm{~atm}\) is flowing in parallel over the upper and lower surfaces of a 3-m-long flat plate at a velocity of \(2.5 \mathrm{~m} / \mathrm{s}\). The gas temperature is \(120^{\circ} \mathrm{C}\) and the surface temperature of the plate is maintained at \(30^{\circ} \mathrm{C}\). Using the EES (or other) software, investigate the local convection heat transfer coefficient and the local total convection heat flux along the plate. By varying the location along the plate for \(0.2 \leq x \leq 3 \mathrm{~m}\), plot the local convection heat transfer coefficient and the local total convection heat flux as functions of \(x\). Assume flow is laminar but make sure to verify this assumption. 7-31 Carbon dioxide and hydrogen as ideal gases at \(1 \mathrm{~atm}\) and \(-20^{\circ} \mathrm{C}\) flow in parallel over a flat plate. The flow velocity of each gas is \(1 \mathrm{~m} / \mathrm{s}\) and the surface temperature of the 3 -m-long plate is maintained at \(20^{\circ} \mathrm{C}\). Using the EES (or other) software, evaluate the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient along the plate for each gas. By varying the location along the plate for \(0.2 \leq x \leq 3 \mathrm{~m}\), plot the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient for each gas as functions of \(x\). Discuss which gas has higher local Nusselt number and which gas has higher convection heat transfer coefficient along the plate. Assume flow is laminar but make sure to verify this assumption.

Step by step solution

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1. Calculations for Hydrogen gas

First, we need to calculate the local convection heat transfer coefficient by knowing basic properties such as thermal conductivity, dynamic viscosity, and heat capacity of hydrogen gas at given temperatures. It's necessary to determine the flow regime (laminar or turbulent) by calculating the Reynolds number. Reynolds number, \(Re = \frac{V \cdot x}{\nu}\) If the Reynolds number is less than 5 x 10^5 (Re < 5 x 10^5), we can consider the flow to be laminar. For laminar flow, we can use the following relation to compute the local Nusselt number: Local Nusselt number, \(Nu = 0.332 Re^{\frac{1}{2}} Pr^{\frac{1}{3}}\) The local convection heat transfer coefficient can be calculated using: Local convection heat transfer coefficient, \(h = \frac{k \cdot Nu}{x}\) Once we have the local convection heat transfer coefficient, we can use it to calculate the local total convection heat flux: \(Local convection heat flux = h \cdot A \cdot \Delta T\) where \(A = width \cdot x\) and \(\Delta T = T_\text{surface} - T_\text{gas}\).

02

2. Plotting Hydrogen gas results

Next, we need to plot these quantities as functions of x for hydrogen gas. We should vary the location along the plate (\(0.2 \leq x \leq 3 \mathrm{~m}\)) and create a plot for the local convection heat transfer coefficient and local total convection heat flux.

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3. Calculations for Carbon Dioxide and Hydrogen gases

Next, we need to repeat the calculations (Reynolds number, Nusselt number, and convection heat transfer coefficient) for carbon dioxide and hydrogen gases at the given conditions. We need to determine and verify if the flow is laminar for both gases, and again, we have to use the laminar flow equation for the local Nusselt number.

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4. Plotting CO₂ and H₂ results

Once we have the results for carbon dioxide and hydrogen gases, we need to plot the local Reynolds number, local Nusselt number, and local convection heat transfer coefficient as functions of x for each gas.

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5. Discussion

Finally, based on the plotted results for both gases, we need to discuss which gas has a higher local Nusselt number and convection heat transfer coefficient along the 3-meter-long flat plate.

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