Question

Saturated liquid propane flows in a circular ASTM rate of $42 \mathrm{~g} / \mathrm{s}\(. The liquid propane enters the tube at \)-50^{\circ} \mathrm{C}$, and the tube surface is maintained isothermal. The tube has an inner diameter of \(25 \mathrm{~mm}\), and its length is \(3 \mathrm{~m}\). The inner surface of the tube has a relative surface roughness of \(0.05\). The ASME Code for Process Piping limits the minimum temperature suitable for using ASTM A268 TP443 stainless steel tube at \(-30^{\circ} \mathrm{C}\) (ASME B31.3-2014, Table A-1M). To keep the tube surface from getting too cold, the tube is heated at a rate of \(1.3 \mathrm{~kW}\). Determine the surface temperature of the tube. Is the ASTM A268 TP443 stainless steel tube suitable under these conditions? Evaluate the fluid properties at \(-40^{\circ} \mathrm{C}\). Is this an appropriate temperature at which to evaluate the fluid properties?

Short answer

Are the fluid properties appropriately evaluated at -40°C?

Step-by-step solution

Calculate propane mass flow rate and flow velocity

First, we'll need to determine the flow velocity of the propane. We can do this by using the mass flow rate (\(\dot{m}\)), which is given as \(42 \mathrm{~g/s}\). We'll need to know the density of the liquid propane (\(\rho\)) at the inlet temperature of \(-50^{\circ} \mathrm{C}\) to calculate. From thermodynamic tables or software, we can find the density of propane at \(-50^{\circ} \mathrm{C}\), which is approximately \(600 \mathrm{~kg/m^3}\). Now we can calculate the flow velocity (\(v\)) using the equation: \(v = \frac{\dot{m}}{\rho A}\), where \(A\) is the cross-sectional area of the tube. Since we know the inner diameter of the tube (\(D = 25 \mathrm{~mm}\)), we can calculate the area as: \(A = \frac{\pi D^2}{4}\). We'll then calculate the flow velocity, \(v\).

Calculate the Nusselt number and heat transfer coefficient

Using flow velocity, we will need to estimate the Reynolds number (\(Re\)) to calculate Nusselt number (\(Nu\)) and heat transfer coefficient (\(h\)). \(Re = \frac{Dv\rho}{\mu}\), where \(\mu\) is the dynamic viscosity of the liquid propane at the given temperature. From thermodynamic tables or software, we can find the dynamic viscosity of propane at \(-40^{\circ} \mathrm{C}\), which is approximately \(8.5 \times 10^{-5} \mathrm{~Pa\cdot s}\). Now we can estimate the Nusselt number for the internal flow of a circular pipe, using the Dittus-Boelter equation: \(Nu = 0.023\mathrm{Re}^{0.8}\mathrm{Pr}^{n}\), where \(\mathrm{Pr}\) is Prandtl number (evaluated at \(-40^{\circ} \mathrm{C}\)) and \(n=0.4\) for heating (since the tube is heated). Once we have the Nusselt number, we can calculate the heat transfer coefficient: \(h = \frac{(Nu)\cdot k}{D}\), where \(k\) is the thermal conductivity of propane at \(-40^{\circ} \mathrm{C}\).

Determine the surface temperature of the tube

Next, we will use the heat transfer coefficient to determine the surface temperature of the tube. The heat rate applied on the tube is given as \(1.3 \mathrm{~kW}\). Using this heat rate and the heat transfer coefficient, we can calculate the temperature difference between the fluid (∆T) by the formula: \(Q = hA\Delta T\). From this formula, we can find the temperature difference: \(\Delta T = \frac{Q}{hA}\). Finally, we can determine the surface temperature (\(T_s\)) of the tube, knowing the fluid's inlet temperature (\(T_i\)), which is \(-50^{\circ} \mathrm{C}\): \(T_s = T_i + \Delta T\).

Evaluate the suitability of the tube and fluid properties

Once we have determined the surface temperature of the tube, we can compare it to the minimum allowed temperature for the ASTM A268 TP443 stainless steel pipe, which is -30°C according to the ASME Code. If the surface temperature is higher than this value, then the selected tube is suitable under these conditions. To evaluate the appropriateness of the fluid properties at \(-40^{\circ} \mathrm{C}\), we need to compare it with the average temperature of the fluid. If the average fluid temperature is close to \(-40^{\circ} \mathrm{C}\), then this temperature is appropriate for evaluating the fluid properties.