Question

A pipe system is mainly constructed with ASTM F441 CPVC pipes. The ASME Code for Process Piping (ASME B31.3-2014, Table B-1) recommends that the maximum temperature limit for CPVC pipes be \(93.3^{\circ} \mathrm{C}\). A double-pipe heat exchanger is located upstream of the pipe system to reduce the hot water temperature before it flows into the CPVC pipes. The inner tube of the heat exchanger has a negligible wall thickness, and its length and diameter are $5 \mathrm{~m}\( and \)25 \mathrm{~mm}$, respectively. The convection heat transfer coefficients inside and outside of the heat exchanger inner tube are $3600 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\( and \)4500 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$, respectively. The hot fluid enters the heat exchanger at \(105^{\circ} \mathrm{C}\) with a flow rate of $0.75 \mathrm{~kg} / \mathrm{s}$. In the cold fluid stream, water enters the heat exchanger at \(10^{\circ} \mathrm{C}\) and exits at \(80^{\circ} \mathrm{C}\). Determine whether this double-pipe heat exchanger should employ the parallel flow or the counterflow configuration to ensure that the hot water exiting the heat exchanger is \(93.3^{\circ} \mathrm{C}\) or lower.

Short answer

Answer: Parallel flow configuration should be employed to ensure that the hot water exiting the heat exchanger is at most \(93.3^{\circ} \mathrm{C}\).

Step-by-step solution

Determine the heat transfer area, A

Calculate the heat transfer area using the length and diameter of the inner tube: \(A = \pi d L\), where \(d = 25 \times 10^{-3}\) meters and \(L = 5\) meters \(A = \pi (25 \times 10^{-3})(5) = 0.3927~ \mathrm{m}^2\).

Calculate the overall heat transfer coefficient, U

To find the overall heat transfer coefficient, U, use the given convection heat transfer coefficients inside and outside of the heat exchanger inner tube: \(\frac{1}{U} = \frac{1}{h_{i}} + \frac{1}{h_{o}}\), where \(h_{i} = 3600~ \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(h_{o} = 4500~ \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\) \(U = \frac{1}{\frac{1}{3600}+\frac{1}{4500}} = 2083.33~ \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\).

Determine the heat transfer rate, q

The hot fluid enters the heat exchanger at \(T_{h1} = 105^{\circ} \mathrm{C}\) and leaves at \(T_{h2}=93.3^{\circ} \mathrm{C}\). The cold fluid enters at \(T_{c1} = 10^{\circ} \mathrm{C}\) and leaves at \(T_{c2} = 80^{\circ} \mathrm{C}\). The flow rate, \(\dot{m_{h}} = 0.75~\mathrm{kg}/\mathrm{s}\), and the specific heat, \(c_{p} = 4.18~\mathrm{kJ}/\mathrm{kg}\cdot\mathrm{K}\). Calculate the heat transfer rate using the hot fluid values: \(q = \dot{m_{h}}c_{p}(T_{h1}-T_{h2})\) \(q = (0.75~\mathrm{kg}/\mathrm{s})(4.18~\mathrm{kJ}/\mathrm{kg}\cdot\mathrm{K})(105-93.3)\) \(q = 36.6~\mathrm{kW} = 36600~\mathrm{W}\).

Determine the temperature difference between the hot and cold fluids in the parallel-flow configuration

In parallel flow configuration, the cold fluid temperature difference is: \(\Delta T_{c}^{\mathrm{parallel}} = T_{c2} - T_{c1} = 80^{\circ} \mathrm{C} - 10^{\circ} \mathrm{C} = 70^{\circ} \mathrm{C}\).

Determine the heat transfer rate in the parallel-flow configuration, q_parallel

Calculate the heat transfer rate for this temperature difference using the overall heat transfer coefficient and the heat transfer area found in Steps 1 and 2: \(q_{\mathrm{parallel}} = U A \Delta T_{c}^{\mathrm{parallel}}\) \(q_{\mathrm{parallel}} = (2083.33~\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K})(0.3927~\mathrm{m}^{2})(70~\mathrm{K})\) \(q_{\mathrm{parallel}} = 57577.3~\mathrm{W}\).

Determine the effectiveness of parallel flow configuration

Check if \(q_{\mathrm{parallel}} > q\) to see whether the parallel flow configuration will be effective in maintaining hot water exit temperature at \(93.3^{\circ} \mathrm{C}\) or lower: \(57577.3~\mathrm{W} > 36600~\mathrm{W}\). The parallel flow configuration is effective, and the hot fluid exit temperature will be \(\leq 93.3^{\circ} \mathrm{C}\).

Conclusion

The parallel flow configuration for the double-pipe heat exchanger should be employed to ensure that the hot water exiting the heat exchanger is at most \(93.3^{\circ} \mathrm{C}\).