Chapter 11: Problem 8
What are the heat transfer mechanisms involved during heat transfer in a liquid-to-liquid heat exchanger from the hot to the cold fluid?
Chapter 11: Problem 8
What are the heat transfer mechanisms involved during heat transfer in a liquid-to-liquid heat exchanger from the hot to the cold fluid?
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Get started for freeGeothermal water $\left(c_{p}=4250 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\( at \)75^{\circ} \mathrm{C}$ is to be used to heat fresh water \(\left(c_{p}=4180 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) at \(17^{\circ} \mathrm{C}\) at a rate of \(1.2 \mathrm{~kg} / \mathrm{s}\) in a double-pipe counterflow heat exchanger. The heat transfer surface area is $25 \mathrm{~m}^{2}\(, the overall heat transfer coefficient is \)480 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$, and the mass flow rate of geothermal water is larger than that of fresh water. If the effectiveness of the heat exchanger must be \(0.823\), determine the mass flow rate of geothermal water and the outlet temperatures of both fluids.
A one-shell-pass and eight-tube-passes heat exchanger is used to heat glycerin $\left(c_{p}=0.60 \mathrm{Btu} / \mathrm{lbm} \cdot{ }^{\circ} \mathrm{F}\right)\( from \)80^{\circ} \mathrm{F}\( to \)140^{\circ} \mathrm{F}$ by hot water $\left(c_{p}=1.0 \mathrm{Btu} / \mathrm{lbm} \cdot{ }^{\circ} \mathrm{F}\right)\( that enters the thin-walled \)0.5$-in-diameter tubes at \(175^{\circ} \mathrm{F}\) and leaves at \(120^{\circ} \mathrm{F}\). The total length of the tubes in the heat exchanger is \(400 \mathrm{ft}\). The convection heat transfer coefficient is $4 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}\( on the glycerin (shell) side and \)50 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}$ on the water (tube) side. Determine the rate of heat transfer in the heat exchanger \((a)\) before any fouling occurs and \((b)\) after fouling with a fouling factor of \(0.002 \mathrm{~h} \cdot \mathrm{ft}^{2}-\mathrm{F} / \mathrm{B}\) tu on the outer surfaces of the tubes.
A heat exchanger is used to condense steam coming off the turbine of a steam power plant by cold water from a nearby lake. The cold water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)$ enters the condenser at \(16^{\circ} \mathrm{C}\) at a rate of \(42 \mathrm{~kg} / \mathrm{s}\) and leaves at \(25^{\circ} \mathrm{C}\), while the steam condenses at $45^{\circ} \mathrm{C}$. The condenser is not insulated, and it is estimated that heat at a rate of \(8 \mathrm{~kW}\) is lost from the condenser to the surrounding air. The rate at which the steam condenses is (a) \(0.228 \mathrm{~kg} / \mathrm{s}\) (b) \(0.318 \mathrm{~kg} / \mathrm{s}\) (c) \(0.426 \mathrm{~kg} / \mathrm{s}\) (d) \(0.525 \mathrm{~kg} / \mathrm{s}\) (e) \(0.663 \mathrm{~kg} / \mathrm{s}\)
Hot oil \(\left(c_{p}=2.1 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) at \(110^{\circ} \mathrm{C}\) and \(12 \mathrm{~kg} / \mathrm{s}\) is to be cooled in a heat exchanger by cold water \(\left(c_{p}=4.18\right.\) $\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K})\( entering at \)10^{\circ} \mathrm{C}$ and at a rate of \(2 \mathrm{~kg} / \mathrm{s}\). The lowest temperature that oil can be cooled in this heat exchanger is (a) \(10^{\circ} \mathrm{C}\) (b) \(24^{\circ} \mathrm{C}\) (c) \(47^{\circ} \mathrm{C}\) (d) \(61^{\circ} \mathrm{C}\) (e) \(77^{\circ} \mathrm{C}\)
How is the NTU of a heat exchanger defined? What does it represent? Is a heat exchanger with a very large NTU (say, 10 ) necessarily a good one to buy?
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