[Yukokano]

A shell-and-tube heat exchanger with one shell pass and two tube passes is to be
designed to condense 3900 kg/hr of steam at 1 atm. The steam may be assumed
to enter the shell side as saturated vapor and leave as saturated liquid. Water is
employed as the cooling fluid in the tubes with an inlet temperature of 40◦C.
Using approximate values for overall heat-transfer coefficients given in Table
10-1, determine a suitable design that specifies (1) the number of tubes in each
tube pass, (2) outlet water temperature, (3) tube diameter and length in each tube
pass, and (4) the mass flow rate of water. Also, estimate the final inside diameter
of the shell that may be required. Consider several alternatives before selecting a
final design and discuss the factors that influenced your design selection.

[Borek]

Please read the forum rules.

[Yukokano]

Hello everyone I'm doing a homework and can't solve this question on my own. I think I should assume exit temperature first then find minimum heat capacity and assume water with minimum flow too. Maybe finding effectiveness will help me to solve problem but I don't know how to start. Table 10-1 is given in attachment. If you can show me the way I 'll do rest of it. Sorry for sharing whole problem but you need every information to have an idea I believe. Here is the question ;
 
A shell-and-tube heat exchanger with one shell pass and two tube passes is to be
designed to condense 3900 kg/hr of steam at 1 atm. The steam may be assumed
to enter the shell side as saturated vapor and leave as saturated liquid. Water is
employed as the cooling fluid in the tubes with an inlet temperature of 40◦C.
Using approximate values for overall heat-transfer coefficients given in Table
10-1, determine a suitable design that specifies (1) the number of tubes in each
tube pass, (2) outlet water temperature, (3) tube diameter and length in each tube
pass, and (4) the mass flow rate of water. Also, estimate the final inside diameter
of the shell that may be required. Consider several alternatives before selecting a
final design and discuss the factors that influenced your design selection.

[Enthalpy]

Hi Yukokano and everyone,

I too understand this as an engineering question, where many solutions exist, and choices are subjective rather than deduced from the goal. Prepare for successive paper trials.

As you pointed out, the output temperature of the coolant is a free parameter between 40°C and 100°C. More coolant flow is a drawback but as it exits cooler then, it makes the exchanger smaller since a bigger temperature difference moves heat. Because condensation transfers heat much more efficiently than the liquid flow of the coolant, I'd take the exit temperature closer to 40°C than 100°C, maybe 60°C. Once you've chosen that, the coolant throughput results from the vapour's throughput and heat of condensation and the coolant's heat capacity.

The given table lets you deduce an exchanger area, not the detailed geometry with lengths and diameters. You have to pick the applicable numbers from it, for the condensation side of the exchanger and for the liquid flow side. Note that some table data refers to a symmetric situation, like liquid-to-liquid, so the liquid-to-wall drops half as much temperature.

As condensation brings heat so efficiently to a surface, maybe the temperature drop at that side of the exchanger elements can be neglected. Please check. But since water is efficient, the drop through the elements' wall is often not negligible and must be evaluated. You need a material that resists corrosion in hot water, there are few (good stainless steel) and they don't conduct heat so well.

The table gives a range of heat transfers. That's real life. The figures can be forecast more accurately (not exactly), but only from semi-experimental data and curves that depend on the flow, especially on turbulence, and need a learning effort. Search keywords: Prandtl number, Nusselt number and so on. Only the very uncommon (and rarely desirable) laminar flows have analytical solutions. Where possible, simple tables like you have save much time. I only wonder how well this table targets heat exchangers.

Once you know an exchanger area, you can choose tubes (or other exchange elements) wider or narrower. Narrow elements reduce the exchanger volume for the same area, and even, they may accept a smaller area if heat has a shorter distance to travel through the fluid to the exchanger's surface. This competes with turbulence, which also brings the heat near to the surface as it moves the fluid itself, and is favoured by wider tubes.

One limit to ever narrower exchange elements is the pressure drop, which can be too big if the area results from narrow long tubes. This is again an engineering choice. The drop too can be estimated from semi-experimental curves (search keywords: Reynolds number), or computed analytically for laminar flows. It relates loosely with 0.5ρV².

One common solution to the pressure drop is to cut a long narrow tube in many short sections that you connect in parallel. Combined with ever narrower elements, this would make the exchanger arbitrarily small. The limits are (a) convenient construction (b) dirt in the fluids. Our lungs and blood vessels do that (to exchange oxygen or glucose, but it's the same problem as heat) down to µm size using a succession or arteries, arterioles, capillaries, and are extremely efficient. If the fluids are clean (closed circuits rather than seawater or atmosphere), then clever manufacturing methods like electrodeposition or lithography can make exchangers tiny.

The other direction, for dirty fluids and easier fabrication, is to favour turbulence at bigger exchanger elements, but without losing too much pressure. This needs specialist skills.