Select Materials for Heat Exchanger Tubes with Substantial Pressure difference

Heat exchanger take heat from one fluid and pass it to a second. The fire-tube array of a steam engine is a heat exchanger, taking heat from the hot combustion gases of the firebox and transmitting it to the water in the boiler. The network of finned tubes in an air conditioner is a heat exchanger, taking heat from the air of the room and dumping it into the working fluid of the conditioner. The radiator in a car performs a similar function. The key element in heat exchanger is the tube wall or membrane which separates the two fluids. It is required to transmit heat and there is frequently a large pressure difference across it.

What are the best materials for making heat exchanger? Or, more specifically, what are the best materials for a conduction-limited exchanger, with substantial pressure difference between the two fluids?

Figure 1 Schematic of a heat exchanger

Design Requirements

Function	Heat Exchanger
Objective	Maximise heat flow per unit area, or per unit weight
Constraints	(a) Support pressure difference Dp (b) Withstand chloride ions (c) Operating temperature up to 150°C (d) Low Cost

Table 1

The Model

First, a little background on heat flow. Heat transfer from one fluid, through a membrane to a second fluid, involves convective transfer from fluid 1 into the tube wall, conduction through the wall, and convection again to transfer it into fluid 2. The heat flux q into the tube wall by convection (in units of W/m2) is described by the heat transfer equation:

(1)

in which h1 is the heat transfer coefficient and DT1 is the temperature drop across the surface from fluid 1 into the wall. Conduction is described by the conduction (or Fourier) equation

(2)

where l is the thermal conductivity of the wall (thickness t) and D T12 is the temperature difference across it.

It is helpful to think of the thermal resistance at surface 1 as 1/h1; that of surface 2 is 1/h2; and that of the wall itself is t/l. Then continuity of heat flux requires that the total resistance 1/U is

(3)

where U is called the 'total heat transfer coefficient '. The heat flux from fluid 1 to fluid 2 is then given by

(4)

where DT is the difference in temperature between the two working fluids. When one of the fluids is a gas, as in an air conditioner, heat transfer at the tube surface contributes most of the resistance; then fins are used to increase the surface area across which heat can be transferred. But when both working fluids are liquid, convective heat transfer is rapid and conduction through the wall dominates the thermal resistance. In this case simple tube elements are used, with their wall as thin as possible to maximise l/t. We will consider the second case: conduction limited heat transfer. Then 1/h1 and 1/h2 are negligible when compared with t/l, and the heat transfer equation becomes

(5)

Consider, now, a heat exchanger with many tubes, each of radius r and wall thickness t with a pressure difference Dp between the inside and outside. Our aim is to select a material to maximise the total heat flow, while safely carrying the pressure difference Dp. The total heat flow is

(6)

where A is the total surface area of tubing.

This is the objective function. The constraint is that the wall thickness must be sufficient to support the pressure difference Dp. This requires that the stress in the wall remain below the elastic limit (yield strength) sel (times a safety factor, which need not be included in this analysis):

(7)

Eliminating t between the last two equations gives

(8)

The heat flow per unit area of tube wall, Q/A, is maximised by maximising the performance index:

(9)

Four further considerations enter the selection. It is essential to choose a material that withstands corrosion in the working fluids, which we take here to be water containing chloride ions (sea water). Cost will naturally be of concern. The maximum service temperature must be adequate and the material should be available as drawn tube.

The Selection

A preliminary selection using the Generic filter is shown in Figures 2-4. The first chart is of elastic limit versus thermal conductivity, to allow us to maximise the value of M1. The second stage shows maximum service temperature plotted as a bar-chart against resistance to sea-water, selecting materials with high temperature resistance and high resistance to corrosion in sea-water. The last stage shows a bar chart of material cost against available forms, selecting cheap materials that are available as sheet or tube.

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Figure 2 A Chart of Elastic Limit versus Thermal Conductivity

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Figure 3 A Bar-chart of Maximum Service Temperature versus Resistance to Sea-Water Corrosion

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Figure 4 Material Cost against Available Forms

The results of this selection are shown in Results Table 1, and they suggest that it may be worth transferring the selection criteria to the coppers database to refine the search for a suitable material.

Results

Material (ranked by M1)	Comment
High Conductivity Coppers	Have the best performance index, but relatively poor corrosion resistance
Brasses	Again, relatively poor corrosion resistance
Wrought Martensitic Stainless Steel	A good choice, but steel is more dense than copper
Aluminium Bronzes	An economical and practical choice

Table 1 The Results of the Selection using the Generic Filter

Material (ranked by M1)	Comment
90/10 Aluminium bronze, cold wkd (wrought)	The aluminium bronzes are cheap
92/8 Aluminium bronze, hard (wrought)
93/7 Aluminium bronze, hard (wrought)
95/5 Aluminium bronze, 1/2 hard (wrought)
95/5 Aluminium bronze, hard (wrought)
Nickel iron aluminium bronze, as extruded (wrought)	The Nickel iron aluminium bronzes are more corrosion resistant
Nickel iron aluminium bronze, hot wkd (wrought)

Table 2 The Results of the Selection by expanding the coppers branch

PostScript

Conduction may limit heat flow in theory, but unspeakable things go on inside heat exchangers. Sea water - often one of the working fluids - seethes with biofouling organisms which attach themselves to tube walls and thrive, creating a layer of high thermal resistance and impeding fluid flow, like barnacles on a boat. Some materials are more resistant to biofouling than others; copper-nickel alloys are particularly good, probably because the organisms dislike copper salts, even in very low concentrations. Otherwise the problem must be tackled by adding chemical inhibitors to the fluids, or by scraping - the traditional winter pass-time of boat owners.

It is sometimes important to minimise the weight of heat exchangers. Repeating the calculation to seek materials for the lightest heat exchanger gives, instead of M, the index:

Equation (10)

where r is the density of the materials from which the tubes are made. This is quite a different index - the strength varies to the power 2 because the weight depends on the wall thickness, and from Eqn 7 we know that wall thickness varies as 1/strength.

Of course, all copper alloys have roughly the same density, so there is little point applying this index within the coppers in the database - but if copper alloys were compared with stainless steel tube at the Generic level, then it would be relevant.

Stainless Steel Relative Cost Data
Costs Of Different Metals Used In Mechanical Engineering
What is the low cost superior optimal Heat Exchangers?
Select Materials for Heat Exchanger Tubes with Substantial Pressure difference