Thermal Aspects Of Heat Exchanger Design

THERMAL ASPECTS OF HEAT EXCHANGER DESIGN

Roger A. Crane

Mechanical Engineering

University of South Florida

Introduction

        The technology of heating and cooling of systems is one of the most basic areas of mechanical engineering.  Wherever steam is used, wherever hot or cold fluids are required a heat exchanger is generally found.  They are used to heat and cool homes, cars and offices.  They are used to process foods, paper, petroleum and industrial gases.  They are found in superconductors, fusion power labs, space craft and advanced computers.  The list of applications, in both low and high tech industries, is virtually endless.  Because heat exchangers serve as a basic component for so much of engineering design, special consideration is warranted to their design and operation. Advanced and post graduate courses are available, both from the USF and other graduate programs and through continuing education as presented by the ASME.  The material presented here is intended to serve as only an introduction.  As such it is to provide those students, entering the profession as operation and maintenance engineers a sufficient understanding of heat exchanger principles to quickly master this type of equipment and as a preparatory work for those wishing to continue their preparation and training in this area.  

        At a first glance heat exchanger design is conceptually quite straightforward.  Certainly the basic thermal and hydraulic principles involved have been well understood for some time.  The complications arise first from the large number of design variations which provide almost endless combinations to be considered.  In addition, operational problems, including flow bypass and contamination of heat transfer surfaces during operation and vibration induced material fatigue, are not well correlated at this time and continue to promote service failures.  

        In regard to the large variety of heat exchangers available, this course will consider only the tube in tube and the tube and shell types.  While numerous other types are available, the tube in tube, because of its inherent simplicity, lends itself to academic study; the shell and tube is included as being the most common for large industrial applications.  It is this type that the graduate mechanical engineer is most likely to encounter.  However, for most types of heat exchangers, there is a great deal of commonality to the design process so that many of the concepts developed here can be applied to a variety of basic types.

        Since the primary thrust of this course is toward heat transfer aspects of design, discussions of metal fatigue failure and flow conditions leading toward heat exchanger vibrations are considered to be outside the intended scope.  The student should recognize that the divisions that we, in academics, place on such subject matter is entirely artificial.  While convenient at the educational level, at the industrial level engineers must deal with not only the thermal design, but also with the hydraulic, structural and mechanical design in addition to the aspects of controls, system dynamics and costing. The mention of the fatigue and vibration problems is intended to caution the student to be aware of these considerations and the need to address them.

        

Basic Heat Exchanger Flow Arrangements

        Basic flow arrangements are as shown in Figure 1.  Parallel and counterflow provide alternative arrangements for certain specialized applications.  In parallel flow both the hot and cold streams enter the heat exchanger at the same end and travel to the opposite end in parallel streams.  Energy is transferred along the length from the hot to the cold fluid so the outlet temperatures asymptotically approach one another.  In counter flow the two streams enter at opposite ends of the heat exchanger and flow in opposite directions.  Temperatures within the two streams tend to approach one another in a nearly linearly fashion resulting in a much more uniform heating pattern.  Shown below the heat exchangers are representations of the axial temperature profiles for each.  Parallel flow results in rapid initial rates of heat exchange but rates rapidly decrease as the temperatures of the two streams approach one another.  Counter flow provides for relatively uniform temperature differences and, consequently, lead toward relatively uniform heat rates throughout the length of the unit.

[pic 1][pic 2]

Figure 1.  Basic Flow Arrangements for Tube in Tube Heat Exchangers.

Figure 2.  Heat Transfer Across Tube Wall.

 

Energy Flow        The energy flow between hot and cold streams, when viewed from one end of the heat exchanger, will appear as shown in Figure 2.  Heat transfer will occur by convection to the outside of the inner tube, by conduction across the tube and by convection to the cooler fluid from the inside tube surface.  Since the  heat transfer occurs across the smaller tube, it is this internal surface which controls the heat transfer process.  By convention, it is the outer surface, termed Ao, of this central tube which is referred to in describing heat exchanger area.  Applying the electrical analogy, an equivalent thermal resistance may be defined for this tube.

 

If we define the heat exchanger coefficient, Uc, as:

Substituting the value of R above this yields:

Both convective coefficients, ho and hi, can be evaluated from experimentally developed convective correlations.  Areas and radii are determined from the geometry of the internal tube.  The thermal conductivity, k, corresponds to that for the material of the internal tube.  In this fashion each of the terms are generally available for determining Uc and the term is well defined for most heat exchangers.

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Fouling

        Material deposits on the surfaces of the heat exchanger tube may add further resistances to heat transfer in addition to those listed above.  Such deposits are termed fouling and may significantly affect heat exchanger performance.  The heat exchanger coefficient, Uc,  determined above may be modified to include the fouling factor Rf.  

        Scaling is the most common form of fouling and is associated with inverse solubility salts.  Examples of such salts are CaCO3, CaSO4, Ca3(PO4)2, CaSiO3, Ca(OH)2, Mg(OH)2, MgSiO3, Na2SO4, LiSO4, and Li2CO3.  The characteristic which is termed inverse solubility is that, unlike most inorganic materials, the solubility decreases with temperature.  The most important of these compounds is calcium carbonate, CaCO3.  Calcium carbonate exists in several forms, but one of the more important is limestone.  As water runs through the Florida aquifer, running primarily through openings in limestone rock, it becomes saturated with calcium carbonate.  Water pumped from the ground and passed through a water heater becomes supersaturated as it is heated, so that CaCO3  begins to crystallizes on the internal passages.  Similar results occur when ground water is used in any industrial cooling process.  The material frequently crystallizes in a form closely resembling marble, another form of calcium carbonate.  Such materials are extremely difficult to remove mechanically and may require acid cleaning.