Chapter 11 Heat Exchangers Heat Exchange between two

Chapter 11: Heat Exchangers • Heat Exchange between two fluids that are at different temperatures and separated by a solid wall. • Specific applications include: space heating and air-conditioning, power production, waste heat recovery, and chemical processing. Heat Exchanger Types • Concentric tube heat exchangers (the simplest heat exchanger, parallel or counter-flow arrangement, Fig. 11. 1). • Cross-flow heat exchangers (Fig. 11. 2). • Shell-and-tube heat exchanger with one shell pass and one tube pass, crosscounterblow mode of operation, Fig. 11. 3). • Shell-and-tube heat exchanger (Fig. 11 -4). (a) One shell pass and two tube passes, (b) Two shell passes and four tube passes. • Compact heat exchanger cores (Fig. 11. 5).

Heat Exchanger Types

THE OVERALL HEAT TRANSFER COEFFICIENT hot fluid Ah q T∞, h, hh δ wall T∞, c, hc Ac cold fluid T∞, h Ts, c Rw or T∞, c

THE OVERALL HEAT TRANSFER COEFFICIENT An overall heat transfer coefficient, analogous to Newton’s law of cooling, is introduced, For a heat exchanger, fins are often added to surfaces exposed to either or both fluids. Surfaces are also subject to fouling by fluid impurities, rust formation, or other reactions between the fluid and the wall material. The subsequent deposition of a film or scale on the surface can greatly increase the resistance to heat transfer between the fluids.

THE OVERALL HEAT TRANSFER COEFFICIENT For a plat surface without fins: For a surface with fins: So , in the expressions for a flat surface, replacing to obtain the expression for a surface with fins: by For fouling , introduce an additional thermal resistance, termed the fouling factor,

TTHE OVERALL HEAT TRANSFER COEFFICIENT The overall surface efficiency can be expressed as: If a straight or pin fin of length L is used an adiabatic tip is assumed:

Log Mean Temperature Difference If Th or Tc varies with position in the heat exchanger, the use of the relation q = UAΔT may Not be appropriate. In this case, it is necessary to work with a rate equation of the form: q = UAΔTm where ΔTm is an appropriate mean temperature difference. The Parallel – Flow Heat Exchanger The temperature difference ΔT is initially large but decays rapidly with increasing x, approaching zero asymptotically. Th, i = Th, l, Th, 0 = Th, 2, Tc, i =Tc, 1, and Tc, 0 = Tc, 2

Log Mean Temperature Difference Applying an energy balance to each of the differential elements of Figure 11. 7, it follows that mhcp, h. Th = dq + mhcp, h (Th + d. Th) or dq = -mhcp, hd. Th = -Chd. Th Similarly, dq = mccp, cd. Tc = Ccd. Tc (11. 10) (11. 11) where Ch and Cc are the hot and cold fluid heat capacity rates, respectively. The heat transfer across the surface area d. A may also be expressed as: dq = UΔTd. A where ΔT = Th – Tc is the local temperature difference between the hot and cold fluids. The differential form of the equation is d(ΔT) = d. Th - d. Tc Substituting Eqs. (11. 10) and (11. 11) into it to obtain

Log Mean Temperature Difference Integrating across the heat exchanger, we obtain Substituting for Ch and Cc from: q = mhcp, h(Th, i - Th, 0) = Ch (Th, i - Th, 0) q = mccp, c(Tc, o – Tc, i) = Cc (Tc, o – Tc, i) Respectively, it follows that

Log Mean Temperature Difference q = UA ΔTlm For the parallel-flow exchanger, ΔT 1 = Th, 1 - Tc, 1 = Th, i- Tc, i ΔT 2 = Th, 2 - Tc, 2 = Th, 0 - Tc, 0 The Counter flow Heat Exchanger ΔT 1 = Th, 1 - Tc, 1 = Th, i- Tc, 0 ΔT 2 = Th, 2 - Tc, 2 = Th, 0 - Tc, i For the same inlet and outlet temperatures, ΔTlm, CF > ΔTlm, PF Also Tc, o can exceed Th, o for counter flow but not for parallel flow.

Log Mean Temperature Difference Special Operating Conditions -- Evaporators and condensers When one of the fluids flowing through a heat exchanger changes phase, that fluid will remain at a constant temperature, provided that its pressure does not change and there is no superheating or subcooling. q = UA ΔTlm = UA = mcp(T 0 – Ti) Take antilog gives = UA

Log Mean Temperature Difference With a circular tube for the cold fluid flowing inside the tube, A =πDx If U = h , Tc = Ts, the above solution is the solution for constant wall temperature in Chapter 8. Multipass and Cross-flow Heat Exchangers ΔTlm = F ΔTlm, CF

Heat Exchanger Analysis: The effectiveness – NTU Method When the fluid inlet temperatures are known and the outlet temperatures are specified or readily determined from the energy balance expressions, it is a simple matter to use the log mean temperature difference (LMTD) method. If only the inlet temperatures are known, use of the LMTD method requires an iterative procedure. The effectiveness – NTU method is more convenient.

The Effectiveness – NTU Method

Effectiveness – NTU Relations

NTU Relations

Effectiveness Relations

Effectiveness-NTU Relations