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HEAT EXCHANGER
Heat exchange is an important unit operation that contributes to efficiency and safety of many processes. In this project you will evaluate performance of three different types of heat exchangers (tubular, plate, and shell & tube). All these heat exchangers can be operated in both parallel- and counter-flow configurations. The heat exchange is performed between hot and cold water.
Concepts to Review Heat exchanger configurations; parallel vs. counter-current flow LMTD and NTU methods for analysis of heat exchangers Convective and conductive heat transfer Reynolds, Prandtl, and Nusselt numbers Energy balance closure Degrees of Freedom and Performance Indicators
The following degrees of freedom can be varied in this experiment:
Hot water feed temperature Th,i and flow rate ݉ ሶ Cold water feed temperature Tc,i and flow rate ݉ ሶ Heat exchanger type (tubular, shell & tube, or plate) Flow direction (parallel or counter-flow)
You will investigate effects of these variables on the following performance indicators: Return temperatures Th,o and Tc,o of the hot and cold water Heat flow rate q Overall heat transfer coefficient U
Objectives
Investigate effects of the control parameters and the heat exchanger configuration on the rate of the heat transfer, q, and the overall heat transfer coefficient, U. Check validity of the theoretical models. Investigate dependence of convective heat transfer coefficients on the Reynolds number and the flow geometry. To accomplish this goal, it is necessary to experimentally determine contributions of individual convective heat transfer coefficients to the overall heat transfer coefficient U. To isolate contribution of one of the coefficients, vary temperature of only one of the fluids. To obtain dependence of this coefficient on the Reynolds number, vary the flow rate of the corresponding fluid.
Theory
Notes
- The theory presented here is based on Ref. 1. Please refer to this book for more details.
- Subscripts h and c refer to the hot and cold fluids, respectively, and subscripts i and o refer to the inlet and outlet of the heat exchanger, respectively. E.g., T (^) h,i denotes temperature of the hot fluid at the inlet and T (^) c,o denotes temperature of the cold fluid at the outlet.
Overall Heat Transfer Coefficient U
Consider energy balance in a differential segment of a single-pass heat exchanger shown schematically in Fig. 1-1. The rate of heat transfer in this segment is ݀ሻݔሺܣ݀ሻݔሺܶ∆ ܷൌ ሻݔሺݍ , (1) where U is the overall heat transfer coefficient, Δ T is the local temperature difference between the hot and cold fluids, and dA is the contact area in the differential segment. The overall heat transfer coefficient is inversely proportional to the total resistance R (^) tot to the heat flow. The latter is the sum of (1) resistance R (^) conv,h to convective heat transfer from the hot fluid to the partition between the fluids, (2) resistance Rp to thermal conduction through the partition, and (3) resistance R (^) conv,c to convective heat transfer from the partition to the cold fluid. Therefore,
ܷൌ
௧௧
௩, ܴ^ ܴ^ ௩,
Figure 1-1. Energy balance in a differential element of a single pass heat exchanger operated in the counter-flow regime. Red, blue, and gray colors represent the hot fluid, cold fluid, and the partition between the fluids, respectively. The dashed rectangle shows a differential segment corresponding to the energy balance Eq. (1). Three resistances ( R (^) conv,h , R (^) p, and R (^) conv,c ) contributing to the total resistance to the heat transfer are indicated schematically.
Convective heat transfer. Resistance to the convective heat transfer is inversely proportional to the convective heat transfer coefficient, h = 1/ Rconv. The convective heat transfer
- There are no phase changes in the fluids
- Heat capacities of the fluids are independent of temperature
- Overall heat transfer coefficient is independent of the fluid temperature and position within the heat exchanger. Since all heat exchangers considered in this experiment have a single pass for both the hot and cold fluids, the discussion below is limited to single-pass heat exchangers. Qualitative dependence of the fluid temperature on position inside a single-pass heat exchanger is shown in Fig. 1-2.
Logarithmic Mean Temperature Difference (LMTD) Method The total heat transfer rate is ݍ ݀ ൌ ݍଵଶ , (7)
where dq is given by Eq. (1) and points 1 and 2 are defined in Fig. 1-2. This integral cannot be computed by a direct integration of Eq. (1), since Δ T typically varies with position in the heat exchanger, as shown in Fig. 1-2.
Figure 1-2. Temperature profiles in (a) counter-flow and (b) parallel flow single pass heat exchangers. Note that in a counter-flow heat exchanger the outlet temperature of the cold fluid can exceed the outlet temperature of the hot fluid but this cannot happen in a parallel flow system.
However, it is possible to obtain q by combining Eq. (1) with energy balances in differential segments of the heat exchanger,
݀ܥെ ൌ ݍ (^) ܶ݀ ܥ ൌܶ݀ (8)
Here, dT (^) k is the temperature change of fluid k ( k = c or h ) in the interval under consideration, and Ck is the heat capacity rate of fluid k ,
ܥ ݉ൌ ሶܿ ݇, ܿൌ ݄or , (9)
where ݉ ሶ and c (^) k are the mass flow rate and heat capacity of fluid k , respectively. This analysis yields
ܶ∆ ܣ ܷൌ ݍ (^) , (10)
where A is the total contact area and Δ Tlm is the logarithmic mean temperature difference (LMTD),
ܶ∆ (^) ൌ
lnሺ∆ܶ (^) ଵ ܶ∆/ (^) ଶ ሻ
Here, Δ Tk refers to temperature difference between the hot and cold fluids at point k ( k = 1 or 2), i.e.
ܶ∆ (^) ଵ ܶൌ (^) , ܶെ (^) , and ∆ܶ (^) ଶ ܶൌ (^) , ܶെ (^) , (12)
for the counter-current flow and
ܶ∆ (^) ଵ ܶൌ (^) , ܶെ (^) , and ∆ܶ (^) ଶ ܶൌ (^) , ܶെ (^) , (13)
for the parallel flow.
Notes
- If heat capacity rates of the cold and hot fluids are the same and the heat exchanger is operated in the counter-flow regime then Δ T is independent of position in the heat exchanger. In this case Eqs. (10), (11) are not applicable and the total heat transfer rate q should be obtained by direct integration of Eq. (1).
- This result holds for single pass heat exchangers only. However, LMTD method can be extended to more complex heat-exchanger designs (e.g., multi-pass and cross-flow systems) using a correction factor (see Ref. 1). Effectiveness-NTU Method LMTD method is useful for determining the overall heat transfer coefficient U based on experimental values of the inlet and outlet temperatures and the fluid flow rates. However, this method is not very convenient for prediction of outlet temperatures if the inlet temperatures and U are known. In this case, one has to solve a nonlinear system of two equations (Eq. (10) and the overall energy balance) for two unknowns ( Th,o and Tc,o ). This solution requires application of an iterative approach. A more convenient method for predicting the outlet temperatures is the effectiveness- NTU method. This method can be derived from the LMTD method without introducing any additional assumptions. Therefore, the effectiveness-NTU and LMTD methods are equivalent. An advantage of the effectiveness-NTU method is its ability to predict the outlet temperatures without resorting to a numerical iterative solution of a system of nonlinear equations. The heat-exchanger effectiveness ε is defined as
