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Cool Thermodynamics Mechanochemistry of Mater ials using none toget none in web,windows applicationc# calculate barcode 128 class 5 . iOS THE FUNDAMENTAL CHILLER MODEL IN TERMS OF READILY-MEASURABLE VARIABLES All exact science is dominated by the idea of approximation. Bertrand Russell A. THE VALUE OF EXPRESSING CHILLER PERFORMANCE IN TERMS OF COOLANT TEMPERATURES Our aim in this chapter is to express the chiller performance equation in terms of readily-measured coolant temperatures, instead of refrigerant temperatures. Coolant temperatures can be measured non-intrusively and can easily be controlled externally.

In contrast, refrigerant temperature measurements usually require intrusive procedures and are problematic to control. Refrigerant temperatures are easily expressed in terms of coolant temperatures through the heat exchanger energy balance equations. This is exactly what we ll be doing in the following sections.

The central pragmatic question is what predictive, diagnostic or optimization capabilities the final result provides. A problem arises because of the complexity of the final formulae. For example, if the objective is to perform diagnostics, or to be able to predict chiller performance over a wide range of operating conditions from a small number of measurements, then for practical purposes the mathematically cumbersome results are of little help.

Nonetheless, in the case studies of s 6 9, we ll show that these unwieldy formulae (in lieu of massive computer simulations) can be used in meaningful chiller optimizations for mechanical and absorption machines. The input to the full inelegant model constitutes independent experimental determination of the model parameters, rather than model parameters arrived at by regression techniques based on a few external measurements. However once the parameters that characterize a given chiller are known, the chiller configuration can be optimized with respect to a number of variables or finite resources of practical interest.

. Fundamental Chiller Model in Terms of Readily-Measurable Variables These are problems commonly of substantial interest to chiller manufacturers and designers. For commercial mechanical chillers, it turns out that approximations can be invoked that convert an unwieldy formula into an equation that is amenable to multiple linear regression. The value and applicability of the fundamental chiller model then extends to the broader user community of cooling engineers and researchers.

We will derive an approximate chiller performance equation with which both diagnostic and predictive studies can be realized. For absorption chillers, the combination of the limited format in which manufacturer catalog data are presented, and the inability to reduce the complete chiller performance formula into one which can be handled with simple regression procedures, restricts the value of the fundamental model to optimization studies only. The formulae will be reviewed in this chapter, but the detailed studies are postponed until 9, where we ll be examining absorption machines (chillers, heat pumps and heat transformers).

. B. DERIVATION FOR MECHANICAL CHILLERS B1. The full expression To the results derived in t none none he preceding chapter, we add the energy balance relations at the heat exchangers in terms of the coolant inlet or outlet temperatures. Qcond = mCE f dT cond evap cond in - Tcond = Qevap = mCE f dT in evap - Tevap mCE i a 1 - E f dT mCE i = a 1 - E f dT cond cond evap evap cond out - Tcond (5.1). out evap - Tevap (5.2). where m is coolant mass flo none for none w rate; C is coolant specific heat; and E is heat exchanger effectiveness; with m, C and E assumed constant. Heat exchanger effectiveness is the ratio of actual to maximum possible heat transfer rates. It is a dimensionless parameter between zero and unity.

The factor E permits us to express the heat transfer equation in terms of the difference between the coolant (inlet or outlet) temperature, and the refrigerant process average temperature, as in Equations (5.1) and (5.2).

The value of E can be calculated for a heat exchanger of known construction, and flows of known m and C values. Formulae for E are tabulated in many texts, e.g.

, [Kreider & Rabl 1994]. The product mCE. Cool Thermodynamics Mechanochemistry of Mater ials is a heat exchanger s effe none none ctive thermal conductance (in units of kW K 1). _________________________________________________________________________ Tutorial 5.1.

For the reader who may not be familiar with the calculation of heat exchanger effectiveness, we offer a simple tutorial. This exercise also highlights the equivalence of a heat exchanger s mCE value and its UA value (U is overall heat transfer coefficient and A is overall heat transfer area). The condenser of a chiller plant comprises a shell-and-tube single-pass counterflow heat exchanger with refrigerant R12 condensing on the shell side.

The refrigerant s condensing temperature is 42 C. The coolant (water) flows in the tubes at an average linear speed of 0.90 m s 1, and has a specific heat C = 4.

2 kJ kg 1 K 1. The coolant enters at 30 C and exits at 33 C. The nominal inner and outer diameters of the tubes are 25 and 30 mm, respectively.

The length of each tube is L = 2.85 m. Assume that the heat transfer resistances from the refrigerant condensing on the tube walls, and from conductance across the tube walls, are negligible.

For evaluating the heat transfer coefficient h t in the tubes, we use the classic Dittus Boelter correlation found in standard textbooks on heat transfer for fully developed turbulent flow in tubes [Holman 1992] to obtain h t = 3.59 kW m 2 K 1 . (i) Determine the overall heat transfer coefficient U of the tubes.

. (ii) Calculate the number o none for none f tubes required for the condenser if the total heat transfer rate required is 450 kW. (iii) Calculate the heat exchanger effectiveness. (iv) Calculate the heat exchanger s effective UA value.

(v) Demonstrate that the heat transfer rate obtained either with mCE or UA is the same. Solution:. (i) With the given approxim ations, we only need to account for the contribution of the coolant flow in estimating the overall heat transfer coefficient U of a single tube. Hence.
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