Objectives Finish Heat Exchanger Dry HX analysis Extend dry analysis to condensing surfaces

Heat exchanger performance (11.3) NTU – absolute sizing (# of transfer units) ε – relative sizing (effectiveness) Criteria NTU εPRP crcr

Counterflow Heat Exchangers Important parameters:

Example HW4 problem For the problem 9 HW assignment # 2 (process in AHU) calculate: a) Effectiveness of the cooling coil b) U o A o value for the CC Inlet water temperature into CC is coil is 45ºF AHU M CC steam RA OA Qcc=195600Btu/h t M =81ºF t CC =55ºF CC (mc p )w t c,in =45ºF

Summary Calculate efficiency of extended surface Add thermal resistances in series If you know temperatures Calculate R and P to get F, ε, NTU Might be iterative If you know ε, NTU Calculate R,P and get F, temps

Fin Efficiency Assume entire fin is at fin base temperature Maximum possible heat transfer Perfect fin Efficiency is ratio of actual heat transfer to perfect case Non-dimensional parameter t F,m

Fin Theory pL=L(h c,o /ky) 0.5 k – conductivity of material h c,o – convection coefficient

Analysis of Moist Coils I Redo fin theory II Energy balance on fin surface, water film, air -I ntroduce Lewis Number - Digression – approximate enthalpy III Redo fin analysis for cooling/ dehumidification (t → h)

1. Redo Fin Theory Same result

II. Energy and mass balances Steady-state energy equation on air Energy balance on water Mass balance on water Lewis number Rewrite energy balance on water surface Reintroduce h g0 (enthalpy of sat. water vapor at 0 °C or °F)

Lewis Number Lewis number, Le = α/D c Ratio of heat transfer to mass transfer Table 9.1 (for forced convection c = 2/3)

Two Important Results 1) – relates process to psychrometric chart

2) Digression – Approximate Enthalpy Over a narrow range of temperature h s = a + bt s a and b based on average values over temperature range

III Fin analysis for wet fins Heat conduction only occurs in y-direction through water film

Overview of Procedure III 1.Same approach as for dry fin with addition of conduction through water film 2.Define “fictitous moist air enthalpy” define at water surface temperature 3.Define heat-transfer coefficient 4.Develop new governing equation

Overall Heat Transfer Coefficients Very parallel procedure to dry coil problem U-values now influenced by condensation See Example 11.6 for details

Real Wet Heat Exchangers

Wet Surface Heat Transfer If you know dry surface heat transfer Reynolds number changes – empirical relationships Approximate wet-surface Does a wet or a dry coil have higher or lower heat exchange? Does a wet or a dry coil have higher or lower pressure drop?

Enthalpy wheel

Psychrometrics of Enthalpy Wheel