Corrigenda for Solar Engineering of Thermal Processes, Fourth Ed. J. A. Duffie and W. A. Beckman

10/20/2014

First Printing Page Where Change 14 Table1.6.1 The values for δ were obtained using Eqn 1.6.1a 15 Example 1.6.1 Cos θ = 0.818 31 Example 1.9.1 Latitude is 45º 63 Table 2.6.1 Add a zero to the last 6 entries of the Midpoint column 219→2190 89 6 lines from top ω2 − 75.0º should be ω2 = −75.0º 93 First line of Solution 0.224 should be 0.244 106 Table header ρs should be ρg 119 3rd line of Solution kT should be k’T 120 Table header K T should be k’T 2nd line after eqn kT should be k’T 125 last line 1.58 should be 0.158 163 Part C solution 6.2 should be 5.4. 186 Column λmid should be 0.416, 0.492, 0.559, 0.627, 0.700, 0.786, 0.885, 1.038, 1.257, 1.750 191 λ at midpoint should be 0.42, 0.49, 0.56. 0.63, 0.70, 0.79, 0.89, 1.04, 1.26, 1,75 229 Eqn 5.11.1 +Ai should be /Ai 230 11 lines up from bottom 0.7 should be 0.3 10 lines up from bottom 1.62 should be 0.70 and 9.18 should be 8.26 8 lines up from bottom 12.2 should be 10.84 7 lines up from bottom 8.18/12.2 = 0.75 should be 8.26/10.84 = 0.76 6 lines up from bottom 75% should be 76% 232 2nd line up from bottom Should read: Instantaneous noon-time measured … 233 Line above Solution Add: ρg is 0.2 243 Eqn 6.4.8 Second Tj should be Ti

Third eqn from bottom (Tp – Tc) should be (Tp + Tc) 245 Line 4 from top Change εg to εc

Third eqn for q Change εp to εc

284 Eqn for F′ (mid page) Missing exponent of 1 on (1/22 + 1/8.3) 286 Eqn for h Exponent should be -1.21 287 Result of ∆p calculation Change 307 Pa to 30.7 Pa 294 Eqn for slope 7.62 should be 7.62 303 Eqn 6.19.4a The 1+ should be like the 1+ of Eqn 6.19.5a 307 Eqn for hfi 8.09 should be 8.9 314 Back-insulation thickness 0.007 m should be 0.07 m 315 15 lines from top Should read: The effective sky temperature … 11 lines from bottom Change 19.75ºC to 19.75º 391 Last Eqn on page Second Ti should be Ti-1 769 Eqn for iη iη 30.7 should be 30.8

Corrigenda for Solar Engineering of Thermal Processes, Third Ed. J. A. Duffie and W. A. Beckman

3/28/2013

Third and subsequent Printings

Page Where Change 8 Table 1.3.1b 1st row Change "0.300–0.364" to "0.250–0.364"

19 Equation for γs ( ) 1 cos70.3sin 43 sin( 2.4)60 cos 66.8

sin 70.3cos 43s SIGNγ − − − = = °

28 Equation for Rb Change “sin 10” in denominator to “sin 40” 36 First line after Solution Change “(2.87-1.05)/1.82” to “(1.82/(2.87-1.05))” 62 15 lines from top Change “1 mm” to “1µm” 66 Second line after Solution Change “Figure 1.10.1” to “either Table or Figure 1.10.1” 71 End of Example 2.8.2 Add black square after table. 90 First lines of Solution Io=2.34, kT=1.04/2.34 = 0.445, Id /I=0.766 Third line of Solution Id = 0.766 × 1.04 = 0.796 Fourth line of Solution Ib = 0.234 × 1.04 = 0.244 91 Eqn for IT 0.253 should be 0.244 and 0.787 should be 0.796 Next row = 0.417 + 0.597 + 0.156 = 1.17 MJ/m2 Next 2 row Change 0.433 to 0.417, 0.590 to 0.597 and 1.18 to 1.17 93 Example 2.16.1 Solution From Example 2.15.1, I = 1.04 MJ/m2, Ib = 0.244 MJ/m2, Id = 0.796 MJ/m2, Io = 2.34 MJ/m2, and Rb = 1.71. From Equation 2.16.3, Ai = 0.244/2.34 = 0.104 The modulating factor f, from Equation 2.16.6, is

0.244 1.04 0.484f = =

Then from Equation 2.16.7,

( )

( ) 3

2

0.244 0.796 0.104 1.71

1 cos600.796 1 0.104 1 0.484sin 30

2

1 cos601.04 0.60

2

0.559 0.567 0.156 1.28 MJ/m

TI = + ×

+ + − +

− + ×

= + + =

104 Example 2.19.1 Remove extra ) after last 60 in Eqn for TH

105 Table header ρs should be ρg 123 Equation 2.23.3 First Rd should be Rb. Second H should be dH .

Equation 2.23.4 Insert large square bracket before first “(“ and after last “)” 126 Eqn 2.23.5a Add absolute value bar to left hand side of “Otherwise”

Eqn 2.23.5c Change the second plus sign to a minus sign Eqn 2.23.6 oI should be oI

161 Last line of solution Change h=310 to h=308 164 Part C solution 6.2 should be 5.4. 169 Line before Eqn 3.17.3 Cp should be Cp 177 6th line from bottom Change “form” to “from’ 192 4 th line from bottom Change ºC to K 207 First equation Add equals sign after τr(0) 210 7 lines from top Change “0.003” to “0.002” 213 Line 2 and Eqn for τ Change “0.003” to “0.002” 218 Second column of table 0.426, 0.508, 0.581, 0.653, 0.732, 0.822, 0.929, 1.080, 1.300, 1.974 235 Example 5.12.1, line 1 Add “radiation on” to “radiation at solar noon on” Second equation Change G to Gb + Gd

Six lines from bottom Change “0.6058” to “0.5576” Five lines from bottom Change “327.8, 440.4, and 768.2” to “377.8, 329.6, and 707.4” 236 Eqn for S/Sref

329.6 377.8 707.4

0.9837 0.926 0.998 0.962 0.854 0.2 0.867 0.146 0.6621000 1000 1000ref

S

S = × + × + × × =

247 Line 4 from top Change εg to εc

Third eqn for q Change εp to εc

254 Solution Line 3 and in two places for Ut, change 0.846 to 0.844 261 First equation Add units to m of 1/m 282 Eqn for F1 The ½ exponent should be 2. 284 Equation 6.14.4 2

2h in denominator should be 2rh

286 Equation for L/Dh Denominator should be 2 × 0.01 287 Equation 6.14.9 The plus sign should be a minus sign

319 Example 6.24.2 Eqn for Kτα should be 1

1 0.161 1cosθ

+ −

335 Example 7.3.2 Second line change 167.3 to 156.9 Equation for Qu, change 10.6 to 3.82 and 6335 to 8971 Equation for ∆T, change 6335 to 8971 and 36.2 to 51.2 Next line change 167.3+36.2=203.5 to 156.9+51.2=208.1 Last equation, change 6335 to 8971 and 14.6 to 17.5 Next line change (167.3 +203.5)/2+14.6 to (156.9 +208.1)/2+17.5 390 Sentence above Eqn 8.5.3 Change “term on the right-” to “term on the left-“ 393 Equation for NTU Change “1.204” to “1.006” and then NTU=68. 394 Last Eqn on page Second Ti should be Ti-1. 417 Example 9.3.1 In the 4th line Change “8.0ºC” to “7.9 ºC” Change denominator in first equation from 12 to 11 and σyr becomes 10.60. The DDs for May through August increase by 1. Change the total DD from 4095 to 4100 and the yearly aT to 7.9.

mσ =1.72, h=0351 and DD=121

459 Equation 11.5.1 when i = d, N/(N+1) should be N/(i+ 1). 472 Equation 11.8.3 Missing right parentheses in denominator of 3rd line. 558 Equation 14.5.5 fNUL should be just fN 577 7 lines from bottom G. G. Jones should be G. F. Jones 679 First row in Table Change “10.2” to “10.1”. 681 8 lines from top Change “0.35” to “0.41” Equation for fL fL=10.8, not 10.7 682 Equation for Cmin Change last × to /. 688 Line above “Solution” Change (τα) to (τα)n. 700 Line after Eqn 21.2.2 Reference to Eqn 5.10.5 should be 5.10.4. 708 Table Change last entry in last row from 129.2 to 127.1 709 Last line. Eliminate reference to Equation 21.3.5 and change 21.3.2 to 21.2.4

710 14 lines up from bottom 0.50

0.471.07

φ = =

711 Equation 21.3.11 Change Qst to LS 711 10 lines from top Eqn 21.4.2 should be 21.3.2 753 Eqn 23.2.7 Tref should be Tc,ref – two places. 754 Eqn 23.2.10b Tref should be Tc,ref 755 Line after Eqn 23.2.12 23.2.10 should be 23.2.7 756 Ex. 23.2.1, 3rd line First word in line, As, should be just A (for amp). Solution

,

,

-10,

,

-9

52.4

0.9352 V

4.549 A

4.782 10

0.567

0.9666 V at 308.2 K

2.432 10 A at 308.2 K

sh ref

ref

L ref

o ref

s ref

o

R

a

I

I

R

a

I

= Ω

=

=

= ×

= Ω

== ×

757 8 lines from top "32.2.8" should be "23.2.8" Solution continued

( )3 22

1026

7

273.15 67.20.9352 1.068 V

273.15 25

0.684 4.549 0.00026 67.2 25 3.119 A

340.35 1.602 10 1.120 1.1074.782 10 exp

298.15 1.381 10 298.15 340.35

2.436 10 A

52.476

0.684

L

o

sh

a

I

I

R

−−

−

−

+= =+

= + − =

× = × − ×

= ×

= =

( )

.7

The result is 2.69 A, 13.2 V, and 35.5 W.

The cell efficiency is then 35.5 / 0.633 648.3 0.086, or 8.6%.

mp mp mpI V P

Ω

= = =

× =

768 Eqn 23.7.4 Replace TI with TG

771 6 lines from bottom (49 – 20) should be (46 – 20) Eqn for iη (8 – 28) should be (8 – 25) and 30.7 should be 30.8

786 Figure 24.2.6 Abscissa caption should be U not U 787 Eqn 24.2.11 Replace π/2 in exponent by π/4 First line of text Replace “With k = 2 …” with “With k = 2 and U = 10 m/s …” 805 Table for P 2.26 Units for I and Ibn should be W-h/m2 812 Problem 6.4 Plate to cover and cover to cover spacing is 25 mm. 815 Problem 6.25 Last line should be “both English and SI units)?” 817 Problem 6.33 Change first paragraph to: For February 16th in Madison, WI for the hour 11 to 12 the incident horizontal radiation is 585 W-hr/m2 and the ambient temperature is -4.4º C. Assume the sky temperature is equal to the ambient temperature and the inlet temperature is 35º C. 818 Problem 7.2 0.91 should be 0.31 Problem 7.5 Add “Assume hfi = 3000 W/m2-K.” 820 Problem 7.8b Replace “τα..." with “FR is 0.9, τα…” Problem 9.1 Replace “building…” with ”building maintained at 21C…”. 822 Last line of Prob. 10.6 Replace “0.056 kg/s.” with “is controlled up to a maximum of 0.056 kg/s so that the air leaving the LHX never exceeds 55º C.” 824 Problem 10.10 Add to end “The test fluid is water.” 826 End of Problem 11.5 Change “…10%.” to “…10%/year.” 831 Problem 19.1 Add to list of conditions: Ground reflectance = 0.2 Single cover Glass KL=0.0125 Normal solar absorptance = 0.9 After Notes Delete first sentence and replace “…can affect…” with “…can significantly affect…” Add Problem 19.3 Repeat Prob. 19.1 for the first week in July using TMY3 data. 832 End of Page Replace 828 with 821 833 Second line Replace 11.9 with 13.7 Prob. 20.4 after “covers” add “of high quality glass” 6th line of Prob.20.5 after “covers” add “with KL = 0.0125” End of text of Prob. 21.1 Replace “…and ρg = 0.2. with “ρg =0.2 and Load = 213 GJ.” 834 Problem 22.1 Delete 4th sentence “For the mean….10.8h.” Problem 22.1a Replace last sentence with “Estimate the required auxiliary energy.” 835 Problem 23.5 Delete the last sentence in brackets and add “What is the maximum power?” 843 B.2, definition of H add “; can also be considered as an average daily rate (J/day-m2)” Definition of I add to end (J/h-m2) 895 Last line RHS Change 360 to 310. 896 Six lines down on RHS Change 338, 360 to 296, 310. 897 Flow rate corrections Change 354 to 307 FR Change 279, 354, 329 to 264, 280, 290, 329

First and Second Printings

Page Where Change 8 Table 1.3.1b 1st row See correction for 3rd printing. 11 footnote "divide" should be "multiply" 14 Eqn 1.6.1b δ is in radians. To convert to degrees multiply RHS by 180/π also, – 0.002679 should be – 0.002697 18 Ex 1.6.3 "angles for a sloped" should be "angles for a 60º sloped" 19 Equation for γs See correction for 3rd printing. 21 Fig 1.7.1 Replace the figure with the following figure.

0 2 4 6 8 10 12 14 16 18 20 22 240

1

2

3

4

5

Time [hr]

Rad

iatio

n [M

J/m

2-h

r] N-S

E-W

β = 45°

N-S

E-W

Last line of figure caption replace "lower" with "dotted" and "upper" with "solid" Eqn 1.7.3a change the minus sign to a plus sign 22 Eqn 1.7.5e in C1 change θs to γs and change -1 otherwise to +1 otherwise 28 Equation for Rb See correction for 3rd printing 36 First line after Solution See correction for 3rd printing 40 Eqn 1.10.4 the first sin δ should be cos δ 62 15 lines from top See correction for 3rd printing 66 Second line after Solution See correction for 3rd printing 68 Line before Eqn 2.8.1a tb should be τb 71 End of Example 2.8.2 Add black square after table. 74 Eqn 2.9.5 missing left paren. just before the first ,maxTK in numerator. 75 Eqn 2.9.c ,maxTK should be ,maxTK 77 footnote 12 0.75 < KT < 0.60 should be 0.75 < KT < 0.80 79 Ex 2.11.1 KT = H/Ho = 23.0/33.3 = 0.69 footnote 13 denominator H should be H 80 Eqn 2.12.1a & b dH H should be dH H 89 6 lines from top (cos ω2 – cos ω1) should be (sin ω2 – sin ω1) 12 & 13 lines from top "82.5" should be = "– 82.5" 9 lines from bottom "5:29 AM" should be "6:29 AM"

3 lines from bottom [cos (-75) – cos (-82.79)] should be [sin (-75) – sin (-82.79)] 90 Ex 2.15.1 Io = 2.34 MJ/m2, kT = 1.04/2.34 = 0.445, Id/I = 0.766. Id = 0.766 × 1.04 = 0.796 MJ/m2 Ib = 0.234 × 1.04 = 0.244 MJ/m2

91 4 lines from top 1 cos60 1 cos60

0.244 1.71 0.796 1.04 0.602 2TI

+ − = × + + ×

20.417 0.597 0.156 1.17 MJ/m= + + = Thus the beam contribution is 0.417 MJ/m2, the diffuse is 0.597 MJ/m2, and the ground-reflected is 0.156 MJ/m2. The total radiation on the surface for the hour is 1.17 MJ/m2.

93 Example 2.16.1 Solution See correction for 3rd printing. 104 Example 2.19.1 See correction for 3rd printing. 151 Eqn 3.11.2 β should be β ' 161 Last line of solution See correction for 3rd printing. 177 6th line from bottom See correction for 3rd printing. 206 Eqn 5.1.7 After first equals sign + should be – 207 First equation See correction for 3rd printing. 210 3 lines from top 0.786 should be 0.768 210 7 lines from top See correction for 3rd printing 211 Eqn 5.3.7 1 + ρ1ρ2 should be 1 – ρ1ρ2 in two places. 213 second line Change “0.003” to “0.002” Eqn for τ 0.665 should be 0.655 and 0274 should be 0.274 and 0.003 should be 0.002 next eqn should be = 0.5(0.948 + 0.518) = 0.733 eqn after ρ should be = 0.5(0.007 + 0.430) = 0.219 eqn for α should be α = 1 – 0.219 – 0.733 = 0.048 232 mid page 3.57 should be 3.59, 6.46 should be 6.50 and 9.14 should be 9.18 in two places. 254 Solution See correction for 3rd printing. 261 First equation See correction for 3rd printing. 282 Eqn for F1 See correction for 3rd printing 284 Equation 6.14.4 See correction for 3rd printing. 286 5 lines from top See correction for 3rd printing. 298 Figure caption Eliminate all after the colon and replace colon with period. 319 Example 6.24.2 See correction for 3rd printing.

334 Eqn 7.3.13 exp r L

p

A U F

mC

′ ɺ

should be exp r L

p

A U F

mC

′− ɺ

335 Eqn for F ′′ "exp(1/24.77)" should be "exp(–1/24.77)" 348 Eqn 7.7.1a Delete Aa 355 Eqn 7.9.2 sin2 should be sin-1 359 3 lines from bottom "102 W/m2" should be "102 kW/m2" 360 4 lines from top "4.41 W/m" should be "4.41 kW/m" 373 8 lines from bottom "UREL" should be "NREL"

393 Equation for NTU See correction for 3rd printing. 417 Example 9.3.1 See correction for 3rd printing. 442 7 lines from bottom "0.110 3750" should be "0.110 × 3750" 472 Eqn 11.8.3 See correction for 3rd printing. 642 Eqn 18.2.2 should be ( )/ /g gg a x bP A k= + 687 Eqn 20.5.1 "11.6 × 1.18Tw" should be "11.6 + 1.18Tw" 679 First row in Table See correction for 3rd printing. 681 Solution to 20.3.2 See correction for 3rd printing. 682 Equation for Cmin See correction for 3rd printing. 688 Line above Solution See correction for 3rd printing. 700 Line after Eqn 21.2.2 See correction for 3rd printing. 753 and 754 See correction for 3rd printing. 754 Fig 23.2.5 Remove "and maximum power point" from the caption. 755 8 lines below Eqn 23.2.12 αref,guess should be aref,guess Above Eqn 23.2.13 second "result" should be "results" 756 and 757 See corrections for 3rd printing. 795 Eqn 24.4.5 CP should be CP,Betz in two places. 802 Prob 1.13g should read "…extraterrestrial horizontal solar…" Prob 2.4 "12 AM" should be "12 PM" 804 Prob 2.20 should read "A south facing window is ….." 805 Prob 2.25 should read "… the beam and estimate the total radiation …" Table for P 2.26 See correction for 3rd printing. 806 Prob 2.26i Change period at end of first sentence to question mark. 812 Problem 6.4 See correction for 3rd printing. 897 Index See correction for 3rd printing.