Issue Section:
Errata
Keywords:
Finite element, Boundary element methods
Topics:
Boundary element methods, Finite element analysis, Heat exchangers, Pressure vessels, Stress analysis (Engineering)

This erratum corrects errors in the originally published paper.

In Appendix C—Sec. C.1 on page 061205-9, the definition of coefficients for Eq. (C4) is corrected as follows:

where a=D1*⁠,  b=+Ha1⁠, and c=2kw⁠.

In Appendix C—Sec. C.1 on page 061205-9, Eq. (C5a) is corrected as follows:
x1, x2=−Ha12D1*±ℝ4(2kw)D1*−Ha122D1*=λ2⋅e±2θℝ
(C5a)
In Appendix C—Sec. C.1 on page 061205-9, Eq. (C5c) is corrected as follows:
2θ=Arc cos [−Ha12/(8kwD1*)]
(C5c)
In Appendix C—Sec. C.1 on page 061205-10, Eqs. (C9a)–(C9c) are corrected as follows:
Ha128kwD1*=|12(Ha1D1*+Ha1D1*)|22kwD1*+kwD1*≪1
(C9a)
ψH1=|12(Ha1D1*+Ha2D2*)|22kwD1*+kwD2*≪1
(C9b)
ψH2=|12(Ha1D1*−Ha2D2*)|22kwD1*+kwD2*≪1
(C9c)

In Appendix C—Sec. C.2 on page 061205-10, the definition of coefficients for Eq. (C16) is corrected as follows:

where a=1⁠, b=+ 2H1⁠, c=α4+H12−H22⁠, and d=−[H2(α14−α24)−H1α4]⁠.

In Appendix C—Sec. C.2 on page 061205-10, Eq. (C19a) is corrected as follows:
Z1,H={A1I0(−x1r)+[C1U0(λr,θ)+C2V0(λr,θ)]A2K0(−x1r)+[A3U¯0(λr,θ)+A4V¯0(λr,θ)]}
(C19a)
In Appendix C—Sec. C.2 on page 061205-11, Eq. (C20) is corrected as follows:
Z1,H=A1I0(−x1r)+[C1U0(λr,θ)+C2V0(λr,θ)]
(C20)
In Appendix C—Sec. C.3 on page 061205-11, Eqs. (C26) and (C29) are corrected as follows:
  ∇2⋅∇2Z2=−(α14−α24)[C1U0(αr,π4)+C2V0(αr,π4)]+2(ζ2Pa1D1*−ζ1Pa2D2*)
(C26)
  ∇2⋅∇2Z2=2(ζ2Pa1D1*−ζ1Pa2D2*)
(C29)
In Appendix C—Sec. C.3; on page 061205-11, Equations (C31a) and (C31b) are corrected as follows:
F1=(ζ2−ζ1)[C1cos4θ−C2sin4θ]
(C31a)
F2=(ζ2−ζ1)[C1sin4θ+C2cos4θ]
(C31b)
In Appendix C—Sec. C.4 on page 061205-12, expressions for b and d are corrected as follows:
b=+2H1  and  d=−[H2(α14−α24)−H1α4]≈0
In Appendix C—Sec. C.4 on page 061205-12, Eq. (C39) and its solution are corrected as follows:
 x3+2H1 x2+α4x=0
(C39)
x2, x3=−H1±ℝα4−H12=λ2⋅e±2θℝ
In Appendix C—Sec. C.4 on page 061205-12, expression for 2θ is corrected as follows:
2θ=Arc cos[−H1α2]→π2
In Appendix E on page 061205-13, Eqs. (E2) and (E4) are corrected as follows:
φf,si=12hf,si3Ef,silnRf,siRsi{−Rm,siMsi−hf,si2Rm,siQsi+(RG,si−Rsi)4(RG,si2−Rsi2)Psi−RB,siWB,si(RB,si−Rsi)+RG,siWG,si(RG,si−Rsi)+Rm,siNsi(Rm,si−Rsi)}
(E2)
φf,si=12hf,si3Ef,silnRf,siRsi{−Rm,siMsi−hf,si2Rm,siQsi+(RG,si−Rsi)4(RG,si2−Rsi2)Psi+Rm,siNsi(Rm,si−RG,si)−RB,siWB,si(RB,si−RG,si)+(RG,si−Rsi)(RG,si2−Rsi2)Psi/2}
(E4)
In Appendix H on page 061205-15, Eqs. (H2) and (H4) are corrected as follows:
  ∇2⋅∇2wAi=Psi−PtiDi
(H2)
  ∇2⋅∇2wAi−H̃ai Di∇2wAi=Psi−PtiDi
(H4)
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