Erratum: “Nanofluids: Synthesis, Heat Conduction, and Extension” [Journal of Heat Transfer, 2009, 131(3), p. 033102]

There was a symbol mix-up in Sec. 3. Therefore corrections are needed in the paper, as follows.

• 1
  Page 033102-4: Eqs. 9,10,11,12,13,14,16,18 should read

  $γβ∂⟨Tβ⟩β∂t=kββΔ⟨Tβ⟩β+kβσΔ⟨Tσ⟩σ+haυ(⟨Tσ⟩σ−⟨Tβ⟩β)$

  9

  $γσ∂⟨Tσ⟩σ∂t=kσσΔ⟨Tσ⟩σ+kσβΔ⟨Tβ⟩β+haυ(⟨Tβ⟩β−⟨Tσ⟩σ)$

  10

  $[γβ∂∂t−kββΔ+haυ−kβσΔ−haυ−kσβΔ−haυγσ∂∂t−kσσΔ+haυ][⟨Tβ⟩β⟨Tσ⟩σ]=0$

  11

  $[(γβ∂∂t−kββΔ+haυ)(γσ∂∂t−kσσΔ+haυ)−(kβσΔ+haυ)2]⟨Ti⟩i=0$

  12

  $∂⟨Ti⟩i∂t+τq∂2⟨Ti⟩i∂t2=αΔ⟨Ti⟩i+ατT∂∂t(Δ⟨Ti⟩i)+αk[F(r,t)+τq∂F(r,t)∂t]$

  13
  14

  $τq=γβγσhaυ(γβ+γσ),τT=γβkσσ+γσkββhaυ(kββ+kσσ+2kβσ)$

  $k=kββ+kσσ+2kβσ,α=kββ+kσσ+2kβσγβ+γσ$

  $F(r,t)+τq∂F(r,t)∂t=kβσ2−kββkσσhaυΔ2⟨Ti⟩i$

  $kkβ=kββ+kσσ+2kβσkβ$

  16
  $τTτq=1+γβ2kσσ+γσ2kββ−2γβγσkβσγβγσ(kββ+kσσ+2kβσ)$

  18
• 2

  Page 033102-4: The line below Eq. 10 should read “where $kββ$ and $kσσ$ are the effective thermal conductivities of the $β-$⁠.”

• 3

  Page 033102-4: The second line below Eq. 14 should read “conduction equation with $((kβσ2−kββkσσ)/(hav))Δ2⟨Ti⟩i$ as the DPL.”

• 4

  Page 033102-4: The fourth line below Eq. (17) should read “nanoparticle-fluid interface due to the term $kββ+kσσ+2kβσ$⁠.”

• 5

  Page 033102-4: The seventh line below Eq. (17) should read “thus focus on $kββ+kσσ+2kβσ$ to develop predicting models of thermo-.”

• 6

  Page 033102-4: The paragraph above Eq. 18 should read “To show the possibility of conductivity enhancement, consider.”

• 7

  Page 033102-4: The second line below Eq. 18 should read “of $γβ2kσσ+γσ2kββ−2γβγσkβσ$⁠. Therefore, by the condition for the ex-.”

• 8
  Page 033102-5: The first equation should read

  $γβ2kσσ+γσ2kββ−2γβγσkβσ<0$
• 9

  Page 033102-5: The eighth line in the second paragraph in Sec. 4 should read “$kβ$-enhancement can occur for all cases with $kββ+kσσ+2kβσ>kβ$ (Eq.”

• 10

  Page 033102-6: In the Nomenclature list the symbols $kβ$ and $kσ$ should be changed into $kββ$ and $kσσ$⁠, respectively.