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

Abstract

There was a symbol mix-up in Sec. 3. Therefore corrections are needed in the paper, as follows.Page 033102-4: Eqs. 9,10,11,12,13,14,16,18 should readDisplay Formulaγβ∂⟨Tβ⟩β∂t=kββΔ⟨Tβ⟩β+kβσΔ⟨Tσ⟩σ+haυ(⟨Tσ⟩σ−⟨Tβ⟩β) (9) Display Formulaγσ∂⟨Tσ⟩σ∂t=kσσΔ⟨Tσ⟩σ+kσβΔ⟨Tβ⟩β+haυ(⟨Tβ⟩β−⟨Tσ⟩σ) (10) Display Formula[γβ∂∂t−kββΔ+haυ−kβσΔ−haυ−kσβΔ−haυγσ∂∂t−kσσΔ+haυ][⟨Tβ⟩β⟨Tσ⟩σ]=0 (11) Display Formula[(γβ∂∂t−kββΔ+haυ)(γσ∂∂t−kσσΔ+haυ)−(kβσΔ+haυ)2]⟨Ti⟩i=0 (12) Display Formula∂⟨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) τq=γβγσhaυ(γβ+γσ), τT=γβkσσ+γσkββhaυ(kββ+kσσ+2kβσ)k=kββ+kσσ+2kβσ, α=kββ+kσσ+2kβσγβ+γσF(r,t)+τq∂F(r,t)∂t=kβσ2−kββkσσhaυΔ2⟨Ti⟩iDisplay Formulakkβ=kββ+kσσ+2kβσkβ (16) Display FormulaτTτq=1+γβ2kσσ+γσ2kββ−2γβγσkβσγβγσ(kββ+kσσ+2kβσ) (18) Page 033102-4: The line below Eq. 10 should read “where kββ and kσσ are the effective thermal conductivities of the β-.”Page 033102-4: The second line below Eq. 14 should read “conduction equation with ((kβσ2−kββkσσ)/(hav))Δ2⟨Ti⟩i as the DPL.”Page 033102-4: The fourth line below Eq. (17) should read “nanoparticle-fluid interface due to the term kββ+kσσ+2kβσ.”Page 033102-4: The seventh line below Eq. (17) should read “thus focus on kββ+kσσ+2kβσ to develop predicting models of thermo-.”Page 033102-4: The paragraph above Eq. 18 should read “To show the possibility of conductivity enhancement, consider.”Page 033102-4: The second line below Eq. 18 should read “of γβ2kσσ+γσ2kββ−2γβγσkβσ. Therefore, by the condition for the ex-.”Page 033102-5: The first equation should readγβ2kσσ+γσ2kββ−2γβγσkβσ<0Page 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.”Page 033102-6: In the Nomenclature list the symbols kβ and kσ should be changed into kββ and kσσ, respectively.