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Nanofins as a Means of Enhancing Heat Transfer: Leading Order Results

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Abstract

The porous media approach is being adapted to a system of nanoparticles that are attached to a solid surface (a metal wire) embedded into a stagnant fluid, forming by design nanofins around the wire. The analyzed system resembles the Transient Hot Wire experimental method used in evaluating the thermal conductivity of a fluid or nanofluid suspensions. Since the attachment of the nanoparticles to the wire is done by design (as distinct from uncontrolled agglomeration around the wire), one major objective in such a design is attempting to enhance the heat transfer from the wire. The latter objective is analyzed via a short times approximation of the solution. Preliminary results based on the leading order solution shows that such a heat transfer enhancement is indeed possible and presents major advantages compared to commonly used macro-fins.

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Abbreviations

A :

Cross sectional area of the wire (m2)

A sf :

Solid–fluid interface heat transfer area (m2)

c p :

Fluid’s specific heat for the single phase (J/kg K) (dimensional)

c p,f, c s :

Fluid and solid phases specific heat, respectively (J/kg K) (dimensional)

Ei:

Exponential integral function

h :

Integral heat transfer coefficient for the heat conduction at the the solid–fluid interface, (W/m3 K) (dimensional)

i :

Electric current passing through the wire (A)

i s :

Electric current supplied by the source (A)

k :

Thermal conductivity of the fluid for the single phase (W/m K) (dimensional)

k s :

Effective thermal conductivity of the solid phase (W/m K) (dimensional)

\({\tilde {k}_{\rm s}}\) :

Thermal conductivity of the solid phase (W/m K) (dimensional)

k f :

Effective thermal conductivity of the fluid phase (W/m K) (dimensional)

\({\tilde {k}_{\rm f}}\) :

Thermal conductivity of the fluid phase (W/m K) (dimensional)

k eff :

Effective thermal conductivity of the medium (W/m K) (dimensional)

\({k_{{\rm eff}}^\ast }\) :

Dimensionless effective thermal conductivity of the medium

L :

The length of the wire (m)

\({\dot {q}_L }\) :

Amount of heat generated per unit length of wire (W/m)

\({q_{r^{\ast}}}\) :

Radial component of the heat flux (W/m2)

r * :

Radial coordinate (m) (dimensional)

r :

Dimensionless radial coordinate, equals \({{r_\ast }/{\sqrt{{k_{\rm f}}/h}}}\)

\({r_{{\rm w}^{\ast}}}\) :

Wire’s radius (m) (dimensional)

R :

Electrical resistance (Ω) (dimensional)

R w :

Electrical resistance of the wire (Ω)

R o :

A reference value of the electrical resistance (Ω)

R 1, R 2 :

Fixed electrical resistances in the Wheatstone bridge (Ω)

R 3 :

Variable electrical resistance [Ω], (potentiometer) in the Wheatstone bridge

R th,eff :

Effective thermal resistance (m K/W)

\({R_{\rm th,eff}^\ast }\) :

Dimensionless effective thermal resistance

t * :

Time (s) (dimensional)

t :

Dimensionless time, equals t * h/γ f

T :

Temperature, equals (T *T o) (K) (dimensional)

T C :

Coldest boundary temperature (K) (dimensional)

V :

Voltage drop across the wire (V)

z * :

Vertical coordinate (m) (dimensional)

α :

Fluid’s thermal diffusivity for the single phase, equals k/ρ c p (m2/s) (dimensional)

α f :

Fluid phase effective thermal diffusivity, equals k f/γ f (m2/s) (dimensional)

α s :

Solid phase effective thermal diffusivity, equals k s/γ s (m2/s) (dimensional)

χ :

Heat capacity ratio, equals γ f/γ s

γ s :

Solid phase effective heat capacity (dimensional)

γ f :

Fluid phase effective heat capacity (dimensional)

γ Eu :

Euler–Mascheroni constant, equals 0.5772156649

\({\varepsilon }\) :

Solid fraction, equals (1 − φ )

θ s :

Dimensionless solid phase temperature, equals \({{(T_{\rm s^{\ast}} -T_{\rm o} )}/{\left( {{\dot {q}_L }/{2\pi k_{\rm f}}}\right)}}\)

θ f :

Dimensionless fluid phase temperature, equals \({{(T_{\rm s^{\ast}} -T_{\rm o} )}/{\left( {{\dot {q}_L }/{2\pi k_{\rm f}}}\right)}}\)

φ :

Porosity/fluid fraction (dimensionless)

\({\phi }\) :

Dependent variable following the transformation \({\phi =\eta \left( {{\partial T}/{\partial \eta }}\right)}\)

ρ e :

Electrical resistivity of the wire (Ω m)

ρ :

Fluid’s density for single phase (kg/m3)

ρ f :

Fluid phase density (kg/m3)

ρ s :

Solid phase density (kg/m3)

σ :

Thermal conductivity ratio, equals k f/k s (dimensionless)

η :

Similarity variable, equals \({{r_{\ast}^{2}}/{4\alpha t_{\ast}}}\) (dimensionless)

κ :

Thermal diffusivity ratio, equals α f/α s = σ /χ (dimensionless)

*:

Corresponding to dimensional values, except for cases where there is no ambiguity as listed in this nomenclature

s:

Related to the solid phase

f:

Related to the fluid phase

References

  1. Assael M.J., Chen C.-F., Metaxa I., Wakeham W.A.: Thermal conductivity of suspensions of carbon nanotubes in water. Int. J. Thermophys. 25, 971–985 (2004)

  2. Bentley J.P.: Temperature sensor characteristics and measurement system design. J. Phys. E 17, 430–439 (1984)

  3. Bonnecaze R.T., Brady J.F.: A method for determining the effective conductivity of dispersions of particles. Proc. R. Soc. Lond. A 430, 285–313 (1990)

  4. Bonnecaze R.T., Brady J.F.: The effective conductivity of random suspensions of spherical particles. Proc. R. Soc. Lond. A 432, 445–465 (1991)

  5. Buongiorno J., Venerus D.C., Prabhat N., McKrell T., Townsend J., Christianson R., Tolmachev Y.V., Keblinski P., Hu L.H., Alvarado J.L., Bang I.C., Bishnoi S.W., Bonetti M., Botz F., Cecere A. et al.: A benchmark study on thermal conductivity of nanofluids. J. Appl. Phys. 106, 094312 (2009)

  6. Buongiorno J., Venerus D.C.: Letter to editor. Int. J. Heat Mass Transfer 53, 2939–2940 (2010)

  7. Carslaw H.S., Jaeger J.C.: Conduction of Heat in Solids, 2nd edn. Oxford University Press, New York (1946)

  8. Choi S.U.S., Zhang Z.G., Yu W., Lockwood F.E., Grulke E.A.: Anomalous thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett. 79, 2252–2254 (2001)

  9. Das S.K., Putra N., Thiesen P., Roetzel W.: Temperature dependence of thermal conductivity enhancement for nanofluids. J. Heat Transfer 125, 567–574 (2003)

  10. Davis R.H.: The effective thermal conductivity of a composite material with spherical inclusions. Int. J. Thermophys. 7, 609–620 (1986)

  11. De Groot J.J., Kestin J., Sookiazian H.: Instrument to measure the thermal conductivity of gases. Physica (Amsterdam) 75, 454–482 (1974)

  12. Eastman J.A., Choi S.U.S., Li S., Yu W., Thompson L.J.: Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 78, 718–720 (2001)

  13. Hamilton R.L., Crosser O.K.: Thermal conductivity of heterogeneous two-component systems. IEC Fundam. 1, 187–191 (1962)

  14. Hammerschmidt U., Sabuga W.: Transient hot wire (THW) method: uncertainty assessment. Int. J. Thermophys. 21, 1255–1278 (2000)

  15. Healy J.J., de Groot J.J., Kestin J.: The theory of the transient hot-wire method for measuring thermal conductivity. Physica 82C, 392–408 (1976)

  16. Jang S.P., Choi S.U.-S.: Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl. Phys. Lett. 84(21), 4316–4318 (2004)

  17. Jeffrey D.J.: Conduction through a random suspension of spheres. Proc. R. Soc. Lond. A 335, 355–367 (1973)

  18. Kestin J., Wakeham W.A.: A contribution to the theory of the transient hot-wire technique for thermal conductivity measurements. Physica 92A, 102–116 (1978)

  19. Kuznetsov A.V., Nield D.A.: Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model. Transp. Porous Med. 81, 409–422 (2010a)

  20. Kuznetsov A.V., Nield D.A.: Effect of local thermal non-equilibrium on the onset of convection in a porous medium layer saturated by a nanofluid. Transp. Porous Med. 83, 425–436 (2010b)

  21. Kuznetsov A.V., Nield D.A.: The onset of double-diffusive nanofluid convection in a layer of a saturated porous medium. Transp. Porous Med 85, 941–951 (2010c)

  22. Lee S., Choi S.U.-S., Li S., Eastman J.A.: Measuring thermal conductivity of fluids containing oxide nanoparticles. ASME J. Heat Transfer 121, 280–289 (1999)

  23. Li C.H., Peterson G.P.: Experimental investigation of temperature and volume fraction variations of the effective thermal conductivity of nanoparticle suspension (nanofluids). J. Appl. Phys. 99, 084314 (2006)

  24. Liu M.S., Lin M.C.C., Tsai C.Y., Wang C.C.: Enhancement of thermal conductivity with Cu for nanofluids using chemical reduction method. Int. J. Heat Mass Transfer 49, 3028–3033 (2006)

  25. Lu S., Lin H.: Effective conductivity of composites containing aligned spheroidal inclusions of finite conductivity. J. Appl. Phys. 79, 6761–6769 (1996)

  26. Martinsons C., Levick A., Edwards G.: Precise measurements of thermal diffusivity by photothermal radiometry for semi-infinite targets using accurately determined boundary conditions. Anal. Sci. 17, 114–117 (2001)

  27. Masuda H., Ebata A., Teramae K., Hishinuma N.: Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7, 227–233 (1993)

  28. Maxwell, J.C.: A treatise on electricity and magnetism, 3rd edn, pp. 435–441. Clarendon Press, 1954 reprint, Dover, New York (1891)

  29. Nagasaka Y., Nagashima A.: Absolute measurement of the thermal conductivity of electrically conducting liquids by the transient hot-wire method. J. Phys. E 14, 1435–1440 (1981)

  30. Nield D.A., Kuznetsov A.V.: The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transfer 52, 5792–5795 (2009a)

  31. Nield D.A., Kuznetsov A.V.: Thermal instability in a porous medium layer saturated by a nanofluid. Int. J. Heat Mass Transfer 52, 5796–5801 (2009b)

  32. Nield D.A., Kuznetsov A.V.: The effect of local thermal nonequilibrium on the onset of convection in a nanofluid. J. Heat Transfer 132, 052405-1/7 (2010)

  33. Özisik M.N.: Heat conduction, 2nd edn. Wiley, New York (1993)

  34. Prasher R., Bhattacharya P., Phelan P.E.: Thermal conductivity of nanoscale colloidal solutions (nanofluids). Phys. Rev. Lett. 94, 025901-1/4 (2005)

  35. Putnam S.A., Cahill D.G., Braun P.V., Ge Z., Shimmin R.G.: Thermal conductivity of nanoparticle suspensions. J. Appl. Phys. 99, 084308-1/6 (2006)

  36. Rusconi R., Rodari E., Piazza R.: Optical measurements of the thermal properties of nanofluids. Appl. Phys. Lett. 89, 261916-1/3 (2006)

  37. Vadasz P.: Absence of oscillations and resonance in porous media dual-phase-lagging fourier heat conduction. J. Heat Transfer 127, 307–314 (2004)

  38. Vadasz P.: Explicit conditions for local thermal equilibrium in porous media heat conduction. Transp. Porous Media 59, 341–355 (2005a)

  39. Vadasz P.: Lack of oscillations in dual-phase-lagging heat conduction for a porous slab subject to imposed heat flux and temperature. Int. J. Heat Mass Transfer 48, 2822–2828 (2005b)

  40. Vadasz P.: Heat conduction in nanofluid suspensions. J. Heat Transfer 128, 465–477 (2006a)

  41. Vadasz P.: Exclusion of oscillations in heterogeneous and bi-composite media thermal conduction. Int. J. Heat Mass Transfer 49, 4886–4892 (2006b)

  42. Vadasz P.: On the paradox of heat conduction in porous media subject to lack of local thermal equilibrium. Int. J. Heat Mass Transfer 50, 4131–4140 (2007)

  43. Vadasz P.: Rendering the transient hot wire experimental method for thermal conductivity estimation to two-phase systems—theoretical leading order results. J. Heat Transfer 132(8), 081601-1/7 (2010)

  44. Vadasz P.: Heat transfer augmentation in nanofluids via nanofins. Nanoscale Res. Lett. 6, 154 (2011). doi:10.1186/1556-276X-6-154

  45. Vadasz J.J., Govender S., Vadasz P.: Heat transfer enhancement in nanofluids suspensions: possible mechanisms and explanations. Int. J. Heat Mass Transfer 48, 2673–2683 (2005)

  46. Vadasz J.J., Govender S.: Thermal wave effects on heat transfer enhancement in nanofluids suspensions. Int. J. Thermal Sci. 49, 235–242 (2010)

  47. Venerus D.C., Kabadi M.S., Lee S., Perez-Luna V.: Study of thermal transport in nanoparticle suspensions using forced Rayleigh scattering. J. Appl. Phys. 100, 094310-1/5 (2006)

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Correspondence to Peter Vadasz.

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Vadasz, P. Nanofins as a Means of Enhancing Heat Transfer: Leading Order Results. Transp Porous Med 89, 165 (2011). https://doi.org/10.1007/s11242-011-9763-4

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Keywords

  • Nanofins
  • Transient hot wire
  • Porous media
  • Nanofluids
  • Effective thermal conductivity