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Numerical Investigation of Heat Transfer of Non-Newtonian Power-Law Fluids Around a Triangular Prism in Time-Periodic Regime

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Abstract

Laminar heat transfer characteristics of non-Newtonian power-law fluids from a long (heated) triangular prism in the time-periodic regime have been explored. Momentum and energy equations were solved using finite volume methodology over the range of non-dimensional control parameters: Reynolds number (Re) = 50–150, Prandtl number (Pr) = 1–50 and power-law index (n) = 0.4–1.8. For the fixed Pr, the local and the time-averaged Nusselt numbers increase with rising Re irrespective of n. However, the local and the time-averaged Nusselt numbers decrease as the fluid nature alters from pseudo-plastic (n < 1) to dilatant (n > 1) for the fixed Re and Pr. Maximum enhancements in the values of time-averaged Nusselt numbers for Pr = 10, 20 and 50 with respect to Pr = 1 are observed to be approximately 180, 273 and 438%, respectively. Further, it is observed that for the fixed n and Pr, the Colburn heat transfer factor (or the jh factor) decreases with rising Re. Finally, the various values of the jh factor at different Re, n and Pr have been correlated via a simple expression, thus enabling its estimation in a new application.

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Abbreviations

b :

Equilateral triangular prism’s side (m)

C D :

Drag coefficient [= 2FD/(ρ\(U_{\infty }^{2}\)b)]

c p :

Specific heat (J kg−1 K−1)

Δt :

Dimensionless time step

f :

Body force (N m−1)

F D :

Drag force (N m−1)

h :

Local heat transfer coefficient (W m−2 K−1)

\(\overline{h}\) :

Mean heat transfer coefficient (W m−2 K−1)

H :

Domain height (m)

I 2 :

Second invariant of the strain tensor rate (s−2)

\(j_{\text{h}}\) :

Colburn heat transfer factor

k :

Thermal conductivity (W m−1 K−1)

L :

Domain length (m)

m :

Consistency index (Pa sn)

n :

Power-law index

n s :

Normal direction

N cell :

Overall cells in domain

Npa :

Overall CVs on each surface of the triangular prism

\(\overline{Nu}\) :

Time-averaged Nusselt number (= \(\overline{h}\)b/k)

Nu L :

Local Nusselt number (= hb/k)

Nu Z :

Normalized Nusselt number

p :

Pressure (N m−2)

Pr :

Prandtl number (\(= mc_{p} \left( {U_{\infty } /b} \right)^{n - 1} /k\))

Re :

Reynolds number (\(= \rho U_{\infty }^{2 - n} b^{n} /m\))

Re c :

Critical Re (for the onset of periodic behaviour)

t :

Time (s)

t′:

Time period for a cycle (s)

T :

Temperature (K)

\(T_{\infty }\) :

Inlet temperature (K)

\(T_{w}\) :

Prism’ surface temperature (K)

\(U_{\infty }^{{}}\) :

Inlet uniform fluid velocity (m s−1)

U x :

x-velocity (= U*x/\(U_{\infty }^{{}}\))

U y :

y-velocity (= U*y/\(U_{\infty }^{{}}\))

U *x , U *y :

x- and y-components of velocity, respectively (m s−1)

Xd, Xu :

Downstream and upstream distances, respectively (m)

x, y :

Coordinates (= \(x^{*} /b\), \(y^{*} /b\))

x*, y*:

Cartesian coordinates (m)

θ :

Dimensionless temperature (= (T − T∞)/(Tw − T∞))

ε :

Component of the strain tensor rate (s−1)

τ :

Shear stress tensor (Pa)

η :

Power-law viscosity (Pa s)

ρ :

Density (kg m−3)

δ :

Smallest grid size (m)

*:

Dimensional value

References

  • Abbassi H, Turki S, Nasrallah SB (2001) Numerical investigation of forced convection in a plane channel with a built-in triangular prism. Int J Therm Sci 40:649–658

    Google Scholar 

  • Agarwal R, Dhiman A (2014) Flow and heat transfer phenomena across two confined tandem heated triangular bluff bodies. Numer Heat Transf A 66:1020–1047

    Google Scholar 

  • Agarwal R, Dhiman A (2015) Confined flow and heat transfer phenomena of non-Newtonian shear-thinning fluids across a pair of tandem triangular bluff bodies. Numer Heat Transf A 68:174–204

    Google Scholar 

  • Agarwal R, Dhiman A (2016) Time-periodic non-Newtonian power-law flow across a triangular prism. J Braz Soc Mech Sci Eng 38:227–240

    Google Scholar 

  • Agarwal R, Dhiman A (2017) Thermal characteristics of non-Newtonian power-law fluid flows around a confined triangular prism. Heat Transf Res 48:1473–1495

    Google Scholar 

  • Ali M, Zeitoun O, Nuhait A (2011) Forced convection heat transfer over horizontal triangular cylinder in cross flow. Int J Therm Sci 50:106–114

    Google Scholar 

  • Ansys Inc (2009) ANSYS user manual. Ansys Inc, Canonsburg

    Google Scholar 

  • Bharti RP, Chhabra RP, Eswaran V (2006) Steady flow of power-law fluids across a circular cylinder. Can J Chem Eng 84:406–421

    Google Scholar 

  • Bijjam S, Dhiman AK (2012) CFD analysis of two-dimensional non-Newtonian power-law flow across a circular cylinder confined in a channel. Chem Eng Commun 199:767–785

    Google Scholar 

  • Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. Wiley, New York

    Google Scholar 

  • Bouaziz M, Kessentini S, Turki S (2010) Numerical prediction of flow and heat transfer of power-law fluids in a plane channel with a built-in heated square cylinder. Int J Heat Mass Transf 53:5420–5429

    MATH  Google Scholar 

  • Buresti G, Lombardi G, Talamelli A (1998) Low aspect-ratio triangular prisms in cross-flow: measurements of the wake fluctuating velocity field. J Wind Eng Ind Aerodyn 74–76:463–473

    Google Scholar 

  • Chatterjee D, Mondal B (2012) Forced convection heat transfer from an equilateral triangular cylinder at low Reynolds numbers. Heat Mass Transf 48:1575–1587

    Google Scholar 

  • Chattopadhyay H (2007) Augmentation of heat transfer in a channel using a triangular prism. Int J Therm Sci 46:501–505

    Google Scholar 

  • Chhabra RP (1996) Hydrodynamics of non-spherical particles in non-Newtonian fluids. In: Cheremisinoff NP, Cheremisinoff PN (eds) Handbook of applied polymer processing technology. Marcel Dekker, New York City

    Google Scholar 

  • Chhabra RP (2011) Fluid flow and heat transfer from circular and non-circular cylinders submerged in non-Newtonian liquids. Adv Heat Transf 43:289–417

    Google Scholar 

  • Chhabra RP, Richardson JF (1999) Non-Newtonian flow in the process industries. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Chhabra RP, Richardson JF (2008) Non-Newtonian flow and applied rheology, 2nd edn. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Coelho PM, Pinho FT (2003a) Vortex shedding in cylinder flow of shear-thinning fluids, I. Identification and demarcation of flow regimes. J Non Newtonian Fluid Mech 110:143–176

    MATH  Google Scholar 

  • Coelho PM, Pinho FT (2003b) Vortex shedding in cylinder flow of shear-thinning fluids, II. Flow characteristics. J Non Newtonian Fluid Mech 110:177–193

    MATH  Google Scholar 

  • Coelho PM, Pinho FT (2004) Vortex shedding in cylinder flow of shear-thinning fluids, III. Pressure measurements. J Non Newtonian Fluid Mech 121:55–68

    Google Scholar 

  • Csiba AL, Martinuzzi RJ (2008) Investigation of bluff body asymmetry on the properties of vortex shedding. J Wind Eng Ind Aerodyn 96:1152–1163

    Google Scholar 

  • Dalal A, Eswaran V, Biswas G (2008) A finite-volume method for Navier–Stokes equations on unstructured meshes. Numer Heat Transf B 54:238–259

    Google Scholar 

  • De AK, Dalal A (2006) Numerical simulation of unconfined flow past a triangular cylinder. Int J Numer Methods Fluids 52:801–821

    MATH  Google Scholar 

  • De AK, Dalal A (2007) Numerical study of laminar forced convection fluid flow and heat transfer from a triangular cylinder placed in a channel. J Heat Transf 129:646–656

    Google Scholar 

  • Dhiman AK (2009) Heat transfer to power-law dilatant fluids in a channel with a built-in square cylinder. Int J Therm Sci 48:1552–1563

    Google Scholar 

  • Dhiman AK (2016) Flow and heat transfer phenomena around an equilateral triangular bluff body: effect of wall confinement. Heat Transf Asian Res 45:608–630

    Google Scholar 

  • Dhiman AK, Kumar S (2013) Non-Newtonian power-law flow across a confined triangular bluff body in a channel. Korean J Chem Eng 30:33–44

    Google Scholar 

  • Dhiman A, Shyam R (2011) Unsteady heat transfer from an equilateral triangular cylinder in the unconfined flow regime. ISRN Mech Eng 2011:1–13

    Google Scholar 

  • Dhiman AK, Chhabra RP, Eswaran V (2006) Steady flow of power-law fluids across a square cylinder. Chem Eng Res Des 84:300–310

    Google Scholar 

  • Dhiman AK, Chhabra RP, Eswaran V (2007) Heat transfer to power-law fluids from a heated square cylinder. Numer Heat Transf A 52:185–201

    Google Scholar 

  • Eiamsa-ard S, Sripattanapipat S, Promvonge P (2012) Numerical heat transfer analysis in turbulent channel flow over a side-by-side triangular prism pair. J Eng Thermophys 21:95–110

    Google Scholar 

  • Farhadi M, Sedighi K, Korayem AM (2010) Effect of wall proximity on forced convection in a plane channel with a built-in triangular cylinder. Int J Therm Sci 49:1010–1018

    Google Scholar 

  • Iungo GV, Buresti G (2009) Experimental investigation on the aerodynamics loads and wake flow features of low aspect-ratio triangular prisms at different wind directions. J Fluids Struct 25:1119–1135

    Google Scholar 

  • Mohsenzedh A, Farhadi M, Sedighi K (2010) Convective cooling of tandem heated triangular cylinders placed in a channel. Therm Sci 14:183–197

    Google Scholar 

  • Patnana VK, Bharti RP, Chhabra RP (2010) Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder. Int J Heat Mass Transf 53:4152–4167

    MATH  Google Scholar 

  • Prhashanna A, Sahu AK, Chhabra RP (2011) Flow of power-law fluids past an equilateral triangular cylinder: momentum and heat transfer characteristics. Int J Therm Sci 50:2027–2041

    Google Scholar 

  • Rao PK, Sahu AK, Chhabra RP (2011) Momentum and heat transfer from a square cylinder in power-law fluids. Int J Heat Mass Transf 54:390–403

    MATH  Google Scholar 

  • Rasool T, Dhiman A, Parveez M (2015) Cross-buoyancy mixed convection around a confined triangular bluff body. Numer Heat Transf A 67:454–475

    Google Scholar 

  • Roache PJ (1998) Verification and validation in computational science and engineering. Hermosa Publishers, Albuquerque

    Google Scholar 

  • Sabiri N-E, Chhabra RP, Comiti J, Montillet A (2012) Measurement of shear rate on the surface of a cylinder submerged in laminar flow of power-law fluids. Exp Therm Fluid Sci 39:167–175

    Google Scholar 

  • Sahu AK, Chhabra RP, Eswaran V (2009a) Forced convection heat transfer from a heated square cylinder to power-law fluids in the unsteady flow regime. Numer Heat Transf A 56:109–131

    Google Scholar 

  • Sahu AK, Chhabra RP, Eswaran V (2009b) Two-dimensional unsteady laminar flow of a power-law fluid across a square cylinder. J Non Newtonian Fluid Mech 160:157–167

    MATH  Google Scholar 

  • Srikanth S, Dhiman AK, Bijjam S (2010) Confined flow and heat transfer across a triangular cylinder in a channel. Int J Therm Sci 49:2191–2200

    Google Scholar 

  • Tiwari AK, Chhabra RP (2014) Effect of orientation on the steady laminar free convection heat transfer in power-law fluids from a heated triangular cylinder. Numer Heat Transf A 65:780–801

    Google Scholar 

  • Zeitoun O, Ali M, Nuhait A (2011) Convective heat transfer around a triangular cylinder in an air cross flow. Int J Therm Sci 50:1685–1697

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editor/reviewers for their valuable suggestions and helpful comments, which have enriched the present work for the wider readership.

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    Amit Kumar Dhiman & Richa Agarwal

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  1. Amit Kumar Dhiman
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Correspondence to Amit Kumar Dhiman.

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Dhiman, A.K., Agarwal, R. Numerical Investigation of Heat Transfer of Non-Newtonian Power-Law Fluids Around a Triangular Prism in Time-Periodic Regime. Iran J Sci Technol Trans Mech Eng 44, 427–441 (2020). https://doi.org/10.1007/s40997-018-0270-x

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  • DOI: https://doi.org/10.1007/s40997-018-0270-x

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