Skip to main content
SpringerLink
Log in

Studies on Mixed Convection and Its Transition to Turbulence—A Review

  • Chapter
  • First Online:
50 Years of CFD in Engineering Sciences

Abstract

Studies on mixed convective fluid flow and heat transfer are much more scarce compared to the large volume of literature available on either forced or natural convection. This is primarily because it was thought that applications of comparable forced and natural convection simultaneously are rather limited. However, the recent advent of high heat flux computing and LASER equipment and the need for their cooling has made mixed convection more relevant. The present review traces the development of studies in mixed convection over the last half a century. The most tricky and complex question in this respect may be that of the onset of turbulent flow in mixed convection. A clear and acceptable criterion for the transition of laminar flow to turbulent in this regime is still evasive. Hence, the review has culminated into a relook into the studies dedicated to these transition characteristics.

The article is dedicated to the memory of Prof. Brian Spalding with whom the corresponding author spent an exciting week at St. Petersburg, Russia during a conference organized by Prof. D. Leontiev. Prof. Spalding’s (along with Prof. Launder) work in turbulent mixed convection is the inspiration behind this review.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

\(Re\) :

Reynolds number (\(\rho VD/\mu\))

\(Ri\) :

Richardson number (\(Gr/Re^{2}\))

\(Pr\) :

Prandtl number (\(\mu C_{p} /k\))

\(Ra\) :

Rayleigh number (\(Gr.Pr\))

\(Nu\) :

Nusselt number (\(hD/k\))

\(Kn\) :

Knudsen number (\(\lambda /L\)); ‘\(\lambda\)’ is mean free path

\(Ha\) :

Hartman number

\(\overline{Nu}\) :

Average Nusselt number

\(Nu_{T}\) :

Nusselt number for forced turbulent convection

\(Gr\) :

Grashof number

\(Gr_{q}\) :

Grashof number based on heat flux (\(g\beta D^{4} \dot{q}/\nu^{2} k\))

\(Gr_{D}\) :

Grashof number based on diameter (\(g\beta D^{3} {\Delta }T/\nu^{2}\))

\(Gr_{L}\) :

Grashof number based on constant wall temperature (\(g\beta L^{3} {\Delta }T/\nu^{2}\))

\(Gr_{T}\) :

Thermal Grashof number (\(g\beta D^{3} {\Delta }T/\nu^{2}\))

\(Gr_{M}\) :

Solutal Grashof number (\(g\beta_{M} D^{3} {\Delta \omega }/\nu^{2}\))

\(\overline{Ra}\) :

Average Rayleigh number

\(\overline{Re}\) :

Average Reynolds number

\(\widehat{Nu}\) :

Weighted average Nusselt number

\(Gz\) :

Graetz number \(\left( {\frac{D}{L}Re.Pr} \right)\)

\(Re_{cr}\) :

Critical Reynolds number

\(Re_{\theta }\) :

Transition momentum thickness Reynolds number

\(Re_{qt}\) :

Reynolds value at the start of quasi-turbulent flow regime

\(Re_{x}\) :

Local Reynolds number

\(Bo\) :

Buoyancy parameter (\(Gr_{q} /Re^{m} Pr^{n}\))

\(Bo_{2}\) :

Buoyancy parameter (\(Gr_{q} /Re^{2.5} Pr\))

\(K\) :

Buoyancy parameter (\(Gr/Re^{2.5}\))

\(ER\) :

Expansion ratio (outlet to inlet height ratio)

E :

Enhancement ratio (ratio of heat input with porosity and without porosity)

ACFD:

Asymptotic Computational Fluid Dynamics

AWF:

Analytical Wall Functions

CFD:

Computational Fluid Dynamics

CMM:

Compound Matrix Method

CMSIP:

Coupled Modified Strongly Implicit Procedure

DNS:

Direct Numerical Simulation

FCD:

Forced Convection Developing

FD:

Fully Developed

LBM:

Lattice Boltzmann Method

LES:

Large Eddy Simulation

MCD:

Mixed Convection Developing

OpenFOAM:

Open source Field Operation And Manipulation

PIV:

Particle Image Velocimetry

RANS:

Reynolds Averaged Navier-Stokes

RNG:

Renormalization Group Method

SST:

Shear Stress Transport

UHF:

Uniform Heat Flux

UWT:

Uniform Wall Temperature

\(\varepsilon\) :

Rate of dissipation of turbulence energy

\(\omega\) :

Specific rate of dissipation

\(\varphi_{v}\) :

Viscosity ratio (\(\mu_{b} /\mu_{w}\))

\(\mu_{b}\) :

Dynamic viscosity at bulk temperature (Pa s)

\(\mu_{w}\) :

Dynamic viscosity at the wall temperature (Pa s)

\(\lambda\) :

Buoyancy parameter (\(Gr/Re^{2}\))

\(\emptyset\) :

Volume fraction

\(\varphi\) :

Angle (degree or radian)

\(\theta\) :

Dimensionless temperature

\(\rho\) :

Density (kg/m3)

\(\gamma\) :

Intermittency in \(\gamma - Re_{\theta }\) transition model

\(\beta\) :

Thermal expansion coefficient (K−1)

k:

Thermal conductivity (W/m K)

\(k\) :

Turbulence kinetic energy (J)

Sp. Gr.:

Specific gravity

g :

Acceleration due to gravity (m/s2)

a, b, c :

Constants in Eqs. 8, 12

\(L\) :

Length (m)

\(D\) :

Diameter (m)

\(D_{h}\) :

Hydraulic diameter (m)

\(d_{e}\) :

Equivalent diameter of a channel (m) (\(2hb/\left( {h + b} \right);\) \(h,b\) are channel height and width)

\(A\) :

Aspect ratio (–)

Q:

Heat rate (W)

\(\dot{q}\) :

Heat flux (W/m2)

\(q_{1}\) :

Cold wall heat flux (W/m2)

\(q_{2}\) :

Hot wall heat flux (W/m2)

\(x, y\) :

Axial and transverse coordinates (m)

\(u, v\) :

Axial and transverse velocities (m/s)

\(X, Y\) :

Dimensionless axial and transverse coordinates

\(U, V\) :

Dimensionless axial and transverse velocity

\(x\) :

Distance from the initial point of heating (m)

\(C_{p}\) :

Specific heat at constant pressure (J/kg K)

\(C_{f}\) :

Skin friction coefficient (–)

̴:

Approximately

©:

Copyright

lam, l:

Laminar

b :

Properties of fluid at bulk temperature

q :

Based on heat flux

M :

Mixed convection in Eq. 7

trans:

Transition

\(c, cr\) :

Critical value

\(lc\) :

Laminar flow at critical Reynolds number

\(cr_{2}\) :

Critical value at second wall

\(x\) :

Local value

t :

Turbulent

References

  1. Abdelmeguid, A. M., & Spalding, D. B. (1979). Turbulent flow and heat transfer in pipes with buoyancy effects. Journal of Fluid Mechanics, 94(2), 383–400.

    Article  Google Scholar 

  2. Abdollahzadeh, M., Esmaeilpour, M., Vizinho, R., Younesi, A., & Pàscoa, J. C. (2017). Assessment of RANS turbulence models for numerical study of laminar-turbulent transition in convection heat transfer. International Journal of Heat and Mass Transfer, 115, 1288–1308. https://doi.org/10.1016/j.ijheatmasstransfer.2017.08.114.

    Article  Google Scholar 

  3. Ackerman, J. W. (1970). Pseudoboiling heat transfer to supercritical pressure water in smooth and ribbed tubes. Journal of Heat Transfer, 92(3), 490. https://doi.org/10.1115/1.3449698.

    Article  Google Scholar 

  4. Aicher, T., & Martin, H. (1997). New correlations for mixed turbulent natural and forced convection heat transfer in vertical tubes. International Journal of Heat and Mass Transfer, 40(15), 3617–3626.

    Article  Google Scholar 

  5. Akyuzlu, K. M. (2013). A numerical study of unsteady mixed convection in a square cavity: Transition from laminar to turbulent flow. In ASME 2013 International Mechanical Engineering Congress and Exposition, V08AT09A047–V08AT09A047.

    Google Scholar 

  6. Al-asadi, M. T., Mohammed, H. A., Kherbeet, A. S., & Al-aswadi, A. A. (2017). Numerical study of assisting and opposing mixed convective nano fluid flows in an inclined circular pipe. International Communications in Heat and Mass Transfer, 85(May), 81–91.

    Google Scholar 

  7. Avramenko, A. A., Tyrinov, A. I., Shevchuk, I. V., Dmitrenko, N. P., Kravchuk, A. V., & Shevchuk, V. I. (2017). Mixed convection in a vertical flat microchannel. International Journal of Heat and Mass Transfer, 106, 1164–1173.

    Article  Google Scholar 

  8. Aydin, O. (1999). Aiding and opposing mechanisms of mixed convection in a shear-and buoyancy-driven cavity. International Communications in Heat and Mass Transfer, 26(7).

    Google Scholar 

  9. Babajani, M., Ghasemi, B., & Raisi, A. (2017). Numerical study on mixed convection cooling of solar cells with nanofluid. Alexandria Engineering Journal, 56(1), 93–103. https://doi.org/10.1016/j.aej.2016.09.008.

    Article  Google Scholar 

  10. Bae, J. H., Yoo, J. Y., & McEligot, D. M. (2008). Direct numerical simulation of heated CO2 flows at supercritical pressure in a vertical annulus at Re = 8900. Physics of Fluids, 20(5), 055108. https://doi.org/10.1063/1.2927488.

    Article  MATH  Google Scholar 

  11. Balaji, C., Hölling, M., & Herwig, H. (2007). A general methodology for treating mixed convection problems using asymptotic computational fluid dynamics (ACFD). International Communications in Heat and Mass Transfer, 34(6), 682–691. https://doi.org/10.1016/j.icheatmasstransfer.2007.03.006.

    Article  Google Scholar 

  12. Barozzi, G. S., Dumas, A., & Collins, M. W. (1984). Sharp entry and transition effects for laminar combined convection of water in vertical tubes. 235–241.

    Google Scholar 

  13. Barrios-Pina, H., Viazzo, S., & Rey, C. (2012). A numerical study of laminar and transitional mixed convection flow over a backward-facing step. Computers & Fluids, 56, 77–91. https://doi.org/10.1016/j.compfluid.2011.11.016.

    Article  MathSciNet  MATH  Google Scholar 

  14. Basak, T., Roy, S., Sharma, P. K., & Pop, I. (2009). Analysis of mixed convection flows within a square cavity with linearly heated side wall(s). International Journal of Heat and Mass Transfer, 52(9–10), 2224–2242.

    Article  MATH  Google Scholar 

  15. Basak, T., Roy, S., Sharma, P. K., & Pop, I. (2009). Analysis of mixed convection flows within a square cavity with uniform and non-uniform heating of bottom wall. International Journal of Thermal Sciences, 48(5), 891–912. https://doi.org/10.1016/j.ijthermalsci.2008.08.003.

    Article  Google Scholar 

  16. Bashir, A. I., & Meyer, J. P. (2017). Heat transfer in the laminar and transitional flow regimes of smooth vertical tube for upflow direction. In 13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics.

    Google Scholar 

  17. Behzadmehr, A., Galanis, N., & Laneville, A. (2002). Laminar-turbulent transition for low Reynolds number mixed convection in a uniformly heated vertical tube. International Journal of Numerical Methods for Heat and Fluid Flow, 12(7), 839–854. https://doi.org/10.1108/09615530210443052.

    Article  MATH  Google Scholar 

  18. Behzadmehr, A., Galanis, N., & Laneville, A. (2003). Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux. International Journal of Heat and Mass Transfer, 46(25), 4823–4833. https://doi.org/10.1016/S0017-9310(03)00323-5.

    Article  MATH  Google Scholar 

  19. Behzadmehr, A., Laneville, A., & Galanis, N. (2008). Experimental study of onset of laminar-turbulent transition in mixed convection in a vertical heated tube. International Journal of Heat and Mass Transfer, 51(25–26), 5895–5905. https://doi.org/10.1016/j.ijheatmasstransfer.2008.04.005.

    Article  MATH  Google Scholar 

  20. Bieder, U., Ziskind, G., & Rashkovan, A. (2018). CFD analysis and experimental validation of steady state mixed convection sodium flow. Nuclear Engineering and Design, 326, 333–343. https://doi.org/10.1016/j.nucengdes.2017.11.028.

    Article  Google Scholar 

  21. Biswas, G., & Eswaran, V. (2002). Turbulent flows: Fundamentals, experiments and modeling. Retrieved from https://books.google.co.in/books?id=2MdXPgAACAAJ.

  22. Boulama, K., & Galanis, N. (2004). Analytical solution for fully developed mixed convection between parallel vertical plates with heat and mass transfer. Journal of Heat Transfer, 126(3), 381–388. https://doi.org/10.1115/1.1737774.

    Article  Google Scholar 

  23. Bradley, D., & Entwistle, A. G. (1965). Developed laminar flow heat transfer from air for variable physical properties. International Journal of Heat and Mass Transfer, 8(4), 621–638. https://doi.org/10.1016/0017-9310(65)90049-9.

    Article  Google Scholar 

  24. Burgos, J., Cuesta, I., & Salueña, C. (2016). Numerical study of laminar mixed convection in a square open cavity. International Journal of Heat and Mass Transfer, 99, 599–612.

    Article  Google Scholar 

  25. Carr, A. D., Connor, M. A., & Buhr, H. O. (1973). Velocity, temperature, and turbulence measurements in air for pipe flow with combined free and forced convection. Journal of Heat Transfer, 95(4), 445. https://doi.org/10.1115/1.3450087.

    Article  Google Scholar 

  26. Chen, K.-H. (1990). A primitive variable, strongly implicit calculation procedure for two and three-dimensional unsteady viscous flows: Applications to compressible and incompressible flows including flows with free surfaces. Iowa State University Capstones, Theses and Dissertations.

    Google Scholar 

  27. Chen, T. S., Armaly, B. F., & Ramachandran, N. (1986). Correlations for laminar mixed convection flows on vertical, inclined, and horizontal flat plates. Journal of Heat Transfer, 108(4), 835–840.

    Article  Google Scholar 

  28. Cheng, T. S. (2011). Characteristics of mixed convection heat transfer in a lid-driven square cavity with various Richardson and Prandtl numbers. International Journal of Thermal Sciences, 50(2), 197–205. https://doi.org/10.1016/j.ijthermalsci.2010.09.012.

    Article  Google Scholar 

  29. Cheng, C., Kou, H., & Huangt, W. (1990). Flow reversal and heat transfer of fully developed mixed convection in vertical channels. Journal of Thermophysics and Heat Transfer, 4(3), 375–383.

    Google Scholar 

  30. Cherif, A. S., Kassim, M. A., Benhamou, B., Harmand, S., Corriou, J. P., & Ben Jabrallah, S. (2011). Experimental and numerical study of mixed convection heat and mass transfer in a vertical channel with film evaporation. International Journal of Thermal Sciences, 50(6), 942–953. https://doi.org/10.1016/j.ijthermalsci.2011.01.002.

    Article  Google Scholar 

  31. Churchill, S. W. (1977). Comprehensive correlating equations for heat, mass and momentum transfer in fully developed flow in smooth tubes. Industrial and Engineering Chemistry Fundamentals, 16(1), 109–116. https://doi.org/10.1021/i160061a021.

    Article  MathSciNet  Google Scholar 

  32. Craft, T. J., Gant, S. E., Gerasimov, A. V., Iacovides, H., & Launder, B. E. (2006). Development and application of wall-function treatments for turbulent forced and mixed convection flows. Fluid Dynamics Research, 38, 127–144. https://doi.org/10.1016/j.fluiddyn.2004.11.002.

    Article  MATH  Google Scholar 

  33. Craft, T. J., Gerasimov, A. V., Iacovides, H., & Launder, B. E. (2002). Progress in the generalization of wall-function treatments. International Journal of Heat and Fluid Flow, 23, 148–160.

    Article  Google Scholar 

  34. Davis, D. V. (1983). Natural convection of air in a square cavity. A bench mark numerical solution. International Journal for Numerical Methods in Fluids, 3, 249–264.

    Article  MATH  Google Scholar 

  35. Dawood, H. K., Mohammed, H. A., Sidik, N. A. C., Munisamy, K. M., & Wahid, M. A. (2015). Forced, natural and mixed-convection heat transfer and fluid flow in annulus: A review. International Communications in Heat and Mass Transfer, 62, 45–57. https://doi.org/10.1016/j.icheatmasstransfer.2015.01.006.

    Article  Google Scholar 

  36. Everts, M., & Meyer, J. P. (2015). Heat transfer of developing flow in the transitional flow regime. In Proceeding of First Thermal and Fluids Engineering Summer Conference (pp. 1051–1063). https://doi.org/10.1615/TFESC1.fnd.012660.

  37. Everts, M., & Meyer, J. P. (2018). Flow regime maps for smooth horizontal tubes at a constant heat flux. International Journal of Heat and Mass Transfer, 117, 1274–1290. https://doi.org/10.1016/j.ijheatmasstransfer.2017.10.073.

    Article  Google Scholar 

  38. Everts, M., & Meyer, J. P. (2018). Heat transfer of developing and fully developed flow in smooth horizontal tubes in the transitional flow regime. International Journal of Heat and Mass Transfer, 117, 1331–1351. https://doi.org/10.1016/j.ijheatmasstransfer.2017.10.071.

    Article  Google Scholar 

  39. Everts, M., & Meyer, J. P. (2018). Relationship between pressure drop and heat transfer of developing and fully developed flow in smooth horizontal circular tubes in the laminar, transitional, quasi-turbulent and turbulent flow regimes. International Journal of Heat and Mass Transfer, 117, 1231–1250. https://doi.org/10.1016/j.ijheatmasstransfer.2017.10.072.

    Article  Google Scholar 

  40. Farrugia, P. S., & Micallef, A. (2012). Turbulent plumes evolving in a vertical flow under a mixed convection regime. International Journal of Heat and Mass Transfer, 55(7–8), 1931–1940.

    Article  Google Scholar 

  41. Fewster, J. (1976). Mixed forced and free convective heat transfer to supercritical pressure fluids flowing in vertical pipes. The University of Manchester.

    Google Scholar 

  42. Fontana, É., Capeletto, C. A., da Silva, A., & Mariani, V. C. (2015). Numerical analysis of mixed convection in partially open cavities heated from below. International Journal of Heat and Mass Transfer, 81, 829–845.

    Article  Google Scholar 

  43. Fu, W.-S., Lai, Y.-C., Huang, Y., & Liu, K.-L. (2013). An investigation of flow reversal of mixed convection in a three dimensional rectangular channel with a finite length. International Journal of Heat and Mass Transfer, 64, 636–646.

    Article  Google Scholar 

  44. Galanis, N., & Behzadmehr, A. (2008). Mixed convection in vertical ducts. In Proceedings of 6th IASME/WSEAS International Conference on Fluid Mechanics and Aerodynamics (pp. 35–43).

    Google Scholar 

  45. Gangawane, K. M. (2017). Computational analysis of mixed convection heat transfer characteristics in lid-driven cavity containing triangular block with constant heat flux: Effect of Prandtl and Grashof numbers. International Journal of Heat and Mass Transfer, 105, 34–57.

    Article  Google Scholar 

  46. Gavara, M. R., Dutta, P., & Seetharamu, K. N. (2012). Mixed convection adjacent to non-isothermal vertical surfaces. International Journal of Heat and Mass Transfer, 55(17–18), 4580–4587.

    Article  Google Scholar 

  47. Gersten, K., & Herwig, H. (1992). Strömungsmechanik, Grundlagen der Impuls-, Wärme-und Stoff-Ubertragung aus Asymptotischer Sicht. Braunschweig/Wiesbaden: Vieweg-Verlag. Google Scholar.

    Google Scholar 

  48. Ghajar, A. J., & Tam, L. M. (1995). Flow regime map for a horizontal pipe with uniform wall heat flux and three inlet configurations. Experimental Thermal and Fluid Science, 10(3), 287–297. https://doi.org/10.1016/0894-1777(94)00107-J.

    Article  Google Scholar 

  49. Ghia, U., Ghia, K. N., & Shin, C. T. (1982). High-Re solutions for incompressible flow using the Navier Stokes equations and a multigrid method. Journal of Computational Physics, 48, 387–411. https://doi.org/10.1016/0021-9991(82)90058-4.

    Article  MATH  Google Scholar 

  50. Grassi, W., & Testi, D. (2006). Developing upward flow in a uniformly heated circular duct under transitional mixed convection. International Journal of Thermal Sciences, 45(9), 932–937. https://doi.org/10.1016/j.ijthermalsci.2005.11.007.

    Article  Google Scholar 

  51. Hall, W. B., & Jackson, J. D. (1971). Heat transfer near the critical point. Advances in Heat Transfer, 7(1), 86.

    Google Scholar 

  52. Hall, W. B., Jackson, J. D., & Watson, A. (1967). Paper 3: A review of forced convection heat transfer to fluids at supercritical pressures. Proceedings of the Institution of Mechanical Engineers, Conference Proceedings, 182(9), 10–22. https://doi.org/10.1243/PIME_CONF_1967_182_262_02.

    Article  Google Scholar 

  53. Hall, W. B., & Price, P. H. (1970). Mixed forced and free convection from a vertical heated plate to air. International Heat Transfer Conference, 4, 19.

    Google Scholar 

  54. Hallman, T. M. (1956). Combined forced and free-laminar heat transfer in vertical tubes with uniform internal heat generation. Transaction ASME, 78(8), 1841–1851.

    Google Scholar 

  55. Hallman, T. M. (1961). Experimental study of combined forced and free laminar convection in a vertical tube, N.A.S.A.T.N. D-1104.

    Google Scholar 

  56. Hanratty, T. J., Rosen, E. M., & Kabel, R. L. (1958). Effect of heat transfer on flow field at low Reynolds numbers in vertical tubes. Industrial and Engineering Chemistry, 50(5), 815–820.

    Article  Google Scholar 

  57. Hsu, Y.-Y., & Smith, J. M. (1961). The effect of density variation on heat transfer in the critical region. Journal of Heat Transfer, 83, 176. https://doi.org/10.1115/1.3680510.

    Article  Google Scholar 

  58. Ismael, M. A., Pop, I., & Chamkha, A. J. (2014). Mixed convection in a lid-driven square cavity with partial slip. International Journal of Thermal Sciences, 82(1), 47–61. https://doi.org/10.1016/j.ijthermalsci.2014.03.007.

    Article  Google Scholar 

  59. Jackson, J. D. (2006). Studies of buoyancy-influenced turbulent flow and heat transfer in vertical passages. International Heat Transfer Conference 13, KN-24. https://doi.org/10.1615/IHTC13.p30.240.

  60. Jackson, J. D. (2013). Fluid flow and convective heat transfer to fluids at supercritical pressure. Nuclear Engineering and Design, 264, 24–40. http://dx.doi.org/10.1016/j.nucengdes.2012.09.040.

    Article  Google Scholar 

  61. Jackson, J. D., Cotton, M. A., & Axcell, B. P. (1989). Studies of mixed convection in vertical tubes. International Journal of Heat and Fluid Flow, 10(1), 2–15.

    Article  Google Scholar 

  62. Jackson, J. D., Lutterodt, K. E., & Weinberg, R. (2003). Experimental studies of buoyancy-influenced convective heat transfer in heated vertical tubes at pressures just above and just below the thermodynamic critical value. In Proceedings of the International Conference on Global Environment and Advanced Nuclear Power Plants (GENES4/ANP2003), 36(4), Paper No. 1177.

    Google Scholar 

  63. Joye, D. D. (1996). Comparison of correlations and experiment in opposing flow, mixed convection heat transfer in a vertical tube with Grashof number variation. International Journal of Heat and Mass Transfer, 39(5), 1033–1038.

    Article  MathSciNet  Google Scholar 

  64. Joye, D. D. (2003). Pressure drop correlation for laminar, mixed convection, aiding flow heat transfer in a vertical tube. International Journal of Heat and Fluid Flow, 24(2), 260–266. https://doi.org/10.1016/S0142-727X(02)00238-2.

    Article  MathSciNet  Google Scholar 

  65. Kamath, P. M., Balaji, C., & Venkateshan, S. P. (2011). Experimental investigation of flow assisted mixed convection in high porosity foams in vertical channels. International Journal of Heat and Mass Transfer, 54(25–26), 5231–5241. https://doi.org/10.1016/j.ijheatmasstransfer.2011.08.020.

    Article  Google Scholar 

  66. Kasagi, N., & Nishimura, M. (1997). Direct numerical simulation of combined forced and natural turbulent convection in a vertical plane channel. International Journal of Heat and Fluid Flow, 18(96), 88–99.

    Article  Google Scholar 

  67. Kemeny, G. A., & Somers, E. V. (1962). Combined free and forced-convective flow in vertical circular tubes-experiments with water and oil. Journal of Heat Transfer, 84(4), 339–345. https://doi.org/10.1115/1.3684389.

    Article  Google Scholar 

  68. Kenning, D. B. R., Poon, J. Y., & Shock, R. A. W. (1973). Local reductions in heat transfer due to buoyancy effects in upward turbulent flow. Atomic Energy Research Establishment.

    Google Scholar 

  69. Kotresha, B., & Gnanasekaran, N. (2018). Investigation of mixed convection heat transfer through metal foams partially filled in a vertical channel by using computational fluid dynamics. Journal of Heat Transfer, 140(11), 112501–112511. https://doi.org/10.1115/1.4040614.

    Article  Google Scholar 

  70. Launder, B. E., & Sharma, B. I. (1974). Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Letters in Heat and Mass Transfer, 1(2), 131–137.

    Article  Google Scholar 

  71. Launder, B. E., & Spalding, D. B. (1974). The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3, 269–289. https://doi.org/10.1016/B978-0-08-030937-8.50016-7.

    Chapter  Google Scholar 

  72. Lawrence, W. T., & Chato, J. C. (1966). Heat-transfer effects on the developing laminar flow inside vertical tubes. Journal of Heat Transfer, 88(2), 214–222. https://doi.org/10.1115/1.3691518.

    Article  Google Scholar 

  73. Li, Z. Y., Huang, Z., & Tao, W. Q. (2016). Three-dimensional numerical study on fully-developed mixed laminar convection in parabolic trough solar receiver tube. Energy , 113, 1288–1303. https://doi.org/10.1016/j.energy.2016.07.148.

    Article  Google Scholar 

  74. Mare, T., Galanis, N., Voicu, I., Miriel, J., & Sow, O. (2008). Experimental and numerical study of mixed convection with flow reversal in coaxial double-duct heat exchangers. Experimental Thermal and Fluid Science, 32(5), 1096–1104. https://doi.org/10.1115/1.3449722.

    Article  Google Scholar 

  75. Marner, W. J., & McMillan, H. K. (1970). Combined free and forced laminar convection in a vertical tube with constant wall temperature. Journal of Heat Transfer, 92(3), 559–562.

    Article  Google Scholar 

  76. Marocco, L. (2018). Hybrid LES/DNS of turbulent forced and aided mixed convection to a liquid metal flowing in a vertical concentric annulus. International Journal of Heat and Mass Transfer, 121, 488–502. https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.006.

    Article  Google Scholar 

  77. Marocco, L., Alberti di Valmontana, A., & Wetzel, T. (2017). Numerical investigation of turbulent aided mixed convection of liquid metal flow through a concentric annulus. International Journal of Heat and Mass Transfer, 105, 479–494. https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.107.

    Article  Google Scholar 

  78. Martinelli, R. C., & Boelter, L. M. K. (1942). Analytical prediction of superimposed free and forced convection in a vertical pipe, 5. University of California. Publications in Engineering, 23–58.

    Google Scholar 

  79. Metais, B., & Eckert, E. R. G. (1964). Forced, mixed, and free convection regimes. Journal of Heat Transfer, 86(2), 295. https://doi.org/10.1115/1.3687128.

    Article  Google Scholar 

  80. Meyer, J. P. (2014). Heat transfer in tubes in the transitional flow regime. In Proceedings of the 15th International Heat Transfer Conference, Kyoto, Paper KN03 (pp. 10–15).

    Google Scholar 

  81. Meyer, J. P., & Everts, M. (2018). Single-phase mixed convection of developing and fully developed flow in smooth horizontal circular tubes in the laminar and transitional flow regimes. International Journal of Heat and Mass Transfer, 117, 1251–1273.

    Article  Google Scholar 

  82. Mikielewicz, D. P. (1994). Comparative studies of turbulence models under conditions of mixed convection with variable properties in heated vertical tubes. The University of Manchester.

    Google Scholar 

  83. Mohammed, H. A., & Salman, Y. K. (2007). Experimental investigation of mixed convection heat transfer for thermally developing flow in a horizontal circular cylinder. Applied Thermal Engineering, 27(8–9), 1522–1533. https://doi.org/10.1016/j.applthermaleng.2006.09.023.

    Article  Google Scholar 

  84. Mori, Y., et al. (1966). Forced convective heat transfer in uniformly heated horizontal tubes 1st report—Experimental study on the effect of buoyancy. International Journal of Heat and Mass Transfer, 9, 453–463.

    Article  Google Scholar 

  85. Morton, B. R. (1960). Laminar convection in uniformly heated vertical pipes. Journal of Fluid Mechanics, 8(2), 227–240. https://doi.org/10.1017/S0022112060000566.

    Article  MathSciNet  MATH  Google Scholar 

  86. Nobari, M. R. H., & Beshkani, A. (2007). A numerical study of mixed convection in a vertical channel flow impinging on a horizontal surface. International Journal of Thermal Sciences, 46(10), 989–997. https://doi.org/10.1016/j.ijthermalsci.2006.11.012.

    Article  Google Scholar 

  87. Onyejekwe, O. O. (2012). Combined effects of shear and buoyancy for mixed convection in an enclosure. Advances in Engineering Software, 47(1), 188–193. https://doi.org/10.1016/j.advengsoft.2011.11.002.

    Article  Google Scholar 

  88. Petukhov, B. S. (1976). Turbulent flow and heat transfer in pipes under considerable effect of thermogravitational forces. In Heat Transfer and Turbulent Buoyant Convection. Seminar of International Centre for Heat and Mass Transfer, Dubrovnik, Yugoslavia, Hemisphere Publishing Corporation, Washington D.C. (Vol. 2, pp. 701–717).

    Google Scholar 

  89. Petukhov, B. S., & Strigin, B. K. (1968). Experimental investigation of heat transfer with viscous-inertial-gravitational flow of a liquid in vertical tubes. Teplofizika Vysokikh Temperatur, 6, 933–937.

    Google Scholar 

  90. Pigford, R. L. (1955). Non-isothermal flow and heat transfer inside vertical tubes. Chemical Engineering Progress Symposium Series, 51, 79–92.

    Google Scholar 

  91. Polyakov, A. F. (1974). Development of secondary free-convection currents in forced turbulent flow in horizontal tubes. Journal of Applied Mechanics and Technical Physics, 15(5), 632–637.

    Article  Google Scholar 

  92. Poskas, P., & Poskas, R. (2003). Local turbulent opposing mixed convection heat transfer in inclined flat channel for stably stratified airflow. International Journal of Heat and Mass Transfer, 46(21), 4023–4032.

    Article  Google Scholar 

  93. Poskas, P., Poskas, R., & Gediminskas, A. (2012). Numerical investigation of the opposing mixed convection in an inclined flat channel using turbulence transition models. Journal of Physics: Conference Series, 395(1), 012098. https://doi.org/10.1088/1742-6596/395/1/012098.

    Article  Google Scholar 

  94. Poskas, R., Poskas, P., & Sabanskis, D. (2005). Local turbulent opposing mixed convection heat transfer in inclined flat channel for unstably stratified airflow. International Journal of Heat and Mass Transfer, 48(5), 956–964. https://doi.org/10.1016/j.ijheatmasstransfer.2004.09.025.

    Article  Google Scholar 

  95. Poskas, P., Poskas, R., Sirvydas, A., & Smaizys, A. (2011). Experimental investigation of opposing mixed convection hear transfer in the vertical flat channel in a laminar-turbulent transition region. International Journal of Heat and Mass Transfer, 54(1–3), 662–668. https://doi.org/10.1016/j.ijheatmasstransfer.2010.09.004.

    Article  Google Scholar 

  96. Poskas, R., Sirvydas, A., & Bartkus, G. (2016). Experimental investigation of opposing mixed convection heat transfer in a vertical flat channel in the transition region. 2. Analysis of local heat transfer in the case of the prevailing effect of buoyancy and generalization of data. Heat Transfer Research, 47(8), 745–751. https://doi.org/10.1615/HeatTransRes.2016012394.

    Article  Google Scholar 

  97. Poskas, R., Sirvydas, A., Kolesnikovas, J., & Kilda, R. (2013). Experimental investigation of opposing mixed convection heat transfer in a vertical flat channel in the transition region. 1. Analysis of local heat transfer. Heat Transfer Research, 44(7), 589–602. https://doi.org/10.1615/HeatTransRes.v44.i7.10.

    Article  Google Scholar 

  98. Prasad, A. K., & Koseff, J. R. (1996). Combined forced and natural convection heat transfer in a deep lid-driven cavity flow. International Journal of Heat and Fluid Flow, 17(5), 460–467.

    Article  Google Scholar 

  99. Rabbi, K. M., Saha, S., Mojumder, S., Rahman, M. M., Saidur, R., & Ibrahim, T. A. (2016). Numerical investigation of pure mixed convection in a ferrofluid-filled lid-driven cavity for different heater configurations. Alexandria Engineering Journal, 55(1), 127–139. https://doi.org/10.1016/j.aej.2015.12.021.

    Article  Google Scholar 

  100. Rahman, M. M., Öztop, H. F., Rahim, N. A., Saidur, R., Al-Salem, K., Amin, N., et al. (2012). Computational analysis of mixed convection in a channel with a cavity heated from different sides. International Communications in Heat and Mass Transfer, 39(1), 78–84. https://doi.org/10.1016/j.icheatmasstransfer.2011.09.006.

    Article  Google Scholar 

  101. Rana, P., & Bhargava, R. (2011). Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids. Communications in Nonlinear Science and Numerical Simulation, 16(11), 4318–4334. https://doi.org/10.1016/j.cnsns.2011.03.014.

    Article  MathSciNet  MATH  Google Scholar 

  102. Reichl, C., Hengstberger, F., & Zauner, C. (2013). Heat transfer mechanisms in a compound parabolic concentrator: Comparison of computational fluid dynamics simulations to particle image velocimetry and local temperature measurements. Solar Energy, 97, 436–446. https://doi.org/10.1016/j.solener.2013.09.003.

    Article  Google Scholar 

  103. Rosen, E. M., & Hanratty, T. J. (1961). Use of boundary-layer theory to predict the effect of heat transfer on the laminar-flow field in a vertical tube with a constant-temperature wall. AIChE Journal, 7(1), 112–123. https://doi.org/10.1002/aic.690070126.

    Article  Google Scholar 

  104. Sakurai, A., Matsubara, K., Takakuwa, K., & Kanbayashi, R. (2012). Radiation effects on mixed turbulent natural and forced convection in a horizontal channel using direct numerical simulation. International Journal of Heat and Mass Transfer, 55(9–10), 2539–2548. https://doi.org/10.1016/j.ijheatmasstransfer.2012.01.006.

    Article  Google Scholar 

  105. Sengupta, T. K., & Subbaiah, K. V. (2006). Spatial stability for mixed convection boundary layer over a heated horizontal plate. Studies in Applied Mathematics, 117(3), 265–298. https://doi.org/10.1111/j.1467-9590.2006.00355.x.

    Article  MathSciNet  MATH  Google Scholar 

  106. Sharma, N., Dhiman, A. K., & Kumar, S. (2012). Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers. International Journal of Heat and Mass Transfer, 55(9–10), 2601–2614. https://doi.org/10.1016/j.ijheatmasstransfer.2011.12.034.

    Article  Google Scholar 

  107. Shitsman, M. E. (2006). Natural convection effect on heat transfer to a turbulent water flow in intensively heated tubes at supercritical pressures. ARCHIVE: Proceedings of the Institution of Mechanical Engineers, Conference Proceedings 1964–1970 (Vols. 178–184), Various Titles Labelled Volumes A to S, 182(39), 36–41. https://doi.org/10.1243/PIME_CONF_1967_182_265_02.

    Article  Google Scholar 

  108. Singh, A. K., Harinadha, G., Kishore, N., Barua, P., Jain, T., & Joshi, P. (2015). Mixed convective heat transfer phenomena of circular cylinders to non-newtonian nanofluids flowing upward. Procedia Engineering, 127, 118–125. https://doi.org/10.1016/j.proeng.2015.11.434.

    Article  Google Scholar 

  109. Skiadaressis, D., & Spalding, D. B. (1977). Prediction of combined free and forced convection in turbulent flow through horizontal pipes. Letters in Heat and Mass Transfer, 4(1), 35–39.

    Article  Google Scholar 

  110. Steiner, A. (1971). On the reverse transition of a turbulent flow under the action of buoyancy forces. Journal of Fluid Mechanics, 47(3), 503–512.

    Article  Google Scholar 

  111. Subhashini, S. V., Samuel, N., & Pop, I. (2011). Effects of buoyancy assisting and opposing flows on mixed convection boundary layer flow over a permeable vertical surface. International Communications in Heat and Mass Transfer, 38(4), 499–503. https://doi.org/10.1016/j.icheatmasstransfer.2010.12.041.

    Article  Google Scholar 

  112. Suga, K., Ishibashi, Y., & Kuwata, Y. (2013). An analytical wall-function for recirculating and impinging turbulent heat transfer. International Journal of Heat and Fluid Flow, 41, 45–54.

    Article  Google Scholar 

  113. Tam, L. M., & Ghajar, A. J. (2006). Transitional heat transfer in plain horizontal tubes. Heat Transfer Engineering, 27(5), 23–38. https://doi.org/10.1080/01457630600559538.

    Article  Google Scholar 

  114. Tanaka, H., Ayao, T., Masaru, H., & Nuchi, N. (1973). Effects of buoyancy and of acceleration owing to thermal expansion on forced turbulent convection in vertical circular tubes—criteria of the effects, velocity and temperature profiles, and reverse transition from turbulent to laminar flow. International Journal of Heat and Mass Transfer, 16(6), 1267–1288.

    Article  Google Scholar 

  115. Tanaka, H., Shigeo, M., & Shunichi, H. (1987). Combined forced and natural convection heat transfer for upward flow in a uniformly heated, vertical pipe. International Journal of Heat and Mass Transfer, 30(1), 165–174.

    Article  Google Scholar 

  116. Tian, C., Wang, J., Cao, X., Yan, C., & Ala, A. A. (2018). Experimental study on mixed convection in an asymmetrically heated, inclined, narrow, rectangular channel. International Journal of Heat and Mass Transfer, 116, 1074–1084. https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.099.

    Article  Google Scholar 

  117. Velusamy, K., & Garg, V. K. (1996). Laminar mixed convection in vertical elliptic ducts. International Journal of Heat and Mass Transfer, 39(4), 745–752.

    Article  MATH  Google Scholar 

  118. Venkatasubbaiah, K., & Sengupta, T. K. (2009). Mixed convection flow past a vertical plate: Stability analysis and its direct simulation. International Journal of Thermal Sciences, 48(3), 461–474. https://doi.org/10.1016/j.ijthermalsci.2008.03.019.

    Article  Google Scholar 

  119. Vilemas, J. V., Poškas, P. S., & Kaupas, V. E. (1992). Local heat transfer in a vertical gas-cooled tube with turbulent mixed convection and different heat fluxes. International Journal of Heat and Mass Transfer, 35(10), 2421–2428.

    Article  Google Scholar 

  120. Walklate, P. J. (1976). A comparative study of theoretical models of turbulence for the numerical prediction of boundary-layer flows. University of Manchester Institute of Science and Technology.

    Google Scholar 

  121. Wang, X. A. (1982). An experimental study of mixed, forced, and free convection heat transfer from a horizontal flat plate to air. Journal of Heat Transfer, 107(3), 738. https://doi.org/10.1115/1.3247494.

    Article  Google Scholar 

  122. Wang, C., Gao, P., Wang, Z., & Tan, S. (2012). Experimental study of transition from laminar to turbulent flow in vertical narrow channel. Annals of Nuclear Energy, 47, 85–90. https://doi.org/10.1016/j.anucene.2012.04.018.

    Article  Google Scholar 

  123. Wang, J., Li, J., & Jackson, J. D. (2002). Mixed convection heat transfer to air flowing upwards through a vertical plane passage: Part 3. Chemical Engineering Research and Design, 80(3), 252–260.

    Article  Google Scholar 

  124. Yang, G., Huang, Y., Wu, J., Zhang, L., Chen, G., Lv, R., et al. (2017). Experimental study and numerical models assessment of turbulent mixed convection heat transfer in a vertical open cavity. Building and Environment, 115, 91–103. https://doi.org/10.1016/j.buildenv.2017.01.016.

    Article  Google Scholar 

  125. You, J., Yoo, J. Y., & Choi, H. (2003). Direct numerical simulation of heated vertical air flows in fully developed turbulent mixed convection. International Journal of Heat and Mass Transfer, 46(9), 1613–1627. https://doi.org/10.1016/S0017-9310(02)00442-8.

    Article  MATH  Google Scholar 

  126. Zeldin, B., & Schmidt, F. W. (1972). Developing flow with combined forced-free convection in an isothermal vertical tube. Journal of Heat Transfer, 94, 211–223. https://doi.org/10.1115/1.3449899.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India

    Somenath Gorai & Sarit K. Das

Authors
  1. Somenath Gorai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sarit K. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sarit K. Das .

Editor information

Editors and Affiliations

  1. ACRI, The CFD Innovators, Los Angeles, CA, USA

    Akshai Runchal

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Gorai, S., Das, S.K. (2020). Studies on Mixed Convection and Its Transition to Turbulence—A Review. In: Runchal, A. (eds) 50 Years of CFD in Engineering Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-15-2670-1_10

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-2670-1_10

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-2669-5

  • Online ISBN: 978-981-15-2670-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation