# Unsteady fluid flow and heat transfer over a bank of flat tubes

- 358 Downloads
- 10 Citations

## Abstract

Transient numerical simulations of fluid flow and heat transfer over a bank of flat tubes have been carried for both in-line and staggered configurations for the following boundary conditions: (a) isothermal and (b) isoflux. The effect of Reynolds number, Prandtl number, length ratio, and the height ratio, on the Nusselt number, and the dimensionless pressure drop are elucidated. Correlations are proposed for both pressure drop and Nusselt number and optimum configurations have been determined.

## Keywords

Nusselt Number Height Ratio Average Nusselt Number Total Heat Transfer Nusselt Number Increase## List of symbols

*A*total area of all tubes, m

^{2}*A*_{t}are a of a single tube, m

^{2}*C*constant in the temperature boundary condition (Eq. 7)

*C*_{p}specific heat, J/kg K

*D*_{a}transverse diameter of flat tube, m

*D*_{b}longitudinal diameter of flat tube, m

*D*_{H}hydraulic diameter, 2H, m

*D*_{P}dimensionless pressure drop, \({\frac{{P_{{\rm in}} - P_{{\rm out}}}}{{\rho U_{b}^{2}}}}\)

*H*height of HEM, m

*h*heat transfer coefficient for single HEM, W/m

^{2}K*k*thermal conductivity, W/m K

*L*length of HEM, m

*m*^{.}mass flow rate of the fluid across the tube bank, kg/s

*Nu*Nusselt number, \({\frac{{h\,D_{H}}}{k}}\)

*P*pressure, Pa

*P*_{in}module inlet pressure, Pa

*P*_{out}module outlet pressure, Pa

- Δ
*P* pressure drop across the tube bank, Pa

*Q*total heat transferred across the tube bank, W

*q*′′constant heat flux on tube surface, W/m

^{2}*Re*Reynolds number, \({\frac{{U_{{\max}} \,D_{H}}}{\upsilon}}\)

*S*_{T}transverse pitch for tube bank, m

*S*_{L}longitudinal pitch for tube bank, m

*T*temperature, K

*T*_{b}bulk temperature at any cross section, K

*T*_{b,m}average of the module inlet and module outlet temperatures, K

*T*_{in}inlet temperature of the fluid, K

*T*_{W}constant temperature of tube surface, K

- Δ
*T* temperature difference, K

*t*time, s

*U*,*V*horizontal and vertical velocities, m/s

*U*_{b}bulk velocity at any cross section, m/s, \({\frac{1}{H}\,{\int\limits_0^H {U\,dy}}}\)

*U*_{in}inlet velocity of the fluid, m/s

*U*_{max}maximum velocity at the minimum cross section, m/s

*X*,*Y*horizontal and vertical co-ordinates, m

## Greek symbols

- μ
dynamic viscosity, N·s/m

^{2}- ρ
density, kg/m

^{3}- ν
kinematic viscosity, m

^{2}/s

## Subscripts

*i*module number

## Abbreviations

- HEM
Heat exchanger module

- IN
Inlet

- MI
Module inlet

- MO
Module outlet

- OUT
Outlet

## References

- 1.Zukauskas A (1972) Heat transfer from tubes in cross flow. Adv Heat Transf 8:93–160Google Scholar
- 2.Launder BE, Massey TH (1978) The numerical prediction of viscous flow and heat transfer in tube banks. ASME J Heat Transf 100:565–571Google Scholar
- 3.Fujii M, Fujii T (1984) A numerical analysis of laminar flow and heat transfer of air in an in-line tube bank. Numer Heat Transf 7:89–102zbMATHCrossRefGoogle Scholar
- 4.Sparrow EM, Kang SS (1985) Longitudinally-finned cross-flow tube banks and their heat transfer and pressure drop characteristics. Int J Heat Mass Transf 28(2):339–350CrossRefGoogle Scholar
- 5.Baughn JW, Elderkin MJ, McKillop AA (1986) Heat transfer from a single cylinder, cylinders in tandem, and cylinders in the entrance region of a tube bank with a uniform heat flux. Trans ASME J Heat Transf 108:386–391Google Scholar
- 6.Faghri M, Rao N (1987) Numerical computation of flow and heat transfer in finned and unfinned tube banks. Int J Heat Mass Transf 30(2):363–372CrossRefGoogle Scholar
- 7.Stanescu G, Fowler AJ, Bejan A (1996) The optimal spacing of cylinders in free stream cross-flow forced convection. Int J Heat Mass Transf 39(2):311–317CrossRefGoogle Scholar
- 8.Wang YQ, Penner LA, Ormiston SJ (2000) Analysis of laminar forced convection of air for cross flow in banks of staggered tubes. Numer Heat Transf Part A 38:819–845CrossRefGoogle Scholar
- 9.Madhani VK, Chhabra RP, Eswaran V (2002) Forced convection heat transfer in tube banks in cross flow. Chem Eng Sci 57:379–391CrossRefGoogle Scholar
- 10.El-Shaboury EMF, Ormiston SJ (2005) Analysis of laminar forced convection of air for cross flow in in-line tube banks with non square arrangements. Numer Heat Transf Part A 48:99–126CrossRefGoogle Scholar
- 11.Ota T, Nishiyama H, TaokaY (1984) Heat transfer and flow around an elliptic cylinder. Int J Heat Mass Transf 27(10):1771–1779CrossRefGoogle Scholar
- 12.Ota T, Nishiyama H, Kominami J, Sato K (1986) Heat transfer from two elliptic cylinder in tandem arrangement. J Heat Transf 108:525–531CrossRefGoogle Scholar
- 13.Matos RS, Vargas JVC, Laursen TA, Saboya FEM (2001) Optimization study and heat transfer comparison of staggered circular and elliptic tubes in forced convection. Int J Heat Mass Transf 44:3953–3961zbMATHCrossRefGoogle Scholar
- 14.Khan MG, Fartaj A, Tang DK (2004) An experimental characterisation of cross flow of cooling of air via an in-line elliptical tube array. Int J Heat Fluid Flow 25:636–648CrossRefGoogle Scholar
- 15.Ala H (2005) Thermal-hydraulic performance of oval tubes in cross flow of air. Heat Mass Transf 41:724–733CrossRefGoogle Scholar
- 16.Webb RL (1993) Principles of enhanced heat transfer, 2nd edn. Wiley, New YorkGoogle Scholar
- 17.Bahaidarah HMS, Anand NK, Chen HC (2005) A numerical study of fluid flow and heat transfer over a bank of flat tubes. Numer Heat Transf Part A 48:359–385CrossRefGoogle Scholar
- 18.Tatsutani K, Devarakonda R, Humphrey JAC (1993) Unsteady flow and heat transfer for cylinder pairs in a channel. Int J Heat Mass Transf 36(13):3311–3328CrossRefGoogle Scholar
- 19.Johnson AA, Tezduyar TE, Liou J (1993) Numerical simulation of flow past periodic arrays of cylinders. Comput Mech 11:371–383CrossRefGoogle Scholar
- 20.Beale SB, Spalding DB (1999) A numerical study of unsteady fluid flow in in-line and staggered tube banks. J Fluids Struct 13:723–754CrossRefGoogle Scholar
- 21.Rosales JL, Ortega A, Humphrey JAC (2000) A numerical investigation of the convective heat transfer in unsteady laminar flow past a single and tandem pair of square cylinders in a channel. Numer Heat Transf Part A 38:443–465CrossRefGoogle Scholar
- 22.Jue TC, Wu HW, Huang SY (2001) Heat transfer predictions around three heated cylinders between two parallel plates. Numer Heat Transf Part A 40:715–733CrossRefGoogle Scholar
- 23.Srinivas M, Nishith V, Chhabra RP (2005) Momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel. Heat Mass Transf doi: 10.1007/s00231-005-0074-6
- 24.Schneider K, Farge M (2005) Numerical simulation of the transient flow behavior in tube bundles using a volume penalization method. J Fluids Struct 20:555–566CrossRefGoogle Scholar
- 25.Horvat A, Leskovar M, Mavko B (2006) Comparison of heat transfer conditions in tube bundle cross flow for different tube shapes. Int J Heat Mass Transf 49:1027–1038CrossRefGoogle Scholar
- 26.Horvat A, Mavko B (2006) Heat transfer conditions in flow across a bundle of cylindrical and ellipsoidal tubes. Numer Heat Transf Part A 49:699–715CrossRefGoogle Scholar
- 27.FLUENT 6.2 documentation, http://www.fluentusers.com, Fluent Inc, USA
- 28.GAMBIT 2.2.30 documentation, http://www.fluentusers.com, Fluent Inc, USA
- 29.Grimison ED (1937) Correlation and utilisation of new data on flow resistance and heat transfer for crossflow of gases over tube banks. Trans ASME 59:583Google Scholar