Skip to main content
SpringerLink
Log in

Natural convection with surface radiation from a planar heat generating element mounted freely in a vertical channel

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

Experiments and numerical simulations have been conducted to study the conjugate heat transfer by natural convection and surface radiation from a planar heat generating element placed centrally between two adiabatic vertical plates. The relevant problem dependent parameters considered in this study are modified Rayleigh number, channel aspect ratio, stream-wise location of the heat generating element, and surface emissivities of the heat generating element and the adiabatic side plates. Experiments are conducted for different values of modified Rayleigh number ranging from 3.2 × 105 to 1.6 × 107 and surface emissivities 0.05, 0.55, 0.75 and 0.85. The interdependence between the heat transfer mechanism and the flow field under the influence of surface radiation on natural convection is explored and discussed. Experimental correlations for total and convective Nusselt number, and dimensionless temperature in terms of relevant parameters have been developed. The mathematical model governing the problem has been numerically solved using a commercial computational fluid dynamics package FLUENT 6.3 and the numerical predictions substantiate the experimental observations.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

A 1 :

Area of lateral surface of the heat generating element (m2)

A e :

Area of top and bottom surface of the heat generating element (m2)

A s :

Total surface area of the heat generating element (m2)

AR :

Channel aspect ratio \((\frac{H}{S})\)

Bi :

Biot number \((\frac{hL_{c}}{k_{s}})\)

b :

Span of the heat generating element (m)

C p :

Specific heat at constant pressure (J/kg K)

E :

Emissive power (W/m2)

F ij :

Shape factor of surface i with respect to surface j

g :

Gravitational acceleration (m/s2)

h c :

Average convective heat transfer coefficient (W/m2 K)

H :

Channel height (m)

I :

Current (A)

J :

Radiosity (W/m2)

k :

Thermal conductivity (W/mK)

L :

Height of the heat generating element (m)

L c :

Characterstic length of the heat generating element \((\frac{v}{A_{s}})\)

\(\dot{m_{f}}\) :

Mass flow rate of fluid (kg/s)

Nu c :

Average convective Nusselt number

Nu r :

Average radiative Nusselt number

Nu t :

Average total Nusselt number

p :

Pressure (Pa)

Pr :

Prandtl number \((\frac{\nu}{\alpha})\)

Q c :

Convective heat transfer (W)

Q l :

Conduction heat loss (W)

Q r1 :

Radiation heat transfer from the lateral surface (W)

Q r2 :

Radiation heat transfer form the top and bottom surface (W)

Q r :

Total radiation heat transfer (W)

Q t :

Power input to the heat generating element (W)

q :

Heat flux (W/m2)

q ″′ :

Volumetric heat generation (W/m3)

q*:

Dimensionless volumetric heat generation

\(\dot q_{b}\) :

Heat transfer rate per unit width of the heat generating element (W/m)

Ra*:

Modified Rayleigh number

S :

Channel spacing (m)

T :

Temperature (K)

t :

Time (s)

U :

Velocity vector (m/s)

u :

Horizontal component of velocity (m/s)

v :

Vertical component of velocity (m/s)

V :

Voltage (V)

w :

Thickness of the heat generating element (m)

x, y, z:

Cartesian co-ordinates (m)

α:

Thermal diffusivity (m2/s)

β:

Isobaric cubic expansivity of fluid (1/K)

\(\epsilon_h\) :

Surface emissivity of heat generating element

\(\epsilon_s\) :

Surface emissivity of side plate

ν:

Kinematic viscosity (m2/s)

θ:

Dimensionless temperature of the heat generating element

ρ:

Density of the fluid (kg/m3)

σ:

Stefan–Boltzmann constant, 5.67 × 10−8 (W/m2K4)

b :

Black body

h :

Hot surface/heat generating element

s :

Side adiabatic plate

f :

Fluid

i :

Initial

r :

Radiative

n :

Normal direction

o :

Stagnation

∞:

Ambient condition

st :

Static

exp :

Experimental

num :

Numerical

th :

Theoretical

References

  1. Doshy I (1984) Relaibility impact of thermal design. In: Technical conference-IEPS, 4th annual international electronic packaging conference, pp 307–317

  2. Kang BH, Jaluria Y (1990) Natural convection heat transfer characteristics of a protruding thermal source located on horizontal and vertical surface. Int J Heat Mass Transf 33:1347–1357

    Article  Google Scholar 

  3. Kelkar MK, Choudhury D (1993) Numerical prediction of periodically fully developed natural convection in vertical channel with surface mounted heat generating blocks. Int J Heat Mass Transf 36:1133–1145

    Article  MATH  Google Scholar 

  4. Fujii M, Gima S,Tomimura T, Zhang X (1996) Natural convection to air from an array of vertical parallel plates with discrete and protruding heat sources. Int J Heat Fluid Flow 17:483–490

    Article  Google Scholar 

  5. Desrayaud G, Fichera A (2003) On Natural convective heat transfer in vertical channels with a single surface mounted heat flux module. ASME J Heat Transf 125:734–739

    Article  Google Scholar 

  6. Desrayaud G, Fichera A, Lauriat G (2007) Natural convection air cooling of a substrate mounted protruding heat source in a stack of parallel boards. Int J Heat Fluid Flow 28:469–482

    Article  Google Scholar 

  7. Carpenter JR,Briggs DG, Sernas V (1976) Combined radiation and developing laminar free convection between vertical flat plates with asymmetric heating. ASME J Heat Transf 98:95–100

    Article  Google Scholar 

  8. Krishnan AS, Balaji C, Venkateshan SP (2004) An experimental correlation for combined convection radiation between parallel vertical plates. ASME J Heat Transf 126:849–851

    Article  Google Scholar 

  9. Balaji C and Venkateshan SP (1993) Interaction of radiation with free convection in a square cavity. Int J Heat Fluid Flow 14(3):260–267

    Article  Google Scholar 

  10. Adams WH, Joshi Y, Blackburn DL (1999) Three-dimensional study of combined conduction, radiation, and natural convection from discrete heat sources in a horizontal narrow-aspect-ratio enclosure. ASME J Heat Transf 121:1992–1001

    Article  Google Scholar 

  11. Ramesh N, Venkateshan SP (1999) Effect of surface radiation on natural convection in a square enclosure. J Thermophys Heat Transf 13(3):299–301

    Article  Google Scholar 

  12. El Hassan R, Mohammed H, Antonio C (2006) Effects of surface radiation on natural convection in a Rayleigh–Bernard square enclosure: steady and unsteady conditions. Int J Heat Mass Transf 42:214–225

    Article  Google Scholar 

  13. Balaji C, Venkateshan SP (1994) Interaction of radiation with free convection in an open cavity. Int J Heat Fluid Flow 15(4): 317–324

    Article  Google Scholar 

  14. Dehghan AA and Behnia M (1996) Combined natural convection–conduction and radiation heat transfer in a discretely heated open cavity. ASME J Heat Transf 118:56–64

    Article  Google Scholar 

  15. Yu E, Joshi YK (1999) Heat transfer in discretely heated side vented compact enclosures by combined conduction, natural convection and radiation. ASME J Heat Transf 121:1002–1010

    Article  Google Scholar 

  16. Ramesh N, Merzkirch W (2001) Combined convective and radiative heat transfer in side-vented open cavities. Int J Heat Fluid Flow 22:180–187

    Article  Google Scholar 

  17. Nouanegue N, Muftuoglu AE (2008) Conjugate heat transfer by natural convection, conduction and radiation in open cavities. Int J Heat Mass Transf 51:6054–6062

    Article  MATH  Google Scholar 

  18. Incropera FP, Dewitt DP (2002) Fundamentals of heat and mass transfer, fifth edn. Wiley, Singapore

    Google Scholar 

  19. Siegel R, Howell JR (1972) Thermal radiation heat transfer, I edn. McGraw-Hill Company, New York

    Google Scholar 

  20. Venugopal G, Deiveegan M, Balaji C, Venkateshan SP (2008) Simultaneous retrieval of total hemispherical emissivity and specific heat from transient multimode heat transfer experiments. ASME J Heat Transf 130:2–8

    Article  Google Scholar 

  21. Marquardt DW (1963) An algoritham for least-squares estimation of nonlinear parameters. J Soc Indust Appl Math 11:431–441

    Article  MATH  MathSciNet  Google Scholar 

  22. Margret F, Singham JR (1962) Table of emissivity of surfaces. Int J Heat Mass Transf 5:67–76

    Article  Google Scholar 

  23. Rao R. Interferometric study of interaction between radiation and free convection in fins and fin arrays, Phd thesis, Department of Mechanical Engineering, Indian Institute of Technology, Madras

  24. Kline SJ, Mcclintock FA (1953) Describing uncertainties in single sample experiments. Mech Eng 75:3–8

    Google Scholar 

  25. Drikakis D and Rider W (2005) High-resolution methods for incompressible and low-speed flows, first edn. Springer, New York

    Google Scholar 

  26. FLUENT 6.3.26 (2006) ANSYS, Incor., 275, Technology Drive, Canonsburg, USA

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering Trivandrum, Trivandrum, India

    M. R. Rajkumar, G. Venugopal & S. Anil Lal

Authors
  1. M. R. Rajkumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Venugopal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Anil Lal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Anil Lal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rajkumar, M.R., Venugopal, G. & Lal, S.A. Natural convection with surface radiation from a planar heat generating element mounted freely in a vertical channel. Heat Mass Transfer 47, 789–805 (2011). https://doi.org/10.1007/s00231-010-0734-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-010-0734-z

Keywords

Search

Navigation