## THERMAL SCIENCE

International Scientific Journal

### THE CHARACTERISTIC LENGTH ON NATURAL CONVECTION FROM A HORIZONTAL HEATED PLATE FACING DOWNWARDS

**ABSTRACT**

Natural convection from a downward facing horizontal heated plate was analyzed. An expression for the thickness of the thermal boundary layer was obtained in terms of Rayleigh number. Assuming this thickness as the characteristic length of the problem, the data published by other authors were modified and an equation for Nusselt number is presented. It was observed that this equation correlates the data more precisely than the commonly known equations in the literature that employ the ratio of the area to the perimeter or the shorter side of the plate as the characteristic length. It is concluded that taking the thermal boundary layer as the characteristic length of phenomenon is a proper approach and correlates all the data closely.

**KEYWORDS**

PAPER SUBMITTED: 2011-01-27

PAPER REVISED: 2013-06-15

PAPER ACCEPTED: 2013-06-15

PUBLISHED ONLINE: 2013-07-06

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**Issue 2**, PAGES [555 - 561]

- Saunders, O. A., Fishendan, M., Mansion, H. D., Some Measurements of Convection by an Optical Method, Engineering, 139(1935), pp. 483-485
- Weise, R., Heat Transfer by Free Convection on Square Plates (in German), Forsch. Geb. Ing.-Wes., 6(1935), pp. 281-292
- Fishenden, M., Saunders, O. A., An introduction to Heat Transfer, Oxford University Press, London, 1961
- Singh, S. N., Birkebak, R. C., Laminar Free Convection from a Horizontal Infinite Strip Facing Downwards, Z. Angew. Math. Phys., 20(1969), pp. 454-461
- Aihara, T., Yamada, Y., Endo, S., Free Convection along the Downward-Facing Surface of a Heated Horizontal Plate, Int. J. Heat Mass Tran., 15(1972), pp. 2535-2549
- Fujii, T., Honda, H., Morioka, I., A Theoretical Study of Natural Convection Heat Transfer from Downward-Facing Horizontal Surfaces with Uniform Heat Flux, Int. J. Heat Mass Tran., 16(1973), 3, pp. 611-627
- Goldstein, R. J., Sparrow, E. M., Jones, D. C., Natural Convection Mass Transfer Adjacent to Horizontal Plates, Int. J. Heat Mass Tran., 16(1973), 5, pp. 1025-1035
- Hatfield, D. W., Edwards, D. K., Edge and Aspect Ratio Effects on Natural Convection from the Horizontal Heated Plate Facing Downwards, Int. J. Heat Mass Tran., 24(1981), 6, pp. 1019-1024
- Gryzagoridis, J., Natural Convection from an Isothermal Downward Facing Horizontal Plate, Int. Comm. Heat Mass Transfer, 11(1984), 2, pp. 183-190
- Schulenberg, T., Natural Convection Heat Transfer to Liquid Metals below Downward Facing Horizontal Surfaces, Int. J. Heat Mass Tran., 27(1984), 3, pp. 433-441
- Schulenberg, T., Natural Convection Heat Transfer below Downward Facing Horizontal Surfaces, Int. J. Heat Mass Tran., 28(1985), 2, pp. 467-477
- Onur, N., Aktas, M. K., An Experimental Study on the Effect of Opposing Wall on Natural Convection along an Inclined Hot Plate Facing Downward, Int. Comm. Heat Mass Transfer, 25(1998), 3, pp. 389-397
- Kwak, C. E., Song, T. H., Natural Convection around Horizontal Downward-Facing Plate with Rectangular Grooves: Experiments and Numerical Simulations, Int. J. Heat Mass Tran., 43(2000), pp. 825-838
- Dubovsky, V., et al., Natural Convection Inside Ventilated Enclosure Heated by Downward-Facing Plate: Experiments and Numerical Simulations, Int. J. Heat Mass Tran., 44(2001), pp. 3155-3168
- Friedrich, M. K., Angirasa, D., The Interaction Between Stable Thermal Stratification and Convection under a Heated Horizontal Surface Facing Downward, Int. J. Non-linear Mech., 36(2001), pp. 719-729
- Radziemska, E., Lewandowski, W. M., Heat Transfer by Natural Convection from an Isothermal Downward Facing Round Plate in Unlimited Space, Applied Energy, 68(2001), pp. 347-366
- Dayan, A., et al., Laminar Free Convection Underneath a Downward Facing Hot Fin Array, Int. J. Heat Mass Tran., 47(2004), 12-13, pp. 2849-2860
- Mittelman, G., et al., Laminar Free Convection Underneath a Downward Facing Inclined Hot Fin Array, Int. J. Heat Mass Tran., 50(2007), 13-14, pp. 2582-2589
- Fujii, T., Imura, H., Natural Convection Heat Transfer from a Plate with Arbitrary Inclination, Int. J. Heat Mass Tran., 15(1972), pp. 755-767
- Restrepo, F., Glicksman, L. R., The Effect of Edge Conditions on Natural Convection from a Horizontal Plate, Int. J. Heat Mass Tran., 17(1974), pp. 135-142
- Lloyd, J. R., Moran, W. R., Natural Convection Adjacent to Horizontal Surfaces of Various Planforms, J. Heat Tran., 96(1974), pp. 443-451
- Kozanoglu, B., Lopez, J., Thermal Boundary Layer and the Characteristic Length on Natural Convection over a Horizontal Plate, Heat Mass Tran., 43(2007), pp. 333-339
- Wagner, C., Discussion on "Integral Methods in Natural Convection Flow", Trans. Am. Soc. Mech. Engrs., 23E(1956), pp. 320-321
- Singh, S. N., Birkebak, R. C., Drake, R. M., Laminar Free Convection Heat Transfer from Downward-Facing Horizontal Surfaces of Finite Dimensions, Prog. Heat Mass Transfer, 2(1969), pp. 87-98
- Clifton, J. V., Chapman, A. J., Natural-Convection on a Finite-Size Horizontal Plate, Int. J. Heat Mass Transfer, 12(1969), pp. 1573-1584