Combined convection plate

In combined convective flow over a horizontal flat surface, the buoyancy forces are at right angles to the flow direction and lead to pressure changes across the boundary layer, i.e., there is an induced pressure gradient in the boundary layer despite the fact that flow over a flat plate is involved. Under some circumstances, this can lead to complex three-dimensional flow in the boundary layer. This type of flow will not be considered here, more information being available in [17] to [23]. 

Oosthuizen, PH. and Hart, R.. A Numerical Study of Laminar Combined Convective Flow Over Flat Plates". J. Heat Trans., Feb., 1973, pp. 60-63. 

A thin metal plate is insulated on the back and exposed to solar radiation at the front surface (Fig. 1-44). The exposed surface of the plate has an absorptivity of 0.6 for solar radiation. If solar radiation is incident on the plate at a rate of 700 W/m and the surrounding air temperature is 25°C, determine the surface temperature of the plate when the heat loss by convection and radiation equals the solar energy absorbed by the plate. Assume the combined convection and radiation heat transfer coefficient to be 50 W/m °C. 

Four identical power transistors with aluminum casing are attached on one side of a 1-cm-thick 20-cm x 20-cm square copper plate (k = 386. W/m - X) by screw that exert an average pressure of. 6 MPa (Fig. 3-18). The base area of each transistor is 8 cm, and each transistor is placed at the center of a. 10-cm X 10-cm quarter section of the plate. The interface roughness is estimated to be about 1.5 /rm. All transistors are covered by a tfdck Plexiglas layer, which is a poor conductor of heat, and thus all the heat generated at the junction of the transistor must be dissipated to the ambierrt at 20X through the back surface of the copper plate. The combined convection/radiation heat transfer coefficient at the back surface can be taken to be 25 W/m C. If the case temperature of the... 

Inli production facility, large brass plates of 4-cm thickness that are initially at a uniform temperature of 20 C are heated by passing them through an oven that is maintained at 500°C (Fig. 4-22). The plates remain in the oven for a period of 7 min. Taking the combined convection and radiation heat transfer coefficient to be / = 120 W/m °C, determine the surface temperature of the plates when they come out of the oven. 

Marchiano and Arvia (M3) also measured mass transfer by thermal and diffusional free convection at a vertical plate. They derived on theoretical grounds a combined Grashof number as follows ... 

The Grashof number given by Eq. (40) appears to have a weaker theoretical basis than that given by Eq. (37), since it is based on an analysis that approximates the profile of the vertical velocity component in free convection, for example, by a quadratic function of the distance to the electrode. The choice of an appropriate Grashof number, as well as the experimental conditions in the work of de Leeuw den Bouter et al. (DIO) and Marchiano and Arvia (M3), has been reviewed critically by Wragg and Nasiruddin (W10). They measured mass transfer by combined thermal and diffusional, turbulent, free convection at a horizontal plate [see Eq. (31) in Table VII], and correlated their results satisfactorily with the Grashof number of Eq. (37). 

It is difficult to solve the system of Eqs. (39)—(41) for these boundary conditions. However, certain simplifying assumptions can be made, if the Prandtl number approaches large values. In this case, the thermal boundary layer becomes very thin and, therefore, only the fluid layer near the plate contributes significantly to the heat transfer resistance. The velocity components in Eq. (41) can then be approximated by the first term of their Taylor series expansions in terms of y. In addition, because the nonlinear inertial terms are negligible near the wall, one can further assume that the combined forced and free convection velocity is approximately equal to the sum of the velocities that would exist when these effects act independently. Therefore, for assisting flows at large Prandtl numbers (theoretically for Pr -> oo), Eq. (41) can be rewritten in the form ... 

Oosthuizen. P.H. and Bassey, M., An Experimental Study of Combined Forced and Free Convective Heat Transfer from Flat Plates to Air at Low Reynolds Numbers , J. Heat Transfer, Vol. 96, pp. 120-121, 1973. 

Oosthuizen, P.H.. A Note on the Combined Free and Forced Convective Laminar Flow Over a Vertical Isothermal Plate". J.S.A. Inst. Mech. Engs., Vol. 15. No. 1, August, pp. 8-13, 1965. 

It is easy to envision cases in which all three modes of heat transfer are present, as in Fig. 1-9. In this case the heat conducted through the plate is removed from the plate surface by a combination of convection and radiation. An energy balance would give... 

This is an interesting example of combined radiation and convection heat-transfer analysis. We designate the black plate as surface 1, the glass as surface 2. and the surroundings as surface 3. We assume no absorption of the solar energy in the glass. For the black plate... 

This completes the definition of the stability problem for the mixed convection flow over the horizontal plate. For a given K and Re, one would be required to solve (6.4.19)-(6.4.38), starting with the initial conditions (6.4.39)-(6.4.58) and satisfy (6.4.63) for particular combinations of the eigenvalues obtained as the complex k and u>. We will use the procedure adopted in Sengupta et al. (1994) to obtain the eigen-spectrum for the mixed convection case, when the problem is in spatial analysis framework. In the process, it is possible to scan for all the eigenvalues in a limited part of the complex k- plane, without any problem of spurious eigenvalues. 

Robertson, G.E., Seinfeld, J.H. and Leal, L.G. (1973). Combined forced and free convection flow past a horizontal flat plate, AIChE, 19(5) 998-1008. 

Schneider, W. (1979). A similarity solution for combined forced and free convection flow over a horizontal plate, Int. J. Pleat Mass Transfer 22 1401-1406. 

Mass How Rate ttirougn ttie Space beLV, een Plates 519 9-5 Natural Convection Inside Enclosures 521 effective Thermal Conductivity 522 Horizontal Rectangular Enclosures 523 Inclined Rectangular Enclosures 523 Vertical Rectangular Enclosures 524 Concentric Cylinders 524 Concentric Spheres 525 Combined Natural Convection and Radiation 525... 

Discussion Note that the heat losses prevent the plate temperature from rising above 33.4 C. Also, the combined heat transfer coefficient accounts for the effects of both convection and radiation, and thus it is very convenient to use in heat transfer calculations when its value is known with reasonable accuracy. 

A plot of the nondimensionalized heal transfer coefficient for combined natural and forced convection on a vertical plate is given in Fig. 9 32 for different fluids. We note from this figure that natural convection is negligible when Gr/Re <0.1, forced convection is negligible when Gr/Re > 10, and neither is negligible when 0.1 < Gr/Re < 10. Therefore, both natural and forced convection must be considered in heal itaiisfer calculations when the Gr and Re are of the same order of magnitude (one is within a factor of 10 times die other). Note that forced convection is small relative to natural convection only in the rare case of extremely low forced flow velocities. 

Variation of the local Nussell number Nu 5 for combined natural and forced convection from a hot isothermal vertical plate. 

Coefficients of heat transfer by natural convection from bodies of various shapes, chiefly plates and cylinders, are correlated in terms of Grashof, Prandtl, and Nusselt numbers. Table 8.9 covers the most usual situations, of which heat losses to ambient air are the most common process. Simplified equations are shown for air. Transfer of heat by radiation is appreciable even at modest temperatures such data are presented in combination with convective coefficients in item 16 of this table. 

A second feature of the subarc mantle is that it is the site of convective flow. In the mantle wedge cold mantle from beneath the overriding plate travels into the mantle wedge "corner" and is dragged deeper by the downgoing slab. Combining these two features - flow within the subarc mantle and chemical fluxes from the slab - leads to a dynamic view of the formation of the subcontinental lithosphere. 

Of course in order to satisfactorily refute a scientific theory it is important to provide a better explanation of the facts. In the case of mantle plumes it is suggested that plate tectonic processes can explain all the features ascribed to mantle plumes. In the case of hot spots this may be achieved by combining a source of melt in the upper mantle with either a propagating fracture zone or with continental margin-edge driven convection in the shallow mantle (Foulger Natland, 2003). 

Combined forced and free convection at a vertical flat plate, where the forced convection velocity is in the same direction as the natural convection flow (the so-called assisting mixed convection case). Here, researchers have combined Sherwood numbers for the pure forced and natural convection cases in the following way [15, 24-26] ... 

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