Horizontal flow surfaces, natural convection

Pera, L. and Gebhart, B., "Natural Convection Boundary Layer Flow Over Horizontal and Slightly Inclined Surfaces , Int. J. Heat Mass Transfer. Vol. 16, p. 1131. 1973. 

FIGURE 9-11. Natural convection flows on the upper and lower surfaces of a horizontal hot plale. 

A solar collector consists of a horizontal copper tube of outer diameter 5 cm enclosed in a concentric thin glass tube of 9 cm diameter. Water is heated as it flows through the tube, and the annular space between the copper and glass lube is filled with air at 1 atm pressure. During a clear day, the temperatures of the tube surface and the glass cover are measured to be bO C and 32°C, respectively. Determine the rale of heat loss from the collector by natural convection per meter length of the tube. Answer 17.4 W... 

For the heated vertical plate and horizontal cylinder, the flow results from natural convection. The stagnation configuration is a forced flow. In each case the flow is of the boimdai7 Kiyer type. Simple analytical solutions can be obtained when the thickness of the du.st-free space is much smaller than that of the boundary layer. In this case the gas velocity distribution can be approximated by the first term in an expansion in the distance norroal to the surface. Expressions for the thickness of the dust-free space for a heated vertical surface and a plane stagnation flow are derived below. 

It was proposed by the author (Stralmann et al., 1988) that thermophores is could be used to suppress particle deposition on wafers during clean room operations in the microelectronics industry. To estimate the effect of an applied temperature gradient on particle deposition, the flow of filtered air over the surface of a horizontal wafer can be approximated by a stagnation flow (Fig. 3.12), For both the plane and axially symmetric stagnation flows, the gas velocity component normal to the surface and the temperature fields depend only on the distance from the surface. In the absence of natural convection, the gas velocity normal to the surface in the neighborhood of the plane stagnation flow is... 

We have already noted that the general class of flows driven by buoyancy forces that are created because the density is nonuniform is known as natural convection. If we examine the Boussinesq approximation of the Navier-Stokes equations, (12-170), we can see that there are actually two types of natural convection problems. In the first, we assume that a fluid of ambient temperature 71, is heated at a bounding surface to a higher temperature I. This will produce a nonuniform temperature distribution in the contiguous fluid, and thus a nonuniform density distribution too. Let us suppose that the heated surface is everywhere horizontal. Then there is a steady-state solution of (12-170) with u = 0, and the body-force terms balanced by a modification to the hydrostatic pressure distribution, such that... 

Introduction. For the problem depicted in Fig. 4.44, the heat transfer by pure forced convection would increase monotonically with Reynolds number along the curve shown. The heat transfer by pure natural convection from the same surface for various Ra is denoted by the horizontal lines in the figure. If Re is slowly increased from zero in the real problem, the measured values of Nu would at first follow the natural convection curve, since the superimposed forced convection velocities are too feeble to affect the heat transfer. If the forced convection assists the natural convection, the Nu curve in Fig. 4.44 will break upward along path A at larger Re and approach the pure forced convection curve from above. If the flows are opposed, Nu passes through a minimum along path B in Fig. 4.44 and approaches the forced convection curve from below. Mixed convection occurs when the heat transfer is significantly different from that for either pure natural convection or pure forced convection. 

Horizontal Flow. For laminar flow over the upper surface of a horizontal heated plate (or over the bottom surface of a cooled plate), the center of the mixed convection regime can again be estimated by equating the forced convection Nusselt number from Eq. 4.154 to that for natural convection from Eq. 4.39c (for detached turbulent convection). This results in... 

A surface heat transfer coefficient h can be defined as the quantity of heat flowing per unit time normal to the surface across unit area of the interface with unit temperature difference across the interface. When there is no resistance to heat flow across the interface, h is infinite. The heat transfer coefficient can be compared with the conductivity the conductivity relates the heat flux to the temperature gradient the surface heat transfer coefficient relates the heat flux to a temperature difference across an unknowm distance. Some theoretical work has been done on this subject [8], but since it is rarely possible to achieve in practice the boundary conditions assumed in the mathematical formulation, it is better to regard it as an empirical factor to be determined experimentally. Some typical values are given in Table 2. Cuthbert [9] has suggested that values greater than about 6000 W/m K can be regarded as infinite. The spread of values in the Table is caused by mold pressure and by different fluid velocities. Heat loss by natural convection also depends on whether the sample is vertical or horizontal. Hall et al. [10] have discussed the effect of a finite heat transfer coefficient on thermal conductivity measurement. 

As mentioned in Chap. 3, for depfli/diameter ratios less than 0.5, such as in large cylindrical LPG and LNG tanks, flie boundary layer flow across the base may be broken by the creation of vertical fliermals spaced horizontally at intervals approximating to the liquid depth according to Rayleigh s instability criteria for natural convection. In aU cases, the heat in-flow is carried by boundary layer flows, and thermals, to the liquid surface. 

A pressure distribution test in the surface of containment was done in a low velocity wind tunnel with various wind speeds, air entrances, yaw and pitch angles. The test shows that the pressure is positive in the area of -35° < 0 < 35°. The influence of wind on natural convection of containment was also done with a 1/50 integral model. The test results revealed that natural convection flow rate was enhanced in general by outside wind and horizontal wind (a = 0) had the better effect than a < 0° or a > 0°. The position of chimney might influence the air flowing around the containment. The distance between containment and chimney should be larger than 4 times of chimney diameter. However, smoke wind tunnel test showed no exhausted hot air was re-circulated under any d outside wind conditions. 

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