Argentum Solutions, Inc.
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David C. Silverman |
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When heat is transferred through a surface, the changing temperature of the fluid affects its density. Increasing temperature decreases density and vice versa. Buoyancy forces imposed on the fluid resulting from the change in density close to the surface working in conjuction with an external force field such as gravity force fluid motion relative to the heat transfer surface. Gravity is not the only external force field possible. A fluid enclosed in rotating equipment is acted on by a rotational force field that can cause natural convection if one of the surfaces is used for heat transfer. Thus, even in the absence of forced convection, a fluid cannot be considered stagnant if one of the surfaces in contact with it transfers heat to or from the fluid. Even under some conditions of forced convection, natural convection can be large enough to be a factor that has to be considered. A practical example is heat transfer through a tank wall that is exposed to different temperatures inside and outside. The result is that the contents of the stagnant tank may not be stagnant. Natural convection in such instances can be as turbulent as forced convection. This figure )
shows the effect of heating a stagnant fluid through a vertical wall.
This situation could represent the wall of a vertical tank in which the
contents are not stirred. If the radius of curvature is much larger than
the distance into the fluid, then the tank wall might be represented as a
vertical flat plate. The resulting flow creates hydrodynamic and thermal
boundary layers. The assumption is no slip at the wall as in the case of
forced convection. The boundary layer begins at the lower edge of the
heated region. The flow in this portion of the boundary layer is laminar.
At some distance, the boundary layer can become turbulent with eddy
mixing replacing the more planar shear of laminar flow.
Many experiments have been conducted to determine empirical correlations to predict the heat transfer coefficient in natural convection systems. Most of the correlations have the form of 
(22)where f means that the properties in the dimensionless groups are evaluated at the mean film temperature and C is a constant. In terms of this figure
the mean film temperature, Tf is defined as
(23)Pr is the Prandtl number and Gr is the Grashof number . This table shows values for C and n in equation (22) for the Nusselt number for natural convection from vertical flat and cylindrical surfaces. For these surfaces, "x" in equation (22) is the length of the surface over which natural convection is occurring.
For the case of GrfPrf between10-1 and 104, the following equation has been found to fit the experimental data 
(24)where the logarithm is a base 10 logarithm. Somewhat different equations have been proposed for horizontal cylinders and horizontal square plates. Free and forced convection occur simultaneously. A practical example is fluid being forced at rather low velocities over a heated surface. The forced flow velocity is supplemented by a convective velocity generated by the buoyancy forces near the heated wall. The relationship between the Nusselt number and the product of the Grashof times Prandtl numbers are different for the two cases above. Simulation of natural convection probably cannot be done easily using the laboratory tools outlined in the section Laboratory Corrosion Testing Under Heat Transfer Conditions - a Critique. For example, the heat flux apparatus when operated without stirring has a horizontal heat transfer surface which cannot simulate a vertical surface. At this point, devices do not exist to simulate corrosion under conditions of natural convection routinely. Previous Page: Heat Exchangers- Effect of Fouling on Heat Transfer Rates Next Page: Laboratory Corrosion Testing Under Heat Transfer Conditions - a Critique |
David C. Silverman, Ph.D. - Primary Consultant |