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6.3. Single-Phase Liquid Heat Transfer

Figure 6.4 shows an idealized form of the flow patterns and the variation of the surface and liquid temperatures in the regions designated by A, B, and C for the case of a uniform wall heat flux. Under steady state one-dimensional conditions the tube surface temperature in region A (convective heat transfer to single-phase liquid), is given by:

equation2378

equation2383

equation2390

and where q;SPMquot; is the heat flux, Per is the heated perimeter, G is the mass velocity, A is the flow area and tex2html_wrap_inline5152 is the liquid specific heat. Also tex2html_wrap_inline5154 is the temperature difference between the wall surface and the mean bulk liquid temperature at a given length z from the tube inlet, h is the heat transfer coefficient to single-phase liquid under forced convection. The liquid in the channel may be in laminar or turbulent flow, in either case the laws governing the heat transfer are well established; for example, heat transfer in turbulent flow in a circular tube can be estimated by the well-known Dittus-Boelter equation.

equation2395

This relation is valid for heating in fully developed vertical upflow in z/D > 50 and Re > 10,000.

equation2402

equation2408

where tex2html_wrap_inline4535 is the hydraulic diameter, tex2html_wrap_inline4471 is the liquid viscosity and tex2html_wrap_inline5038 is the liquid thermal conductivity.

For the case of a given constant wall temperature, the temperature difference will decrease, as well as the heat flux. From an energy balance this is represented by a logarithmic decrease in the temperature difference.


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Last Modified: Tue Sep 2 15:06:55 CDT 1997