![]() ![]() ![]() ![]() For instance, it's 4.36 with a state of constant heat flux along the length of passage and 3.66 for constant wall temperature, and that's because the shape of the temperature profile is different for these different conditions. The laminar Nusselt number also depends on the heat transfer make up of the flow. For the entrance region of the pipe, the profile is still developing, and the laminar Nusselt number is not constant, changing with axial distance. The Nusselt number is constant only when this temperature profile becomes fixed (fully developed). The motion produces a boundary layer and temperature profile, as well as a velocity profile. In the limit of laminar flow, there is really no convection, all the heat transfer is by conduction (diffusion), but not like conduction through a solid, because of the moving fluid. Q is the heat transferred between the surface across the fluid to where the reference temperature is defined. The film coefficient is a convenient definition, made in the simplest way to capture the essential physics h = Q/(Ts - Tref), where Q is the bulk heat transferred, Ts the temperature of the heated/cooled surface, and Tref is a reference temperature, chosen for convenience. The Nusselt number is the ratio of convective heat transfer to conductive heat transfer, given by hD/k, where h is the film coefficient, D pipe diameter, and k fluid thermal conductivity. With laminar flow, heat is also diffused by molecule bumping into molecule. Such packets, however small, still contain many billions of molecules. With larger Reynolds numbers, inertia becomes important and momentum transfer occurs at a larger length scale, on the order of small packets of fluid. At that level, the momentum is "diffused" across the streamlines, being transferred by molecule bumping into molecule. When inertial forces are small enough, viscosity dominates, and the transfer of momentum across minute streamlines is solely because of friction (viscosity), and it occurs on a molecular level. The Reynolds number is a ratio of inertial forces to viscous forces, VD/Nu, where V is fluid velocity, D pipe diameter, and Nu fluid kinematic viscosity. For small enough Reynolds number, the flow is laminar and the nature of the laminar flow is such that fluid inertia has negligible influence, resulting in a constant value for the laminar Nusselt number, but only when the internal flow is "fully developed." For laminar flow in the entrance region of the pipe, the Nusselt number is not constant, and its value is different for different heat transfer configurations. ![]() In general, heat transfer with internal flows - like flows in a pipe - does depend on Reynolds Number. ![]()
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