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Results were generalized to apply to the situation of arbitrary longitudinal variation of the wall temperatures of the annulus. As an illustration of the method, an extension is explicitly given for a linear increase of all temperature with axial distance.
"The general problem of heat transfer in a concentric annulus with hydrodynamically fully established laminar flow is considered. Under the assumptions that the fluid in the annulus is incompressible, has constant properties, and that internal viscous generation is negligible, the differential equation for the temperature field is solved for certain special or fundamental boundary conditions. These fundamental solutions can be superposed to satisfy any general axially symmetric boundary conditions."--P. i.
Laminar Flow Forced Convection in Ducts is a sourcebook for compact heat exchanger analytical data. This book describes the analytical solutions for laminar fluid flow and forced convection heat transfer in circular and noncircular pipes, including applicable differential equations and boundary conditions involving velocity and temperature problems of fluid flow. The book also discusses fluid flow—how much power is required to pump fluids through the heat exchanger, as well as the heat transfer—the determination of q" distribution, and the temperature of fluid and walls. The text also analyzes the coolant or heat transfer fluid flows in a nuclear power reactor composed of a bundle of circular section fuel rods located inside a round tube. R.A. Axford addresses fluid flow and heat transfers results for the rod bundle geometry in "Heat Transfer in Rod Bundles." The book also provides an overview and guidelines that can be used for the designer and the applied mathematician. This book is suitable for engineers working in electronics, aerospace, instrumentation, and biomechanics that use cooling or heating exchanges or solar collection systems.