Convection dimensional equations, simplified

A schematic estimate of the strength of the dynamo components, and an approximate scaling law, results from the quantitative side of this picture. Differential field stretching causes poloidal to toroidal conversion, which takes place at a rate Su /L. Vorticial motion of rising convective eddies transforms toroidal to locally poloidal field at a rate f, which is a pseudo-scalar quantity whose sign depends on the hemisphere. The dynamo equations simplify by dimensional analysis. For the poloidal field, which is given by a vector potential field. 

Samalam [43] modeled the convective heat transfer in water flowing through microchannels etched in the back of silicon wafers. The problem was reduced to a quasi-two dimensional non-linear differential equation under certain reasonably simplified and physically justifiable conditions, and was solved exactly. The optimum channel dimensions (width and spacing) were obtained analytically for a low thermal resistance. The calculations show that optimizing the channel dimensions for low aspect ratio channels is much more important than for large aspect ratios. However, a crucial approximation that the fluid thermophysical properties are independent of temperature was made, which could be a source of considerable error, especially in microchannels with heat transfer. 

Considering the one-dimensional diffusion and convection. Equation 7.8 can be simplified as follows ... 

SCDAP/RELAP5/M0D3 uses a one-dimensional, two-fluid, nonequilibrium, six-equation hydrodynamic model with a simplified capability to treat multidimensional flows. This model provides continuity, momentum, and energy equations for both the liquid and vapor phases within a control volume. The energy equation contains source terms that couple the hydrodynamic model to the heat structure conduction model by a convective heat transfer formulation. The code contains special process models for critical flow, abrupt area changes, branching, crossflow junctions, pumps, accumulators, valves, core neutronics, and control systems. A flooding model can be applied at vertical junctions. 

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