## Natural Circulation Loop with Heat Exchanger Boundary Conditions

The basic natural circulation loop case is modeled with heat source and sink. The high and low temperatures for the fluid are expressed in terms of the source and sink temperatures and the characteristics of the heat exchangers. The transient and steady state model equations are developed, the steady state solution presented, the model equations are given in dimensionless form, and the linearized versions of the equations developed.

Additional work is required to finish analyses of the stability of the system.

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## Coupled Natural Circulation Loops

Coupled natural circulation loops (NCLs) have not been much investigated. Single natural circulation loops, on the other hand, have been the subject of experimental, analytical and numerical research for several decades since the early 1950s. The literature is very extensive with investigations continuing to this day. Much of the research has been directed toward various systems of electric power generation by nuclear power plants.

The objectives of the present notes include; (1) development of model equations for steady-state and transient flows in coupled NCLs, (2) giving the steady state solutions for the steady state equations, (3) linearization of the transient equations for use in stability analyses, and (4) incorporation of realistic boundary-condition representations into the model equation systems for coupled NCLs.

The results are distilled to a system of equations that will be used for investigations into the stability of coupled natural circulation loops.

The design of such systems, also an interesting problem, is not addressed here.

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## Numbers? You want numbers . . . we’ve got numbers.

V & V? Not so much.

For decision support all you need is numbers.

## Two Nodes Coupled by a Link

**Method of Exact Solutions Verification Problems for Transient Compressible Flows: Two Nodes Coupled by a Link**

The analysis given in these previous notes:

Implicit Function Theory Introduction

Initial Method of Exact Solutions Calculations

Single Isolated Node Calculations

Two Fluid Systems Mechanically Coupled Through a Wall

are expanded to include the case of two fluid nodes coupled by a link. Numerical and analytical solutions results are given for an illustrative application.

The mathematical model, an exact continuous analogue of the discrete approximations used in many numerical solution methods, provides analytical and numerical-benchmark problems for verification by the Method of Exact Solutions ( MES ).

I have uploaded a file.

## Fluid Systems Mechanically Coupled Through a Wall

**Method of Exact Solutions Verification Problems for Transient Compressible Flows: Two Fluid Systems Mechanically Coupled Through a Wall**

The analysis given in these previous notes:

Implicit Function Theory Introduction

Initial Method of Exact Solutions Calculations

Single Isolated Node Calculations

are expanded to include the case of coupled fluid systems. Numerical solution results are given for an illustrative application.

The mathematical model, an exact continuous analogue of the discrete approximations used in many numerical solution methods, provides analytical and numerical-benchmark problems for verification by the Method of Exact Solutions ( MES ).

I have uploaded a file.