Use of conducting sheet analogy for solution of heat transfer problems in a nuclear reactor

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Virginia Polytechnic Institute

The temperature distribution in a volume element with internal heat generation satisfies Poisson's equation and for two dimensional cases, this equation becomes

∂²T/∂x² + ∂²T/ ∂Y² = -9(x,y)/KT

where q(x,y) is function describing the heat generation. k,is the thermal conductivity. The voltage distribution in a flat plate with current input normal to the plate is

∂²Y/∂x² + ∂²Y/ ∂Y² = -pi(x,y)

Where, p is the resistivity of the plate.

i(x,y) is the function describing the current input.

The development of the nuclear reactor for the production of commercial power has made necessary the rapid, economical solution of some of the problems involved. The direct analytical solution of some problems encountered are either impossible or difficult and time consuming.

This thesis makes use of the analogy existing between equations (1) and (2) for the solution of certain two dimensional heat flow problems in a reactor.

Teledeltos Conducting Paper was used for making the analogue models. The current was introduced into the paper by use of probes protruding through the paper. The desired temperature distribution was found by use of the equation

ΔT = 9e/KT ΔV/ΔVsTd

where ΔV is potential difference between two points on the analogue model.

ΔVstd is the potential drop across a standard resistance through which all current flows.

qt is total heat generated in the element being simulated.

ΔTis the temperature difference between two points in the simulated element corresponding to the two points on the analogue model between which AV is measured.

The accuracy of the analogue was checked by solving two problems, the solution of which could be determined analytically. A problem involving complex heat generation and boundary conditions was then solved.