Nonlinear Boundary Value Problems in Heat-Electricity Conversion for Space Nuclear Reactors
This work explores the direct transformation of heat energy to electricity in space nuclear reactors using a system of nonlinear boundary value problems. The focus is on the effective generation of electrons from heated emitters in a series of elements, utilizing a cathode made of uranium heated to 1600°C. Electrons are emitted into a cesium-filled backlash at 600°C, significantly enhancing energy extraction compared to traditional thermoelectric converters. We present a mathematical model addressing unique solutions to the boundary-value heat problem on the cathode.
Nonlinear Boundary Value Problems in Heat-Electricity Conversion for Space Nuclear Reactors
E N D
Presentation Transcript
Nonlinear Boundary Value Problems andSimulation of Heat-ElectricityProcess forSpace Nuclear InstallationsV.A.Galkin, I.V.GalkinaDept. of Applied Mathematics, National Research Nuclear University,IATE, Obninsk, Russia
EGE • The process of direct transformation of heat energy to electricity is considered for space nuclear reactor. The effect is based on electrons generation on heated emitters in chain of elements (EGE) which are connected in series.
THERMOEMISSION • Uranium is concluded in the metal cover which is the cathode. It is warmed up by nuclear energy to 1600°С. In the backlash filled with cesium of 0,5 mm electrons fly to the anode, at which 600°С. These high temperatures also allow to select from the reactor of more energy and provide the superiority over other similar installations. For comparison we will tell that in thermoelectric converters temperature on the hot party to 1000°С, on cold - to 400°С.
The mathematicalmodel of above mentioned phenomenon is based on system of nonlinear boundary - valueproblems for nonlinear equations
Equation for temperature on cathode(boundary-value heat problem on cathode)
Theorem 1 • For given non-negative flux q(x) and non-negative constants there exists unique non-negative solution of boundary-value heat-cathode problem.
