Effects of Transverse Magnetic Field with Different Alternating Currents on Heat Flux Density Distributions of Plasma Arc
An external transverse-alternating magnetic field with sinusoidal and triangular alternating currents was applied to a combined plasma arc to create a plasma arc for expanding the cross section of arc column and flatting the distributions of arc temperature. Two mathematical models were developed to describe the heat flux density distributions of the combined plasma arc driven by a transverse-alternating magnetic field with sinusoidal and triangular alternating currents. The behavior of plasma arc under the external transverse-alternating magnetic field imposed perpendicular to the plasma current was discussed theoretically and experimentally by changing various parameters such as working gas flux, arc current, magnetic flux density including its wave form and the standoff from the nozzle to the workpiece. The analytical results show that it is feasible to adjust the shape and heat flux density of the combined plasma arc by the transverse- alternating magnetic field, which expands the region of combined plasma arc thermal treatment and uniforms the heat flux density upon the workpiece. Changing the waveform of the alternating current can also control the heat flux density distribution. As well as, calculated heat flux density distributions of combined plasma arc driven by the external transverse-alternating magnetic field show a good agreement with experimental data. The magnetic field with triangular alternating current can flat the heat flux density distribution on the anode rather than sinusoidal one. This approach to flat the heat flux density distribution on the anode surface will give an effective controllability to the combined plasma arc application.
Magnus Effect on Arc Driven by Alternating Magnetic Field in Swirling Plasma Gas
An arc driven by an alternating magnetic field was investigated theoretically and experimentally in swirling plasma gas flow. The governing equation to ascertain the arc motion was assumed to include not only an electromagnetic force term but also a Magnus force one. The electromagnetic force term derives from interaction between the arc current and the imposed magnetic field. The Magnus force is produced when the rotating gas travels in the surrounding gas. The obtained equation was solved numerically using commercial software (Mathematica). Numerical calculation revealed that the movement of the magnetically driven arc is twisted by the Magnus force. The twist direction depends on that of the swirling motion of the plasma gas. Clockwise-swirling plasma gas produces clockwise twisted arc movement. The amplitude of the oscillatory arc motion decreases concomitantly with increasing swirling strength. The experiment was performed to examine the theoretical predictions. Results from experimental observations showed that the theoretical modeling was reasonable.
Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type
<jats:p>We consider the discrete Volterra type equation of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">o</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>, for given nonpositive real <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>, as a measure of approximation.</jats:p>