An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

<table>The temperature rise for a periodic pulse-shaped MFP having a pulse width of <svg height="14.7125" id="M104" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 36.299999 14.7125" width="36.299999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="17.704248" y="0">𝑇</tspan>
</text>
<text transform="matrix(1,0,0,-1,-47.36,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan>
</text>
</g>
</g>
</svg> plotted as a function of the observation point located at a distance, <svg height="7.0124998" id="M105" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.0125)">
<g transform="translate(72,-66.39)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
</text>
</g>
</g>
</svg> from the surface of the MNP, <svg height="7.0124998" id="M106" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.0125)">
<g transform="translate(72,-66.39)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
</text>
</g>
</g>
</svg> ranging from 0 nm to 10 nm for a core radius of 10 nm, and the number of indexed summed is 25.</table>

Journal of Atomic and Molecular Physics

fig5

Figure 5

Figure 5: An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle 