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We present measurements of the thermal resistivity $\rho(t,P,L)$ near thesuperfluid transition of $^4$He at saturated vapor pressure and confined incylindrical geometries with radii $L=0.5$ and 1.0 $\mu$m ($t\equivT/T_\lambda(P) - 1$). For $L = 1.0 \mu$m measurements at six pressures $P$ arepresented. At and above $T_\lambda$ the data are consistent with a universalscaling function $F=(L/\xi_0)^{x/\nu}(R/R_0)$, $X= (L/\xi_0)^{1/\nu}t$ validfor all $P$ ($R_0$ and $x$ are the pressure-dependent amplitude and effectiveexponent of the bulk resistivity $R$ and $\xi = \xi_0 t^{-\nu}$ is thecorrelation length)

physical review letters

Finite-Size Scaling and Universality of the Thermal Resistivity of Liquid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mn>4</mml:mn></mml:mmultiscripts></mml:math>near<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>λ</mml:mi></mml:msub></mml:math>

Finite-Size Scaling and Universality of the Thermal Resistivity of LiquidHe4nearTλ