Diameter Aluminum

One end of a 33 cm long aluminum rod with a diameter of 2.0 cm is kept at 400°C?
One end of a 33 cm long aluminum rod with a diameter of 2.0 cm is kept at 400°C, and the other is immersed in water at 22°C. Calculate the heat conduction rate along the rod.
___W
Assuming one-dimensional heat flow through a plane layer is given by [1]:
∆Q/∆t = k∙A∙∆T/∆x
(k thermal conductivity of the layer material, A cross-sectional area of the layer, ∆T temperature difference between the two sides of the layer, ∆x thickness of the layer)
Here
k = 237 WK⁻¹m⁻² (for pure aluminum [2])
A = (π/4)∙D² = (π/4) ∙ (0.02m)² = 3.1416×10⁻⁴m²
∆T = 400°C – 22°C) = 20°C = 378°C = 378K
∆x = 33cm = 0.33m
=>
∆Q/∆t = 237 WK⁻¹m⁻² ∙ 3.1416×10⁻⁴m² ∙ 378K / 0.33m
= 85.75 W
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