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5- The heat rate (Q) transferred through a metal rod depends on the thermal conductivity (K)...

5- The heat rate (Q) transferred through a metal rod depends on the thermal conductivity (K) of the metal, the cross-sectional area of the rod (A) and the temperature gradient (Y) across the rod. Find the relation by the use of the dimensional analysis taking the units of (K) (W/mK).
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Answer #1

We can write the dimensional equation as,

The heat rate has units joules per second, Area has units meter^2 Temperature gradient has unit Kelvin, and thermal conductivity has unit as Joules per second per meter per Kelvin. Substituting in dimensions we get, (K is kelvin)

Comparing we get the equations as,

Solving we get,

Substituting we get the equation as,

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