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I am currently studying a chapter regarding the thermal properties of materials. Inside the lecture slides given by my lecturer, I came across an equation that I have no idea how to derive. Please help. enter image description here

How could I derive the equation above from $Q=-kdT/dx$?

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Let Q be the total rate of heat flow (per unit length of cylinder) through any surface of constant r within the system. This radial rate of heat flow does not change with r (since the heat has nowhere else to go). The heat flux (per unit area) through the surface of constant r is given by: $$q=-k\frac{dT}{dr}$$ So the total rate of heat flow per unit length of cylinder is given by:$$Q=-(2\pi r)k\frac{dT}{dr} $$So now all one needs to do is integrate this equation between the two boundaries.

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