11. Temperature Profile for One Dimensional Steady State Heat Conduction

  • For flow across flat surfaces: \(T\) vs. \(x\) is linear; \(\dfrac{dT}{dx} = \text{ constant}\).
  • For flow across cylindrical surfaces: \(T\) vs. \(\ln r\) is linear; \(\dfrac{dT}{dr} \propto \dfrac{1}{r}\)
  • For flow across spherical surfaces: \(T\) vs. \(1/r\) is linear; \(\dfrac{dT}{dr} \propto \dfrac{1}{r^2}\)