CONDUCTION HEAT TRANSFERHeat TransferThe surface area (A) for transferring heat through the pipe (neglecting the pipe ends) is directlyproportional to the radius (r) of the pipe and the length (L) of the pipe.A = 2prLAs the radius increases from the inner wall to the outer wall, the heat transfer area increases.The development of an equation evaluating heat transfer through an object with cylindricalgeometry begins with Fourier’s law Equation 2-5.Qk ADTDrFrom the discussion above, it is seen that no simple expression for area is accurate. Neither thearea of the inner surface nor the area of the outer surface alone can be used in the equation. Fora problem involving cylindrical geometry, it is necessary to define a log mean cross-sectionalarea (Alm).(2-7)AlmAouterAinnerlnAouterAinnerSubstituting the expression 2prL for area in Equation 2-7 allows the log mean area to becalculated from the inner and outer radius without first calculating the inner and outer area.Alm2 p router L2 p rinner Lln2 p router L2 p rinner L2 p LrouterrinnerlnrouterrinnerThis expression for log mean area can be inserted into Equation 2-5, allowing us to calculate theheat transfer rate for cylindrical geometries.HT-02 Page 12 Rev. 0
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