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Help needed! transport problems involving bessel eqn

  1. Oct 16, 2008 #1
    Hi everybody... i would like to seek help for the problem below. the assumptions i've considered is that transfer is radial only since it is a very long cylinder (infinitely long) that transfer in z direction is negligible, thermal radiation is zero, and wood properties are constant. Starting from the general energy equation i've come with a form similar to a modified bessel function of zero order but I'm stuck after that. i hope you may be able to help me. thanks a lot in advance.

    Problem : Burning of a wooden dowel

    In a fire research experiment, a long wooden dowel ( around rod), diameter 1.00 inch, temperature 74°F, is placed in a stream of 1,500°F air. The heat transfer coefficient between gas and surface is 5 Btu/h-ft2-F. Estimate the exposure time up to ignition of the rod on the assumption that ignition takes place when the surface temperature reaches 750°F.
    Wood Properties at 74°F
    Ρ= 50 lb/ft3
    k = 0.10 Btu/h-ft-F
    cp = 0.6 Btu/lb-F

    assume that the wood properties are constant up to 750°F. Neglect the possible role of thermal radiation.
  2. jcsd
  3. Oct 17, 2008 #2


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    Hi aelisha1079, welcome to PF. I would check first if conduction within the rod can be ignored (i.e., calculate the Biot number). If it can, then a lumped capacitance approach can be used. If not, then the standard approach is to start with the time-dependent solution for the heat equation in cylindrical geometry; there's no reason to try to re-derive it.
  4. Oct 17, 2008 #3
    hi mapes! thanks for the reply. I've tried to derive the equation because i cant find a reference with the same case as unsteady heat conduction in an infinitely long cylinder. I would appreciate if you can provide me some referance for the problem. thanks so much
  5. Oct 18, 2008 #4


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    Check Incropera and Dewitt's Fundamentals of Heat and Mass Transfer.
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