1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Heat transfer - Transient state involving a solid and a surface

  1. Nov 17, 2012 #1
    1. The problem statement, all variables and given/known data

    A thermometer for medical applications to determine the time required for the tip to reach a temperature of 37.95 C when in contact with the skin temperature of 38 C, starting from an initial value of 25 ° C.

    Admit that the tip of the thermometer is completely metallic (all sides except the bottom) in contact with the skin of a person.

    The tip material is stainless steel with a thermal diffusivity of 0.05 cm2 / s, the specific heat at constant pressure of 451 J / (kg.K) and thermal conductivity of 17.2 W / mK.
    The contact resistance between the skin and the metal end is estimated at 31.529 K / W.

    Assume that the metallic end of the thermometer can be considered a system with internal resistance to heat conduction negligible.

    Suppose that the tip of the thermometer is a cylinder of 1 cm in length and 0.6 cm diameter


    2. Relevant equations

    k -> thermal conductivity
    c-> specific heat
    [itex]\alpha[/itex] -> thermal diffusivity

    Fo = [itex]\alpha[/itex] * t/r^2

    [itex]\alpha[/itex]= k/(ρ*c)

    Bi= hc*ro/k

    Diagrams for dimensionless transient temperatures and heat flow

    and many more...

    3. The attempt at a solution

    At first, there's no convection in the problem, so Bi = 0, in the diagram, the curves 1/Bi would be equal to 0 because hc -> ∞. Okay, and making the temperatures difference
    (T-T(∞))/(T(0)-T(∞)) = -0.05/-13 = 0.00385
    So looking into the diagram for dimensionless transient temperatures and heat flow for a long cylinder, I will find Fo = 1
    When I put the values in formula -> Fo = [itex]\alpha[/itex]*t/r^2 it doesn't seem to work (I have converted [itex]\alpha[/itex](thermal diffusivity) to m^2/s, so it will be 5*10^-6 m2/s).
    After that, I tried making ρ*c*V*dT/dt = Q, making Q equal to the (T-T(∞))/(Rk+Rcontact)
    I'm really lost in this problem, because I get used to solve problem that involved a solid and a fluid, this problem is related to fins and transient state, but I can't find a way through in this problem.

    Well, the answer should be around t= 170,52 seconds as it says on the answer.

    I would appreciate a help for tackling out this problem, any sugestions, ideas, solutions are welcome. Thanks !
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Heat transfer - Transient state involving a solid and a surface
  1. Heat Transfer (Replies: 0)

  2. Heat Transfer (Replies: 0)

Loading...