Question

interest. This alloy steel bracket (K-47 W/mK) is mounted securely to a worktable by its feet, while a hot cylindrical rod is placed within the bracket's cylindrical opening at the other end for processing work. It is known that when the rod is in contact with the bracket, it transfers a heat flux to the bracket of 1.2 W/cm2. Meanwhile, the large table upon which the bracket is mounted keeps its bottom surfaces at a constant 27 °C as shown in the drawing. All other surfaces of the bracket experience a convection environment at 300 K with h 12.5 Wm2K. Based on this information, a) use a 3D SolidWorks simulations to obtain the steady-state temperature distribution within the bracket. Print a screenshot for submission with homework b) OSHA specifies that the maximum safe touch temperature for bare hands be 60 °C. When holding a heated rod, would the bracket be safe to touch bare-handed or would a warning sign need to be placed in the vicinity/protective gloves be required? c) Determine the temperature at the points of interest labeled Point A and Point B in the drawing

Answer 1

Given that,

    the heat flux , x = 1.2 X 10⁴ W / m²

                       k = 47 W / mk

                       L = 36

               T₁ - T_x / T₁ - T₂   = x / L

          from this by substituting we get the steady state temperature distribution, T₁ - T₂

                 300 - T_x / 300 - T₂ = 1.2 X 10⁴ / 36

             T_x and T₂ will be directly proportional and they are double to each other,

      T_x is double of the T₂ hence, this temperaturezs distributions can be easily varied.

b) As 60⁰ is not a huge temperature , by heating the rod with 60⁰ and inserting in the bracket will doesnt transfer much heat to the bracket,

     Hence the heat transfer amount will be less with the 60⁰ to the bracket

     so, we can touch the bracket bare hanede without any problem and the usage of gloves is not required and not necessary.

   we have the formula, Q = T₁ -T₂ / R

      R = L / KA

        = 36 / 47 X 36 X 25

       = 0.085

    Q = 60 - 25 / 0.085

       = 411.7 W

Hence we can touch the bracket with bare hand.

c) we have the formula,

    T_c = T + RQ / 2h

         = 60 + 0.085 X 411 / 2 x 12.5

        = 60 + 1.4

        = 61.4⁰

The temperature at point A = 61.4⁰

The temperature at point B = ?

    T_b = T + RQ / 2h

        = 27 + 1.4

        = 28.4⁰

Hence the temperatues at both the points has been determined.