Emerald ash borers invasive insects have been killing a larg

Emerald ash borers (invasive insects) have been killing a large number of ash trees in the US. Extreme cold weather however may destroy a large percentage of emerald ash borer larvae. A recent study from the Forest Service (vendetta and Abraham son) in Minnesota showed that 5% of the insects die at 0 degree F (-18 degree), 34% at -10 degree F, 79% at -20 degree F and 98% at -30 degree F (-34 degree). a) If the outside temperature of a large tree (idealized as a semi-infinite solid with a radius of 35 cm) has reached -40 degree, how deep inside a tree should an ash borer be buried to avoid dying from cold exposure with a 95% survival probability? How deep inside will the temperature reach -34 degree? Assume that the surface temperature of a tree has plunged to -40 degree and stays at this temperature for 10 hours, from an initial temperature of -10 degree. Neglect the curvature of the tree trunk. Use the following properties for an ash tree wood: k = 0.17 W/m K, p = 850 kg/m3, Cp = 1200 J/kg K. Note that interpolation will likely be necessary. Compute the heat flux at the surface of the ash tree at 5 hours. You will need to know the properties of the error function with respect to its derivatives.

Solution

1. Calculate the degree of undermines “n”;

2. Choose a rational analysis scheme for method of force

3. Calculate diagrams from unit loads and actual forces;