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A thin wire coated in polypropylene (melting temperature 160C ) is buried in soil at a depth of 2 meters. The soil is initially at uniform temperature 80C. Suddenly (t=0) a uniform constant heat flux q is applied at the surface of the soil. The thermophysical properties of soil (thermal conductivity k and thermal diffusivity ) are provided in the diagram below. (a) What is the quantitative criterion for determining whether a system undergoing transient conduction can be approximated as a semi-infinite medium? Write the expression for the relevant dimensionless number and the accepted quantitative requirement for use of the approximation. (b) If one wishes to calculate the temperature of the buried wire at its indicated depth as a function of time up to 1 month, determine whether this system meets the criterion in (a). (c) Determine the heat flux q if it is observed that the polypropylene coating begins to melt exactly 1 month after the heat flux begins. Ignore the thickness of the wire and coating