4.3. Transient Conduction with a Constant-Flux Boundary Condition Suppose that a solid of indefinite thickness is subjected to a constant heat flux q0 at x=0. rginning at t=0. It occupies the space x>0 and its initial temperature is uniform at T. (a) State the equations that govern T(x,t), and use order-of-magnitude reasoning to infer how the temperature at x=0 varies with time. What variable transformations does this suggest when seeking a similarity solution? (b) Use the similarity method to determine T(x,t). [Hint: The solution involves an integral of the complementary error function, denoted as ierfc and defined as ierfc(x)=xerfc(s)ds. The properties of this and other integrals of erfc are described in Abramowitz and Stegun (1970, p. 299). This integral error function can be evaluated from erfc(x) as ierfc(x)=xerfc(x)+ex2] (c) How does T(0,t) from the similarity solution in part (b) compare with the order-ofmagnitude estimate in part (a)