Consider the cooking of a steak in a convection oven. In this process, the pan is heated in the oven till it approximately reaches the oven temperature. The steak is then put on the pan, and for safety considerations cooked till the center temperature reaches 77C. The oven temperature is at 205C, and the convective heat transfer coefficient is 15W/m2K. The pan surface provides a heat flux of qo=20W/m2. The initial temperature of the steak is 15C. You are required to find the cooking time. i. Write down the governing equation for the problem. ii. Write down the initial and boundary conditions. iii. Note: This case requires a different a bit more general analytical solution than the ones given in class. The solution is Governing Equation tT=x22T0xL Initial Conditions: t=0,T=TinVx Boundary Conditions: kvT(0,t)=q0 and kvT(L,t)=h(T(L,t)T) Where TL is the ambient air temperature in contact with the surface at L. Solution is T(x,t)=T+kq0[Lx]+hqo+n=1Ancos(nLx)exp[n2L2t] Where n are the roots of the equation ntann=khL And An=2L[1+nSin(2n)](TinTkq0Lhq0)nLSin(n)+kq0L2(n1Sin(n)+n21(Cos(n)1)) At steady state (t), the solution becomes T(x,)=T+kq0(Lx)+hq0 This solution is just a more general solution than the one given in class for the case of the finite surface resistance. We will discuss it briefly in class. Show that the solution satisfies the governing equation you wrote in (i). Show that the solution satisfies the boundary conditions you wrote in (ii). Calculate the cooking time if the steak is 3cm thick. Assume the meat has thermophysical properties of water