A heat exchanger connects two pieces of machinery. At the left end of the exchanger (z = 0), the machinery is held at a constant temperature, Tref, The machine at the other end produces a constant flux of heat go. Along the exchanger's length, heat is lost to the surrounding environment air at a temperature To by convection. Given Tref, qo, To, the length L of the heat exchanger, its surface area per unit length a, its thermal conductivity K and the convection heat transfer coefficient η, we seek a model for the steady- state temperature distribution along the length of the exchanger This is a problem in conservation of energy, namely, the conservation of heat. We are interested in finding the temperature along the length of the bar, which suggests that we can assume that the domain is one-dimensional. In other words, the temperature T(x) is a scalar field defined along the bar's length z E [0,L]. Heat flux q(z) is a vector field that is related to the gradient of the temperature through Fourier's Law, dT q(z) =-K The governing equation is derived by considering that heat (energy) is conserved: at steady state, the negative divergence of the flux at any point must be equal to the rate at which the heat is leaving the bar through convection at that point. The sink term qconv(x) is a scalar field defined along the length of the exchanger. Convection is described by Newton's law of cooling Formulate the continuous problem. A helpful trick in doing this is to define a relative temperature, u(z) = T(z)-T, ef. Recall that the complete problem statement includes boundary conditions. When the governing equation has been obtained, write out the finite difference scheme for the problem, which will include a stencil specifying the equation at each node in terms of the node index i