A resistance heating appratus for a fluid consists of a thin wire immersed in a fluid. In order to design the appratus, it is necessary to determine the temperature in the fluid as a function of he heat flux from the wire. For the purposes of the calculation, the wire can be considered of infinite length so that the heat conduction problem is effectively a two dimensional problem. In addition, the thickness of the wire is considered small compared to any other length scales in the problem, so that the wire is a line source of heat. The wire and the fluid are initially at a temperature T0. At time t = 0, the current is switched on so that the wire acts as a source of heat, and the heat transmitted per unit length of the wire is Q. The heat conduction in the fluid is determined by the unsteady state heat conduction equation = 2 and the heat flux (heat conducted per unit area) is KT where K is the thermal conductivity of the fluid. (a) Choose an appropriate coordinate system, and write down the unsteady heat conduction equation. (b) What are the boundary conditions? Give special attention o the heat flux condition at the wire, and note that the wire is considered to be of infinitesimal radius. (c) Solve the heat conduction equation using the simplest method, and determine the temperature field in the fluid. (d) Use the boundary conditions to determine the constants in the expression for the temperature field.