The block shown below is insulated on all sides except the left-hand-side - heat transfer to/from the block only occurs on the left surface. The block dimensions are LL. The block is initially floating on water, but at t=0, when its temperature is Ti, it instantaneously begins sinking. The total height of the block is [m], but for t>0, the height above the water surface is (Dt)[m], where D is a constant with units [m/s]. As a result, the block's area on the left is increasingly exposed to water, with height exposed equal to Dt[m]. The area above the water level is exposed to air at temperature T with heat transfer coefficient h1. The area below the water level is exposed to water at temperature T with heat transfer coefficient h2 In the diagram, k is thermal conductivity, is mass density, c is mass specific heat capacity. (a) In this scenario, what is the criterion for assuming that the temperature within the solid wall is spatially uniform? You may assume an average h to account for all convection heat transfer occurring in this scenario. What is this assumption called? (b) Write the most simplified form of an energy balance for this case using these terms: Ein,Egen,Eout,Est. (c) Assume the criterion in (a) is met - the wall temperature is spatially uniform. You may assume that convection causes heat transfer from the wall to the fluid for all times (it is cooling: T>T ). Use the energy balance in (b) to set up a differential equation governing this system. (d) Solve for the temperature of the block as a function of time, using only variables given in the diagram