You are being asked to determine the time death of a human in a suspected homicide. You are to employ a method that is based on unsteady heat transfer in a multidimensional system. Approximate an adult human as a cylinder of length 1.8m and diameter of 0.35m. The temperature of the surrounding air remained constant since the death at 21C. The temperature at the center of the body is 26C. Assume the temperature of the body at the time when death occurred to be 37C. During this time the body was subjected to circulating air resulting in a convective heat transfer coefficient of 14W/m2K. The thermal properties of the body can be approximated as that of liquid water (=998kg/m3,cp=4182 J/kgK,k=0.602W/mK)._For the problem: i. Write down the governing differential equation along with the appropriate initial and boundary conditions. ii. Define dimensionless temperature =ToTT(r,z,t)T, dimensionless distance Z=Lz and dimensionless radius =rR to convert the governing equation to a dimensionless form. Here R and L are the radius and length of the cylinder respectively. iii. Convert the boundary and initial condition to the dimensionless form. iv. Write down the solution to the governing equation in (ii) subject to the initial boundary conditions in (iii). v. Calculate the time of death assuming that heat transfer from the body occurs (a) radially only, (b) axially only, and (c) both radially and axially