Complete this assignment with your homework partner. By printing both of your names above, you are indicating that you have both contributed substantially to this assignment and that *all* work on this assignment is representative of *both* of your abilities. In other words, everything written below must be clearly understood by both partners. For this assignment, you will complete a homework assignment with your partner while watching a video. In the video, a student (aided by an instructor) will be solving an analogue of the problem you will complete with your partner. Thus, you can apply the principals and methods detailed in the video to help complete your own assignment. Work interactively with your homework partner to complete the following problems. (1) Attach all work to the back of these pages. (2) Scan to PDF and submit to the assignment on Blackboard. (3) You and your homework partner should each bring a hardcopy to class so that you can complete the self-grading during or after class. Infrared absorption by skin: You are designing an experiment to understand how skin and underlying muscle absorb infrared (IR) light and convert it to heat. You design a testing apparatus that will shine IR light uniformly on a tissue sample. Important note: IR light is not absorbed and converted to heat at the surface (i.e., is NOT a radiation boundary condition for the skin tissue); IR light penetrates into the tissue so is absorbed and converted to heat all throughout the tissue as described below. To simplify the analysis, you have insulated the sides of the apparatus so that no heat will flux perpendicular to the IR source. The apparatus is also insulated on the bottom (undereath the muscle) so that no heat will flux out of the bottom of the testing apparatus. The top (epidermal layer) is open to air so cooling will occur in that direction as normal. IR light source Tissue sample _ " Side and bottom are \"well insulated\" (i.e., no flux) Your hypothesis is that the tissue absorbs IR light proportional to the intensity of the IR light; but, since some is being absorbed as the IR light goes further into the tissue, intensity of IR light will decrease with penetration depth. Based on this, you hypothesize that absorption will decrease linearly with penetration depth which should result in conversion of IR light to heat. The function to describe this will depend on which way you define your coordinate system. If ou define z=0 as the top surface (air interface), the conversion of IR light to heat will =[(d z)/(dJ*A, where A has units of J/m' and d is the depth (distance in axial direction) of the tissue sample and has units of m. If you define z=0 as the bottom of the tissue sample, the conversion of IR light to heat will = [z/d]*A. Assume that you know the thermal conductivity (x) of the tissue sample and that it is uniform throughout the tissue and not a function of temperature. Also assume that you know the heat transfer coefficient (h) from the tissue sample to the air at the top interface. You can assume that the tissue sample is at room temperature (T.) before the IR lamp is turned on. You place temperature probes (thermocouples) at several depths so that you can measure the temperature profile in the tissue to test your hypothesis. If your hypothesis is correct, what temperature profile do you expect to measure after the IR lamp has been on for a long time and the temperatures have stopped changing? Step 1: Write the simplified Conservation of Energy equation and boundary conditions. Step 2: Solve for the temperature profile OK to include unsolved for integration constants, Step 3: Solve for the temperature at the top surface of the skin. Then solve for the 2" integration constant. Step 4: Write your final expected temperature profile as a function of known constants