Learning Goal: To practice Problem-Solving Strategy17.3 Heat conduction Animals in cold climates often depend on two layers of insulation: a layer of body fat (of thermal conductivity 0 200 W/(m - K) ) surrounded by a layer of air trapped inside fur or clown. We can model a black bear asa sphere 1.50 min diameter having a layer of fat :1.de 1 0'2 m thick, as shown in the gureujgure 1) In studies of bear hlbernation, it was found that the outer surlaoe layer ofthe fur is all To = 2.?0 l'C during hibernation while the Inner surface or the fat layer is at T3 = 31 0 0C. HOW thick should the air layer (contained Wi'lhin the fur) be 50 that the bear loses heat at a rate 01'5013 W ? Thermal conductivity ofair is km : 2.40x1u'2 W/{m - K) . Figure Black Tr Bear ' Problem-Solving Strategy 17.3: Heat conduction IDENTIFY the relevant concepts: The concept of heat conduction comes into play whenevertwo objects at dierent temperature are placed tn contact. SET UP the problem using the following steps 1. Identify the direction or heat flow in the problem (from hot to cold). In the equation _ dQ _ TilTC H _ a: _ kA L L is always measured along that direction and A is always an area perpendicularlo that dlreclion. Oen, when a box or olher container has an irregular shape. but uniform wall thickness. you can approximate it as a flat slab with the same thickness and total wall area. 2. Identify thetarget variable. EXECUTE the solution as follows: 1. If heat ows through a single object, use the above equation to solve for the target variable 2. In some problems, the heat ows through two different matenals in succession. The temperature T at the interrace between the two matenals is then inten'hediate between Thand Tc: In steadyistate heat flow. the same heat has to pass through both materials in succession, so the heat current H must be the same in both matenals. 3. If there are two paiallel heat ow paths, so that some heat ows through each. then the total H l5 the sum of the quantities H1 and H: for the separate paths. 4. As always, it Is essential to use a consistent set of units. EVALUATE your answer. As always, asK yourself whether the results are physically reasonable. IDENTIFY the relevant concepts ln this problem there is heat flow through two different materials in succession. The temperature at the interface for the fur and fat must be some number between the ex1ernal and internal temperature of the bear Assuming the data in the problem are for a steady state, then the heat current tn both materials I'HUSl be the same. SET UP the problem using the following steps V PartA V Part0 How many inches thick should the bears fur layer (LIE) be to hold a layer of air Lnu so that adequate insulation is provided? Express VIIILII answer IO three significant leIH'ES. D View Available Hint{s} Exam: 4'5 0 0-]? Iran = 79.1 in Previous Answers ' X Incorrect; Try Again; 2 attempts remaining