A10-cm-thick aluminum plate (α = 97.1 × 10−6 m2/s) is being heated in liquid with temperature of 475°c. the aluminum plate has a uniform initial temperature of 25°c. if the surface temperature of the aluminum plate is approximately the liquid temperature, determine the temperature at the center plane of the aluminum plate after 15 s of heating. solve this problem using the analytical one-term approximation method.

The chart shows the costs and shipping times for materials that a company needs to build a new product. which describes the best trade-off if the company needs to start building their product within the next two years? they should order the domestic materials because it is always best to choose the fastest shipping time. they should order the imported materials because it is always best to choose the lowest cost for materials. since the shipping time is longer, they should order the domestic materials because the additional cost is worth it to get the materials in time. even though the shipping time is longer, they should order the imported materials because they are less expensive and should arrive in plenty of time to build the product.