b) Using the mesh in Figure 2, form the basis functions associated with element 2 and write the FEM approximation over the element. 1 2 3 1 2 1m 1m Figure 2: Mesh of 2 elements. Elements are numbered with underlines.

Given that P=120lb and Q=130lb, find the rectangular representation of P+Q.

5.19 Suppose that the graph below shows measured values of for air in forced convection over a cylinder of diameter D. plotted on a logarithmic graph of as a function of ReD Pr. Write an appropriate dimensionless correlation for the average Nusselt number for these data and state any limitations to your equation.

Use integration to verify the formula given in Table 9.2 for Ixy of a half parabolic complement.

Determine Ix for the triangular region shown.

A differential equation is d2ydt2=Ay2+Byt where y represents a distance and t is time. Determine the dimensions of constants A and B for which the equation will be dimensionally homogeneous.

5.2 Evaluate the Prandtl number from the following data: , .

Use integration to find Ix,Iy, and Ixy for the shaded region shown.

1.77 Explain each in your own words. (a) What is the mode of heat transfer through a large steel plate that has its surfaces at specified temperatures? (b) What are the modes when the temperature on one surface of the steel plate is not specified, but the surface is exposed to a fluid at a specified temperature?

Using the information in Problem 1.22, estimate the ambient air temperature that could cause frostbite on a calm day on the ski slopes. 1.22 In order to prevent frostbite to skiers on chair lifts, the weather report at most ski areas gives both an air temperature and the wind-chill temperature. The air temperature is measured with a thermometer that is not affected by the wind. However, the rate of heat loss from the skier increases with wind velocity, and the wind-chill temperature is the temperature that would result in the same rate of heat loss in still air as occurs at the measured air temperature with the existing wind. Suppose that the inner temperature of a 3-mm-thick layer of skin with a thermal conductivity of 0.35W/mKis35C and the air temperature is 20C. Under calm ambient conditions the heat transfer coefficient at the outer skin surface is about 20W/m2K (see Table 1.4), but in a 40-mph wind it increases to 75W/m2K. If frostbite occurs when the skin temperature drops to about 10C, do you advise the skier to wear a face mask? What is the skin temperature drop due to the wind?