Question

. Use the explicit method to solve for the temperature distribution of a long, thin rod with a length of 10 cm and the following values: k'=0.49 cal/(s - cm 0). Ax=2 cm, and At=0.1 s. At i = 0, the temperature of the rod is zero and the boundary conditions are fixed for all times at T(0) = 100°C and T(10) = 50 C. Note that the rod is alu- minum with C=0.2174 cal/g. "C) and p=2.7 g/cm'. Therefore, k =0.49/(2.7.0.2174) 0.835 cm/s and 2 =0.835(0.1)/(2)2 =0.020875.

Answer 1

To calculate the heat-conduction rate through the steel rod and the aluminum rod at the joint, use the formula: Heat-conduction rate = (thermal conductivity) * (cross-sectional area) * (temperature difference). The heat-conduction rates through both rods should be equal at the joint.

Step-by-step explanation:

To calculate the heat-conduction rate through the steel rod and the aluminum rod at the joint, we need to use the formula:

Heat-conduction rate = (thermal conductivity) * (cross-sectional area) * (temperature difference)

For the steel rod:

Heat-conduction rate = (80 W/m °C) * (7.85 × 10^−5 m²) * (100 °C – T)

For the aluminum rod:

Heat-conduction rate = (220 W/m °C) * (7.85 × 10^−5 m²) * (T – 50 °C)

Since the rods are welded end to end, the heat-conduction rates through both rods should be equal at the joint.