In a thermal system, the volume flow rate R of a fluid through a duct due to a fan is given in terms of the pressure difference P, which drives the flow as Here, R is in m 3 /s and P is in N/m2. The first equation represents the characteristics of the fan and the second one that of the duct. Simulate this system by the successive substitution and NewtonRaphson methods to obtain the flow rate and pressure difference. Q236 Numerically simulate the casting of a metal plate of thickness L = 0.2 m in a mold of wall thickness W = 0.05 m, assuming one-dimensional solidification, no energy storage in

In a thermal system, the volume flow rate R of a fluid through a duct due to a fan is given in terms of the pressure difference P, which drives the flow as Here, R is in m 3 /s and P is in N/m2. The first equation represents the characteristics of the fan and the second one that of the duct. Simulate this system by the successive substitution and NewtonRaphson methods to obtain the flow rate and pressure difference. Q236 Numerically simulate the casting of a metal plate of thickness L = 0.2 m in a mold of wall thickness W = 0.05 m, assuming one-dimensional solidification, no energy storage in the solid formed, uniform temperature in the mold, and initial liquid temperature at the melting point T m = 1200 K. A convective loss at heat transfer coefficient h = 20 W/(m 2 K) occurs at the outer surface of the mold on both sides of the plate to an ambient medium at temperature T a = 20C. Find the total time needed for casting. Determine the effect of varying h, using values in the range of 10 to 40 W/(m 2 K), and of varying W, using values in the range of 0.02 to 0.1 m. Take density, specific heat, and thermal conductivity of the cast material as 9000 kg/m 3 , 400 J/kgK, and 50 W/mK, respectively. The corresponding values for the mold are 8000, 500, and 200, respectively. The latent heat of fusion is 80 kJ/kg.

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