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The initial temperature of an iron bar is zero (T = 0°C ) for all points on the bar, except at x = 0.0m as shown in Figure 1. The bar is heated at x 0.0m where the temperature is kept at T = 8°C at all time. The bar is fully insulated. Therefore, the temperature at the other end of the bar is always same with the temperature at its %3D %3D dT neighboring point ( = 0 at x = 1.0m). %3D T=8 °C T=0 °C x=0.0m x=1.0m Figure 1: Initial condition of the bar Please state the general formula to approximate the temperature T(x,t) using numerical method. Then, by using calculator, calculate the value of temperature at any point x and any time t from t=0 until t= 0.15 for At = 0.025, Ax = 0.25 and the thermal conductivity k = 1. Δε Please justify the choice of 1 = k -, that you use to approximate the temperature. (Ax)2 Leave your answer in 4 decimal places.

The initial temperature of an iron bar is zero (T = 0°C ) for all points on the bar, except at x = 0.0m as shown in Figure 1. The bar is heated at x 0.0m where the temperature is kept at T = 8°C at all time. The bar is fully insulated. Therefore, the temperature at the other end of the bar is always same with the temperature at its %3D %3D dT neighboring point ( = 0 at x = 1.0m). %3D T=8 °C T=0 °C x=0.0m x=1.0m Figure 1: Initial condition of the bar Please state the general formula to approximate the temperature T(x,t) using numerical method. Then, by using calculator, calculate the value of temperature at any point x and any time t from t=0 until t= 0.15 for At = 0.025, Ax = 0.25 and the thermal conductivity k = 1. Δε Please justify the choice of 1 = k -, that you use to approximate the temperature. (Ax)2 Leave your answer in 4 decimal places.

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The initial temperature of an iron bar is zero (T = 0°C ) for all points on the bar, except at x = 0.0m as shown in Figure 1. The bar is heated at x = 0.0m where the temperature is kept at T = 8 °C at all time. The bar is fully insulated. Therefore, the temperature at the other end of the bar is always same with the temperature at its %3D %3D dT neighboring point E = 0 at x = 1.0m). T=8 °C T=0 °C x=0.0m x=1.0m Figure 1: Initial condition of the bar Please state the general formula to approximate the temperature T(x, t) using numerical method. Then, by using calculator, calculate the value of temperature at any point x and any time t from t = 0 until t = 0.15 for At = 0.025, Ax = 0.25 and the thermal conductivity k = 1. Please justify the choice of 1 = k- that you use to approximate the temperature. At (Ax)2 Leave your answer in 4 decimal places.
Transcribed Image Text:The initial temperature of an iron bar is zero (T = 0°C ) for all points on the bar, except at x = 0.0m as shown in Figure 1. The bar is heated at x = 0.0m where the temperature is kept at T = 8 °C at all time. The bar is fully insulated. Therefore, the temperature at the other end of the bar is always same with the temperature at its %3D %3D dT neighboring point E = 0 at x = 1.0m). T=8 °C T=0 °C x=0.0m x=1.0m Figure 1: Initial condition of the bar Please state the general formula to approximate the temperature T(x, t) using numerical method. Then, by using calculator, calculate the value of temperature at any point x and any time t from t = 0 until t = 0.15 for At = 0.025, Ax = 0.25 and the thermal conductivity k = 1. Please justify the choice of 1 = k- that you use to approximate the temperature. At (Ax)2 Leave your answer in 4 decimal places.
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