The Inner Surface Temperature Against Time And Tile Thickness

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From Fig.2, it shows that the inner surface temperature against time and tile thickness. On the right hand side, it is shown that the Forward and the Dufort-Frankel method are very unstable. Both methods had an infinite inner surface temperature at start, which is not ideal. For Backward and Crank Nicolson methods, both of them had a smooth curve and did not have much fluctuation. On the left hand side, it shows the temperature at the inner surface against time. Forward and Dufort-Frankel deviated very soon after the tile get heated. This time, the Backward method moved away from the starting temperature which is a sign of unstable. Therefore, Crank Nicolson was selected to be the most appropriate method to solve this problem. In theory, forward differencing and Dufort-Frankel methods were explicit method, and backward differencing and Crank Nicolson were implicit methods. It was suggested that the implicit method was more stable than the explicit as it solved the equation involving both the current state and the next step rather than just using the current state. The dx, dt were found using Fig.2. dt was found where the Crank Nicolson line started to fluctuate heavily at around 14s (Fig.3), and dx was found when the line started to bend on the right hand side. Using the maximum temperature and tile thickness, the parameters, nt and nx, were calculated and used in the ‘shuttle’ function. The left hand side of Fig.4 shows that the inner surface temperature across a range

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