1. The temperature field has been established in a rectangular plate by the thermal arrangement shown in Figure 1. The t

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1 The Temperature Field Has Been Established In A Rectangular Plate By The Thermal Arrangement Shown In Figure 1 The T 1 (181.83 KiB) Viewed 31 times

1. The temperature field has been established in a rectangular plate by the thermal arrangement shown in Figure 1. The temperature distribution at the right side (x = a) πν b constant temperature To. The plate is thermally insulated at the bottom (y = 0), and the upper side of the plate is attached to a heater with a heat flux q sin (m). The conductivity of the plate is K. of the plate is To +To cos(7), the temperature at the left side (x = 0) is kept at = 7TX (a) Write the governing equation for the temperature within the plate in terms of the excess temperature 0 = T-To, and state the boundary conditions. (5 marks) (b) By using the superposition principle, set the excess temperature in 1(a) as 0 = 01 + 02 , with proper boundary conditions for 0, and O2 , such that the Fourier series methods can be applied to solve 0, and O2 respectively. Sketch the thermal arrangement for O, and 02, and state their governing equations together with the boundary conditions. (10 marks) (c) Solve 0, and 02 set in 1(b) respectively. (10 marks) у TUX v v qsin(n) b Το лу To +To cos b x 0 Thermal insulation a Figure 1