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Show The wall thickness of the boiler tubes (x=i) as well as the temperature on the cold side of the boiler tubes are constant for a given boiler. The temperature distribution from the hot side of the boiler tubes (at x=0) to the cold side (at x=l) can only be changed by changing the surface temperature of the hot side of the boiler tubes. The transfer of heat from hot to cold side, therefore, only depends on the heat flux which is obtained from the distribution of temperature in the tube wall. For the calculations carried out here the boiler tube walls were assumed to be flat and of 5 m m thickness. The thermal conductivity and thermal diffusivity were assumed to be 155J/m-h and 0.042 m2/h respectively. These values are representative of about 1 % carbon content steel. Flat Steel Wall K =0.042 nr^/h I = 0.005m 6 I: constant JC=0 Fig. 4.3 Unsteady-state Heat Conduction of a Finite Slab with Steady Boundary Condition Initial Condition: 6(x,t)lm0 = f(x) = 60 + (0, - 00)x 11 Boundary Condition l:6(xj)x_Q = 6Q Boundary Condition 2: 6(x,t)x_l = 6i (4.6) (4.7) (4.8) 0-6 46 °° I / K n_02rt+ 1 exp 2(g/-e0)^(-ir + • -£ exp- (2n + \)jrx at sin- (2/z + \)xx 1 K n-1 n njz\ . mix - at >sm / / I / (4.9) 2 " I / nn \ . njix _' ^ . njzE ^ The temporal distribution oi temperature in the wall was obtained by changing the surface temperature in a step function. Equation (4.8) shows the solution of Equation (4.1) through the use of boundary conditions given in equations (4.6) - (4.8). The resulting temperature distribution, derived from equation (4.9) [6], is shown in Fig.4.4. The results show that the temperature profile remains unchanged after approximately 1.0 second. The temporal variation of heat flux to the cold side ( x=l), shown in Fig. 4.5, reaches the asymptotic value in a very short time. Equation (4.10) gives the solution as a function of time when the temperature, Go , is changed periodically. However, some other technique for solution must also be used here since for x=0, the value of do -0. 14 11-8 |