(3) Let us consider some specific examples of the influence of the ambient temper- ature on...

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(3) Let us consider some specific examples of the influence of the ambient temper- ature on the heated plate. The differential equation is Eq. (3.3.10) and assume that the ends are insulated Eq. (3.3.9). Consider the following profiles for the ambient temperature. (a) (b) T(x)/a for L/2 |2x - L| < L, To(x) = 2a 4a (2x/L-1)², for |2x - L < L/2. Construct the solutions and compare the results by graphing them. Answer: The temperature profiles for the two cases are shown below for the choice BL = 5. 2 1.5 1 To(x) = a + a sin 0.5 0.2 0.4 (2). x/L 0.6 (a) (b) 0.8 dT dT = -(L) = 0. dr (3.3.9) How do we now construct the solution for the differential equation with a forcing term that varies spatially? - (0) dx d²T 2 (x) — 3² T(x) = -3² To(x). (3.3.10) (3) Let us consider some specific examples of the influence of the ambient temper- ature on the heated plate. The differential equation is Eq. (3.3.10) and assume that the ends are insulated Eq. (3.3.9). Consider the following profiles for the ambient temperature. (a) (b) T(x)/a for L/2 |2x - L| < L, To(x) = 2a 4a (2x/L-1)², for |2x - L < L/2. Construct the solutions and compare the results by graphing them. Answer: The temperature profiles for the two cases are shown below for the choice BL = 5. 2 1.5 1 To(x) = a + a sin 0.5 0.2 0.4 (2). x/L 0.6 (a) (b) 0.8 dT dT = -(L) = 0. dr (3.3.9) How do we now construct the solution for the differential equation with a forcing term that varies spatially? - (0) dx d²T 2 (x) — 3² T(x) = -3² To(x). (3.3.10)