EXAMPLE 5.3 Analysis: To assess the validity of the lumped capacitance approxima

Question

EXAMPLE 5.3 Analysis: To assess the validity of the lumped capacitance approximation, we begin by calculating Biot numbers for the heating and cooling p A 3-mm-thick panel of aluminum alloy(k-177 W/m.K, c 875 J/kg K, and p 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above T, = 150°C for at least 5 min. The production line for the curing operation involves two steps: (1) heating in a large oven with air at T 175°C and a convection coefficient of ho 40 W/m2.K, and (2) cooling in a large chamber with air at Ts 25°C and a con- vection coefficient of he = 10 W/m2. K. The heating portion of the process is conducted over a time interval t which exceeds the time t required to reach 150°C by 5 min tete300 s). The coating has an emissivity of 0.8, and the temperatures of the oven and chamber walls are 175 and 25°C, respectively. If the panel is placed in the oven at an initial temperature of 25°C and removed from the chamber at a safe-to-touch tempera- ture of 37°C, what is the total elapsed time for the two-step curing operation? h,L (40 W/m2 K)(0.0015 m) 34 x 10 -4 h L (10W/m2 K)(0.0015 m) Hence the lumped capacitance approximation is excellent. To determine whether radiation exchange between the panel and its surroundings should be considered, the radiation heat transfer coefficient is determined from Equation 1.9. A representative value of h, for the heating process is associated with the cure condi tion, in which case SOLUTION Kno: Operating conditions for a two-step heating/cooling process in which a coated aluminum panel is maintained at or above a temperature of 150°C for at least 5 min. 0.8 × 5.67 × 10 8 W/m2-K0423 + 448K(4232 + 4482)K? - 15 Wm2 K Find: Total time required for the two-step process. Schematie: Using T-150°C with Tsur,C-25°C for the cooling process, we also obtain hre- 8.8 W/m2.K. Since the values of ho and h are comparable to those of ho andh respec- tively, radiation effects must be considered. Tur 25C With V-2LA, and AA, Equation 5.15 may be expressed as A, Selecting a suitable time increment, ?, the equation may be integrated numerically to obtain the panel temperature at t-??, 2??, 3??, and so on. Selecting ?t-10s, calcula- tions for the heating process are extended to t 300 s, which is 5 min beyond the time required for the panel to reach T 150°C. At ie the cooling process is initiated and continued until the panel temperature reaches 37°C at . The integration was performed using IHT, and results of the calculations are plotted as follows: E 08 Alurninurn, TO)-Ti-25 C T)37C Step 1: Heating (0 sts Step 2: Coolingts The total time for the two-step process is Assumptions: = 989 s 1. Panel temperature is uniform at any instant. 2. Thermal resistance of epoxy is negligible 3. Constant propertics. with intermediate times of t 124 s and t-424 s

Explanation / Answer

In this condition ,the red box equation given the the coefficient of radiation heat transfer. by using this equation if you iterate and using boundary condition as (dT/dt) = 10 sec then you will get the ans as total time = 989sec=16.5 min.

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