Question

The temperature of piston head in a combustion engine during the worming up period can be modelled by equation (6): ----------------------------------------------- 𝑇=𝐾𝑇𝑜(𝐿+𝑡2𝑐𝑜𝑠𝑡3) ------------------------------------------------------------------------------------------------------------ Where T is the piston head instant temperature in Kelvin, K and L are constants for a given engine, t is time in second, and T be the environment temperature in Kelvin. ------------------------------------------------------------------------------------------------------------ Considering the following parameters for the given engine including 𝐾=3, 𝐿=3.4×10−3𝑠2and To=295 K. --------------------------------------------------------------------------------------------------------------- a) Calculate the mean temperature for piston head between t=0 and t=2 s. ------------------------------------------------------------------------- b) A numerical integration technique (n=8 intervals) to find the mean over a range of0≤𝑥≤𝜋.