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Problem II (30 Points): The following table depicts the values of the oth order Bessel function of first kind which appears frequently in heat transfer problems involving cylindrical geometry. a) Determine the first and second derivative of this Bessel function at x = 0 using forward differences. b) Using the results of the part (a) and Taylor's theorem, express this Bessel function as an approximate second degree polynomial. c) Determine the heat flux, q, (J/m-sec) at x = 1.0 using the Fourier's law given by Heat Flux = q = -kla dT dx Where the thermal conductivity k = 0.1 (J/m.sec.K), and the temperature T = 500 degrees Kelvin. X T(x) 0.0 1.0000 0.2 0.9900 0.36 0.9604 0.57 0.9120 0.8 0.8463 1 0.7652 Problem II (30 Points): The following table depicts the values of the oth order Bessel function of first kind which appears frequently in heat transfer problems involving cylindrical geometry. a) Determine the first and second derivative of this Bessel function at x = 0 using forward differences. b) Using the results of the part (a) and Taylor's theorem, express this Bessel function as an approximate second degree polynomial. c) Determine the heat flux, q, (J/m-sec) at x = 1.0 using the Fourier's law given by Heat Flux = q = -kla dT dx Where the thermal conductivity k = 0.1 (J/m.sec.K), and the temperature T = 500 degrees Kelvin. X T(x) 0.0 1.0000 0.2 0.9900 0.36 0.9604 0.57 0.9120 0.8 0.8463 1 0.7652