Consider a pipe that carries steam Heat is lost to the ambie

Consider a pipe that carries steam. Heat is lost to the ambient air and the surrounding surfaces by convection and radiation. The total flow of heat per unit time, Q, can be estimated from the following equation: Q = ndL[h (T_s - T_air) + epsilon sigma_SB (T^4_s - T^4_suTT)] where d is the diameter of the pipe (m), angle is the length of the pipe, e is the radiative emissivity of the surface of the pipe (Stefan-Boltzman constant, W/m^2/K^4), h is the heat transfer coefficient (W/m^2/K), and T is temperature. The subscripts s, air, and surr refer to the temperatures at the surface of the pipe, in the air, and the surrounding surface. Use the secant method to determine the temperature at the surface of the pipe given the data below. Use the starting points of 100 and 200. Compute the approximate relative error after each iteration. Solve to 2 significant figures.

Solution

Answer is 423K

i	x	f(x)	Relative error
0	100	-36720.3374	-0.763593381
1	200	-28336.2234	-0.527186761
2	537.975	27450.87285	0.271808908
3	371.669	-8635.195818	-0.121348829
4	411.465	-2099.416682	-0.027268366
5	424.249	232.7735609	0.00295207
6	422.973	-5.521967947	-6.42014E-05
7	423.002	-0.014113332	5.69394E-06
8	423.002	8.58414E-07	5.87304E-06
9	423.002	3.63798E-12	5.87303E-06