Question

Problem 2. A long 6.5 cm diameter solid cylinder steel (K 16.3 W/m. K,p 7817 kg/m3, Cp 460 J/kg.k). It's initially at a uniform temperature of T 150°C. It is suddenly exposed to a convection environment with h-285 W/m2 K and Too 50°C. Calculate the temperature at 1.) the axis of the cylinder, and 2.) a 2.5 cm radial distance after 5 min of exposure to the cooling flow. (20%)

Answer 1

Given: D = 6.5 cm = 0.065m R = 0.0325 m K = 16.3 w/m - k rho = 7817 kg/m^3 h = 285 w/m^2 - k c_p = 460 s/kg k T_2 = 150 degree c T_ infinity = 50 degree c Now this question can be solved using HIESLER CHART because in this question it is asked to find temperature ab function of time and space. I am also providing the image of Heister chart to make you understand the solution more clearly Now rightarrow i) temperature at center of cylinder after 5 min. rightarrow step 1: calculating Fourier number F_0 = alpha t/L_c ^2 where alpha = thermal diffusivity = k/rho c t = time L_c = characteristic dimension For Heister chart L_c = R so, F_0 = alpha t/ L_c^2 = kt/rho e L_c^2 = 16.3 times 5 times 60/7817 times 460 times 0.0325^2 F_0 = 1.287 step 2) Finding inverse of biot No. 1/Bi = k/hL_c 1/Bi = 16.3/285 times 0.0325 1/Bi = 1.759