Question

The upper and lower sides of the rectangular aluminum block L-10mm, D 3mm) are insulated as shown below. The left and right sides have temperature boundary conditions and convective boundary conditions, respectively Surface temperature T 100 C, Outside temperature T-20 C Heat transfer coefficent h 120W/(m2 k) Alumium thermal conductivity K-220 W/(m k), density p-2707kg/m Specific heat C896J/(kg K) Assuming the aluminum block is a two-dimensional shape, calculate the temperature on the plane(x-y) as follows. 1) Calculate the temperature of the right side surface under steady-state conditions using one-dimensional thermal resistance. 2) The two-dimensional thermal diffusivity equation is solved by a numerical analytical approach, and compared with the one-dimensional result obtained in Problem 1 (as.ay= 1mm) 3) When the initial temperature of the aluminum block is 20 C, Calculate the time for the temperature on the right side to reach steady state 4) The shape of the section(0.3L 〈x〈 0.7L) is changed so as to double the time obtained in Problem 3. Design the shape of the aluminum block satisfying these conditions

Answer 1

91 A K A. 0.0l O 83.33 T2 - , 8 333 33 20 353.33 33.566 ℃ 12 20 C en

913 tey Suc SL-C 七 2xo .osx 8 doukl Vn 2 2loo L C