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 te Heat transfer coefficent h 120W/(m2k) mperatureT -20 C Alumium thermal conductivity K-220 W ( Specific heat C-896J/ (kg K) k), density p 2707kg/m3, 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 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

You will need to use program like Matlab.

Answer 1

ANSWER From tha given puestion we have vectangular aluminium block 어ㅜ. Lower sides and D3mm =10 mm are Gven Suracetempe rature (00 20 C Outhde tenmperature T. na wlmK) Hart traner Caiciemt Coc KE220W Imk) S=240 Kglm Specificheat =67/gK nlow, heattransjer rate 3- T T2-7 Q s L K => (73-7) 1 B3substiteting all values o (20-T3) Oolo 143.337 i8333.320D - T

164 33T P18353 33 7,t9s bb 1 initial temperatur At Length og bloLk LesvIAL), = 0 005 Ah t Soc o-T3 ld e Ti-T3 - hbeet e -12-O 220-1o O 2407 X(D xu.005 X340 e 200-10D Cy soluing we t2.558 Sec doubled ti's when Mos t 2.55682 tor td 5.118 Se LeFo.01 Lo 02m D1.5mm