Explain and solve the following question: 2. Assm e thata rectanular block of st

Question

Explain and solve the following question:

2. Assm e thata rectanular block of steel aitially SSue has a uniforrn temperature of T . IF he sicdesof ock have lengths m the x, y and a, b and c respectively) only one side at x:a, is erfect 1 in sulated and at fime t: o fhe hlock s immers flvid of constant temperature ) find the temperature Txy,2t within the block for all subseqvent Hme. If, the block is 30x 5oxo e what are h e decay ime constauts of the three longest lived temperature modes? For Steel e900 kg m

Explanation / Answer

The rectangular block of steel has a uniform temperature of T0 initially.
Given that the sides of block have lenghts in x,y,z directions as a,b,c respectively.
The rectangular block is insulated perfectly only in X axis at X=a.
Now at time t=0 the block is immersed in a fluid of constant temperature T1.
The change in temperature is given by T1-T0 ;
Given that Specific density S= 7900 kg/m3 ; specific heat capacity is given by C = 436 J/kg K;
thermal conductivity = 67 W/m K
In this case the temperature changes with time , as at time t=o the temperature is going to change.
T(x,y,z,t) = (7900/30) +(7900/50)+ (7900/90) = 139.411 K
Decay time constants are e-30t , e-50t , e-90t

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