Question

Determine the transient temperature distribution in a one-dimensional (1-D) fluid with a thermal diffusivity a=2 and velocity u = 0.1, if the initial temperature in the fluid is 0.0° and if at all subsequent times, the temperature of the left side is held at 0° while the right side is held at To=2º. The distance between the two walls is L=1 meter. T=0 TT 0 The governing differential equation is the 1-D heat convection diffusion equation at at 22T + u =a at ax дх2

$b) Fill the following matrix, then use it in MATLAB (X = A\B) to solve the 1-D heat convection conduction equation up to time$

Answer 1

от tu OT a du 2 ot (ETCS) R n n n n n! 2 u; - Uit re-ui-i t ze dt (dz) 2 2 (da) 711 rudt 2 dae U;- - Liti U n uiti + -24 tun) ( a dt (dx)2 mt! Y n u; (BTCS) nti 72 72+1 12. u n+1 Uit, -u; - U;-) (dx)2 n+1 riti - U;-, 2(2x) + u dt n! ni nul nt n1+1 -ui '+u;-1 **) udt 2 da ntl 2e; + Miti (d) 2 |

adt + n41 $) 2dx n+ L +(14 odt n+ 1 + udt 2 dx adt (du)2 n+1 + 1 n a u;-1 + bui na1 + cuiti b= udt + adt 2dx (de)? 1+ adt (dx)² udt adt 2 dre (de) 2 n+ no a b ent b ON uz *+1 7141 4,기 U ugh - 0 0 1 43 n! uh ni А B. 0.25 0:50 0.75 1.00 T O 0.00 0.01 0.02 0 0.0317 O O 0 6.1315 0.3574 01191 0:5139 0.9583 2. 2 2 2 0:03 0 10.2423 0.6596 1.3687