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consider laterally insulated stainless steel bar L = lm length K=16 W/M-k Therma

ID: 1414059 • Letter: C

Question

consider laterally insulated stainless steel bar L = lm length K=16 W/M-k Thermal conductivity Sigma=500 J/kgK specific heat density p=7.610^3kg/m^3 Both ends are at fixed temperature of 0degreeC the temperature delta/deltat u distribution is given by u(x,0) = -2x(1 - x) u is in celsius and x is in meter Questions which PDE should be used to describe the temperature distribution of the bar? Write the equation. what is the rate of change of the temperature delta/deltat u at the point x=0.5 m at time=0 ? what is the temperature distribution at all later times t>0?

Explanation / Answer

1)   K * (d2T/dx2) + D * (dT/dx) + c = 0

2) Rate of change of temperature = 2 * 0.5 * ( 1 - 0.5) * 500/16

                                                       = 15.625 K/sec

3) Temperature distribution

=> T (x , 0)   = x2(1 - 2x)