You and your colleagues were tasked with analyzing the thermal stresses on a sol

Question

You and your colleagues were tasked with analyzing the thermal stresses on a solid metal base. Your team collected temperature data at various locations on the base over the period of several days. You curve fit the data in Excel and found the temperature distribution to be:

T(x,y,z)=x2 ?2y2 +z2 ?xy+2yz Assume constant material properties and no internal heat generation.

a) Determine the regions where the temperature changes with time.

b) No boundary conditions are given for this problem. What are the implications relative to

knowing a specific temperature (T) at a given location (x, y, z) at any given time (t)?

Explanation / Answer

the tempreture depends only on co-ordinates of the slab and not on time.hence, T at a given point will remain constant throughout the time.

no boundarty condition are given . so if we know the tempreture at a given point at time = t, it will reamin same all the time.

( this is actual answer to your question. if there was a boundary condition was given, then the tempreture would have varied. now, it means that the tempreture depends only on co-ordinates. )

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