How Is Temperature Calculated in a Heated Copper Block?

[Froskoy]

Hi,

Suppose a copper block is heated on one side so that one end is at 800K. Given the dimensions of the copper block, is there a way of calculating the temperature of a point in the block distance x from the heated end after a given time?

With many thanks,

Froskoy.

 

[Andy Resnick]

This is a standard problem exhaustively treated in, for example, Mikhailov and Ozisik's "Unified analysis and solutions of heat and mass diffusion".

 

[technician]

If it can be assumed that there are no heat losses from the sides of the block then the equation for rate of heat flow is:
ΔQ/Δt = k A Δθ/Δx Δθ/Δx is the temperature gradient

 

[Froskoy]

Thanks! Your replies were really useful.