# Exponential Fuctions

• Dec 10th 2007, 02:54 AM
richard_c
Exponential Fuctions
Can anyone give me any hints on the following question:

Temperature of a thin slab exposed to convective heating at both sides varies with time acording to the following expression:

T(infinity) - T
T (infinity) - To = exp(-ht/rpc)

Where To and T (infinity) refer to intital and final (gas stream) temperatures respectively and 'r' is the thickness of the slab. Obtain the ignition 't' in terms of other variables using logarithmic laws. Discuss what factors t is directly and indirectly proportional to.
• Dec 10th 2007, 05:18 AM
TKHunny
This is just an algebra problem.

$ln(T_{\infty}-T)\;-\;ln(T_{\infty}-T_{0})\;=\;\frac{-ht}{rpc}$

Can you finish?
• Dec 10th 2007, 06:14 AM
richard_c
The rest?
Hi TKHunny,

so is it just a matter now of time'sing the inverses by 'rpc' to leave you with the -ht ?
Then adding the +h onto the left hand side to leave you with 't'?

Is it that simple or is there a lot more to it?
• Dec 10th 2007, 01:06 PM
TKHunny
Two things:

1) I would prefer you stick to better language. use "multiplication" and "multiply".

2) Addition? I think not. It looks like division to me.