# [SOLVED]Why is alpha mentioned?

#### dwsmith

##### Well-known member
Why is $\alpha$ mentioned? I don't see an $\alpha$.

With proper non-dimensionalization and assuming for convenience that the ratio of convection and conduction parameters $h/k = 1$, the cooling process is described by the following equations:
\begin{alignat*}{4}
T_t & = & T_{xx} & \\
T_x(0,t) & = & 0 & \\
T_x + T & = & 0 & \quad \text{at} \ x = 1\\
T(x,0) & = & f(x) &
\end{alignat*}
Here, $x$ and $t$ are dimensionless positions and times wherein the original interval has been mapped from $[0,L]$ to $[0,1]$ and a time-scale based on the diffusivity $\alpha$ has been used; also, the temperature definition is such that the ambient temperature has a reference value of zero.

#### Sudharaka

##### Well-known member
MHB Math Helper
Why is $\alpha$ mentioned? I don't see an $\alpha$.

With proper non-dimensionalization and assuming for convenience that the ratio of convection and conduction parameters $h/k = 1$, the cooling process is described by the following equations:
\begin{alignat*}{4}
T_t & = & T_{xx} & \\
T_x(0,t) & = & 0 & \\
T_x + T & = & 0 & \quad \text{at} \ x = 1\\
T(x,0) & = & f(x) &
\end{alignat*}
Here, $x$ and $t$ are dimensionless positions and times wherein the original interval has been mapped from $[0,L]$ to $[0,1]$ and a time-scale based on the diffusivity $\alpha$ has been used; also, the temperature definition is such that the ambient temperature has a reference value of zero.
Hi dwsmith, Well, the conduction timescale is based on diffusivity $$(\alpha)$$. That is,

$t_{0}^{c}=\frac{L^2}{\alpha}$

where $$t_{0}^{c}$$ is the initial time. This is what is meant by "......time-scale based on the diffusivity $\alpha$ has been used......"

Reference: Analytical Heat Transfer by Mihir Sen (Page 6)

Kind Regards,
Sudharaka.

#### dwsmith

##### Well-known member
Hi dwsmith, Well, the conduction timescale is based on diffusivity $$(\alpha)$$. That is,

$t_{0}^{c}=\frac{L^2}{\alpha}$

where $$t_{0}^{c}$$ is the initial time. This is what is meant by "......time-scale based on the diffusivity $\alpha$ has been used......"

Reference: Analytical Heat Transfer by Mihir Sen (Page 6)

Kind Regards,
Sudharaka.
So I can just solve this problem without having to worry about it then, correct?

#### Sudharaka

##### Well-known member
MHB Math Helper
So I can just solve this problem without having to worry about it then, correct?
Yes, solving the partial differential equation doesn't involve $$\alpha$$ since it's related to the scale used for measuring time.