- #1

- 9

- 0

Differential equation

\begin{align}

\frac{{\partial}^2 T (x,t)}{\partial x^2} = \frac{1}{\alpha}\frac{\partial T(x,t)}{\partial t},

\end{align}

boundary conditions

\begin{equation}

\begin{aligned}

T(x, 0) = T_\infty \\

-k\frac{\partial T(0,t)}{\partial x}= h(T_{max} - T(0,t)) \\

-k\frac{\partial T(l,t)}{\partial x}= h(T(l,t) - T_\infty).

\end{aligned}

\end{equation}

It is 1D transient heat diffusion problem. x[0,L] represents a 1D spatial domain and t[0,tao] represents a time domain. T(x,t) is temperature distribution over the spatial and temporal domain. \alpha = k/(cp*rho), where k is thermal conductivity, cp heat capacity and \rho thermal conductivity.

\begin{align}

\frac{{\partial}^2 T (x,t)}{\partial x^2} = \frac{1}{\alpha}\frac{\partial T(x,t)}{\partial t},

\end{align}

boundary conditions

\begin{equation}

\begin{aligned}

T(x, 0) = T_\infty \\

-k\frac{\partial T(0,t)}{\partial x}= h(T_{max} - T(0,t)) \\

-k\frac{\partial T(l,t)}{\partial x}= h(T(l,t) - T_\infty).

\end{aligned}

\end{equation}

It is 1D transient heat diffusion problem. x[0,L] represents a 1D spatial domain and t[0,tao] represents a time domain. T(x,t) is temperature distribution over the spatial and temporal domain. \alpha = k/(cp*rho), where k is thermal conductivity, cp heat capacity and \rho thermal conductivity.

Last edited by a moderator: