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### 5.4. NUMERICAL FINITE-DIFFERENCE METHODS FOR UNSTEADY-STATE CONDUCTION

#### 5.4A. Unsteady-State Conduction in a Slab

##### 1. Introduction

As discussed in previous sections of this chapter, the partial differential equations for unsteady-state conduction in various simple geometries can be solved analytically if the boundary conditions are constant at T = T1 with time. Also, in the solutions the initial profile of the temperature at t = 0 is uniform at T = T0. The unsteady-state charts used also have these same boundary conditions and initial condition. However, when the boundary conditions are not constant with time and/or the initial conditions are not constant with position, numerical methods must be used.

Numerical calculation methods for unsteady-state ...

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