Heat conduction in a rectangular slab

Consider the following transient heat conduction problem in a slab.[1-3] The governing equation is  

The governing equation and the boundary condition at x = 0 are converted to the Laplace domain  

The given partial differential equation is transformed to an ordinary differential equation in the Laplace domain since 

the dependent variable in the Laplace domain is solved using the dsolve command since (see chapter 3.1.6)  

4 Partial Differential Equations in Semi-infinite Domains 

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The thermal diffusivity can also be measured directly by employing transient heat conduction. The basic differential equation (Fourier heat conduction equation) governing heat conduction in isotropic bodies is used in this method. A rectangular copper box filled with grain is placed in an ice bath (0°C), and the temperature at its center is recorded [44]. The solution of the Fourier equation for the temperature at the center of a slab is used ... 

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