  Multilayer diffusion problems have found significant important that they
arise in many medical, environmental and industrial applications of heat and
mass transfer. In this article, we study the solvability of one-dimensional
nonhomogeneous multilayer diffusion problem. We use a new generalized integral
transform, namely, $ \bb M_{\rho,m} -$transform [Srivastava et al.,
https://doi.org/10.1016/S0252-9602(15)30061-8]. First, we reduce the
nonhomogeneous multilayer diffusion problem into a sequence of one-layer
diffusion problems including time-varying given functions, followed by solving
a general nonhomogeneous one-layer diffusion problem via the $ \bb M_{\rho,m}
-$transform. Hence, by means of general interface conditions, a renewal
equations' system is determined. Finally, the $ \bb M_{\rho,m} -$transform and
its analytic inverse are used to obtain an explicit solution to the renewal
equations' system. Our results generalize those ones in [Rodrigo and Worthy,
http://dx.doi.org/10.1016/ j.jmaa.2016.06.042].
