Some analytical solutions of one-dimensional advection-diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green's function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant's mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.

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Monolayer MoS 2 and few-layer MoS 2 have been widely studied fundamentally, and for application purposes, however, less investigated bilayer or trilayer MoS 2 may demonstrate properties at the interface of monolayer and fewlayer MoS 2 . Here, we study the physical properties of bilayer MoS 2 with a triangular shape, prepared over a SiO 2 /Si substrate via a chemical vapor deposition method. We analyze the thermal sensitive quantum confinement behavior of bilayer MoS 2 by a temperature-dependent photoluminescence study to understand its semiconducting nature. We also examine the phonon confinement behavior and its thermal response for bilayer MoS 2 , which can play a key role in the performance and thermal management of MoS 2based optoelectronic devices. The optothermal Raman technique has been used to measure the thermal behavior of the prepared MoS 2 over the SiO 2 /Si substrate. We obtain interfacial thermal conductance and thermal conductivity at room temperature for supported bilayer MoS 2 to be around 1.264 ± 0.128 MW m −2 K −1 and 42 ± 8 W m −1 K −1 , respectively, suggesting its suitability for thermal management in optoelectronic devices.