In this paper, new analytical solutions are presented to quantify interaction of water between a sloping aquifer and stream of varying heads in presence of a thin vertical sedimentary layer. The initial hydrogeological setting consist of an unconfined sloping aquifer of semi-infinite extent, a fully penetrating stream of varying water level, and a vertical layer of streambank deposits that acts as an interface between stream and aquifer. Unsteady groundwater flow is characterized by a nonlinear Boussinesq equation subject to Robin boundary condition (also referred to as third kind and Cauchy boundary condition). Unlike existing results, which focus only on step changes in stream stage, the current study accounts for gradual rise and decline in stream level. A closed-form analytical solution for water head distribution, discharge rate, and net volumetric exchange of water between stream and aquifer are developed from the solution of a linearized advection-diffusion equation. Performance of the anal...

The development of certain aspects of hybrid special polynomials after incorporating monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research. By using the monomiality principle, new outcomes are produced, thus in line with prior facts, our aim is to introduce the degenerate 2D bivariate Appell polynomials ${\mathbb{R}}_j^m(u,v;h)$. Further, we obtain some well-known main properties and explicit forms satisfied by these polynomials. Also, generating relations corresponding to the degenerate 2D bivariate Bernoulli, Euler, and Genocchi polynomials are established, they will further be helpful in establishing the corresponding results for these polynomials.

Diethyl Ether (DEE) is a promising oxygenated renewable bio-base resource fuel used for diesel engines, owing to its high ignition quality. An experimental investigation has been carried out to evaluate the effects of DEE blends with diesel on the combustion, performance and emission characteristics of a direct injection diesel engine. The engine tests are carried out for 10%, 25%, 50%, 75% and 100% of the full load. In this study, 2%, 5%, 8%, 10%, 15%, 20% and 25% of DEE (by volume) are blended with diesel. Beyond 25% DEE blend, the viscosity and density of the blended fuel reduces as compared to the acceptable limits, that can further reduces the lubricity and create potential wear problems in sensitive fuel injection pump and fuel injector design.The laboratory fuel tests showed that DEE can be mixed in any proportion in diesel fuel. The blended fuel retains the desirable physical properties of diesel fuel but includes the cleaner burning capability of DEE.The experimental results indicated that the blends of DEE with diesel up to 25% are possible. The most favourable blend found is DE15D resulting in low smoke, low NOx, high brake thermal efficiency and low brake specific fuel consumption as compared to other blends and neat diesel. In addition, it is observed that unburned hydrocarbon increases and CO emissions reduces as compared to the neat diesel.

In this study, we develop new analytical solution to estimate the transient behavior of phreatic surface in an anisotropic unconfined aquifer which is overlying a leaky base and subjected to multiple recharge and withdrawal. The hydrologic setting consists of a rectangular unconfined leaky aquifer adjacent to two water bodies of constant water head along the opposite faces of the aquifer. The remaining two faces of the aquifer have no flow conditions. The flow of seepage is approximated using two-dimensional Boussinesq equation, and solved analytically using mixed finite Fourier transform. Application of the new solution is demonstrated using an illustrative example.