Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier “tick,” studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease’s incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution’s qualitative attributes is included. According to the established basic reproductio

Density data of alum chrom in water and in aqueous solution of poly (ethylene glycol) (1500) at different temperatures (288.15, 293.15, 298.15) k have been used to estimate the apparent molar volume (Vθ), limiting apparent molar volume (Vθ˚) experimental slope (Sv) and the second derivative of limiting partial molar volume [δ2 θ v° /δ T2] p .The viscosity data have been analyzed by means of Jones –Dole equation to obtain coefficient A, and Jones –Dole coefficient B, Free activation energy of activation per mole of solvent, Δμ10* solute, Δμ20* the activation enthalpy ΔH*,and entropy, ΔS*of activation of viscous flow. These results have been discussed in terms of solute –solvent interaction and making/breaking ability of so

Chromium tanned leather wastes (CTLW) and vegetable tanned leather wastes (VTLW) were used as adsorbent materials to remove the Biebrich scarlet dye (BS), as an anionic dye from wastewater, using an adsorption method. The effects of various factors, such as weight of leather waste, time of shaking, and the starting concentration of Biebrich scarlet dye, temperature and pH were studied. It described the adsorption process using Langmuir and Freundlich isotherm models. The obtained results agreed well with the Langmuir model, and the maximum adsorption capacities of CTLW and VTLW were 73.5294 and 78.1250 mg.g⁻¹, respectively, suggesting a monolayer adsorption process. The adsorption kinetic was found to follow a pseudo-second-order kinetic