Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine

The aim of this research is to study the effect of high concentrations of salts, pressure and temperature on the performance of the RO membrane with time. Four different (Na2CO3) concentrations (5000, 15000, 25000 and 35000) ppm and various pressures such as (1, 3 and 5) bars at different temperatures of the feed solution (i.e., 25, 35 and 45) ◦C were used in this work. It was found that, as the concentration of salt and feed temperatures increase, the rejection of the salt decrease. While the salt rejection of the membranes increases with increase of transmembrane pressure.

Nanofluids, liquid suspensions of nanoparticles (Np), are an effective agent to alter the wettability of oil-wet reservoirs to water-wet thus promoting hydrocarbon recovery. It can also have an application to more efficient carbon storage. We present a series of contact angle (θ) investigations on initially oil-wet calcite surfaces to quantify the performance of hydrophilic silica nanoparticles for wettability alteration. These tests are conducted at typical in-situ high pressure (CO2), temperature and salinity conditions. A high pressure–temperature (P/T) optical cell with a regulated tilted surface was used to measure the advancing and receding contact angles at the desired conditions. The results showed that silica nanofluids can alte

The optimum conditions for the production of neutral protease from local strain Aspergillus niger var carbonarius by solid – state fermentation system (Wheat bran) moisted with 0.2 M phosphate buffer (PH7.0) . the hydration ratio was 1:5 (V:W) . the concentration of inoculum was 1×106 spores per 10 gram of solid materials , initial P H 6.5 and 96 hours of incubation period at 30? C .the enzyme activity was 1300 unit / ml and specific activity was 1550 unit / mg protein .

The steady state performance of the counter rotating floating ring Journal bearing is analyzed with isothermal finite bearing theory. The effect of different parameters affecting the performance of the bearing (namely speed ratio, clearance ratio and radii ratio), have been investigated. The load carrying capacity of the bearing increasing with decreasing the radii ratio (R₂/R₁) of the ring and clearance ratio (c₁/c₂), in the other hand, the coefficient of friction increases with increasing the clearance and radii ratios, while decreases with incre4asing the bearing to journal speed ratio (γ). It is shown during this work that different operating conditions are greatly enhanced the performance

Design of experiments (DOE) was made by Minitab software for the study of three factors used in the precipitation process of the Sodium Aluminate solution prepared from digestion of α-Al₂O₃  to determine the optimum conditions to a produce Boehmite which is used in production of ɤ-Al₂O₃ during drying and calcination processes, the factors are; the temperature of the sodium aluminate solution, concentration of HCl acid added for the precipitation and the pH of the solution at which the precipitation was ended. The design of the experiments leads to 18 experiments.

   The results show that the optimum conditions for the precipitation of the sodium aluminate solution which

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s