Time-dependent Reaction Research Articles

An experimental and numerical investigation into the influence of wind effects on wind turbines with tubular towers

This study delves into investigating the profound impact of wind loads on the structural integrity of wind turbines. To comprehensively assess the influence of wind loads, a two-pronged approach was adopted: first, a meticulously crafted 1/100 scale model was employed within a wind tunnel, and second, advanced numerical simulations based on computational fluid dynamics (CFD) were conducted. Moreover, the study takes into account the intricate factor of turbine proximity in the wind tunnel setup. The design of the tower structure takes into consideration an array of loads, including lateral and gravitational forces. Notably, a substantial load arises from the rotational force generated by blade motion, which exerts its effects on the structure. Calculations of this force were executed using ABAQUS software. This multifaceted analysis involves the application of angular velocity to the blades, subsequently enabling the computation of time-dependent support reactions via dynamic numerical analysis employing the Newmark method. Furthermore, the study encompasses the determination of static equivalent forces. It is noteworthy that the maximum displacement experienced by the structure coincides with the initial phase of blade movement.

Kinematic–kinetic compliant acetabular cup positioning based on preoperative motion tracking and musculoskeletal modeling for total hip arthroplasty

The invention of the surgical robot enabled accurate component implantation during total hip arthroplasty (THA). However, a preoperative surgical planning methodology is still lacking to determine the acetabular cup alignment considering the patient-specific hip functions during daily activities such as walking. To simultaneously avoid implant edgeloading and impingement, this study established a kinematic–kinetic compliant (KKC) acetabular cup positioning method based on preoperative gait kinematics measurement and musculoskeletal modeling. Computed tomography images around the hip joint and their biomechanical data during gait, including motion tracking and foot–ground reaction forces, were collected. Using the reconstructed pelvic and femur geometries, the patient-specific hip muscle insertions were located in the lower limb musculoskeletal model via point cloud registration. The designed cup orientation has to be within the patient-specific safe zone to prevent implant impingement, and the optimized value selected based on the time-dependent hip joint reaction force to minimize the risk of edgeloading. As a validation of the proposed musculoskeletal model, the predicted lower limb muscle activations for seven patients were correlated with their surface electromyographic measurements, and the computed hip contact force was also in quantitative agreement with data from the literature. However, the designed cup orientations were not always within the well-known Lewinnek safe zone, highlighting the importance of KKC surgical planning based on patient-specific biomechanical evaluations.

Mid-Infrared Dispersion Spectroscopy as a Tool for Monitoring Time-Resolved Chemical Reactions on the Examples of Enzyme Kinetics and Mutarotation of Sugars.

Ongoing technological advancements in the field of mid-infrared (MIR) spectroscopy continuously yield novel sensing modalities, offering capabilities beyond traditional techniques like Fourier transform infrared spectroscopy (FT-IR). One such advancement is MIR dispersion spectroscopy, utilizing a tunable quantum cascade laser and Mach-Zehnder interferometer for liquid-phase analysis. Our study assesses the performance of a custom MIR dispersion spectrometer at its current development stage, benchmarks its performance against FT-IR, and validates its potential for time-resolved chemical reaction monitoring. Unlike conventional methods of IR spectroscopy measuring molecular absorptions using intensity attenuation, our method detects refractive index changes (phase shifts) down to a level of 6.1 × 10-7 refractive index units (RIU). This results in 1.5 times better sensitivity with a sevenfold increase in analytical path length, yielding heightened robustness for the analysis of liquids compared to FT-IR. As a case study, we monitor the catalytic activity of invertase with sucrose, observing the formation of resultant monosaccharides and their progression toward thermodynamic equilibrium. Anomalous refractive index spectra of reaction mixtures, with substrate concentrations ranging from 2.5 to 25 g/L, are recorded, and analyzed at various temperatures, yielding Michaelis-Menten kinetics findings comparable to the literature. Additionally, the first-time application of two-dimensional correlation spectroscopy on the recorded dynamic dispersion spectra correctly identifies the mutarotation of reaction products (glucose and fructose). The results demonstrate high precision and sensitivity in investigating complex time-dependent chemical reactions via broadband refractive index changes.

Salt freezing-thawing damage evolution model based on the time-dependent hydration reaction incorporating rice husk ash and recycled coarse aggregate

Rice husk ash (RHA), an abundant agricultural by-product, has led to significant environmental pollution due to current treatment methods. To achieve resource utilization, the feasibility of RHA recycled concrete subjected to the salt freezing-thawing resistance was assessed, including the macroscopic properties, microstructure and sustainability, and an evolutionary model of salt freeze-thaw damage was established based on the time-dependent hydration reaction of the cement paste. The results indicate that RHA particles effectively retard damage by limiting chloride ion diffusion and preventing salt crystallization, while deteriorating the concrete performance due to reduced hydration products at high RHA replacement ratios. The established salt freeze-thaw damage evolution model has an R2 as high as 0.9817, which indicates that the model fits with high accuracy and can capture the performance variations of different types of RHA recycled concrete under extreme environmental conditions. Additionally, the synergistic preparation of concrete using RHA with a 20 % replacement ratio and recycled coarse aggregate (RCA) with a 50 % replacement ratio reduces the total global warming potential (GWP) by 16.65 %, which means that it has the potential to advance low-carbon sustainable development in the construction industry while meeting the engineering requirements. This research is expected to provide a theoretical reference for applying and promoting biobased low-carbon concrete with RHA in saline-alkali cold areas.

Time-Dependent Multi-Particle Model Describing the Hydrogen Absorption of Nanocrystalline Magnesium Powders: A Case Study

Classical kinetic models describing the hydrogen absorption of nanocrystalline metallic hydrides generally do not involve any parameter related to the change in the crystallite size during the hydrogenation at constant temperature. In the present investigation, ball-milled nanocrystalline Mg powders exhibiting lognormal crystallite size distribution have been subjected to hydrogen absorption in a Sievert-type apparatus. Partially absorbed states were achieved by interrupting the hydrogenation cycle at different hydrogen content, i.e., when 15%, 50%, and 90% of Mg powder transformed to MgH2. The evolution of the characteristic size of the nucleating MgH2 phase was determined from X-ray diffraction analysis. Considering the crystallite size distribution of the as-milled powder agglomerate as well as the growth during the isothermal hydrogenation process, a time-dependent multi-particle reaction function ∝CV¯t;R(t) was developed. It was shown unambiguously for this case study that the measured hydrogen absorption curve of the ball-milled Mg powder shows the best correlation with this model when it is compared to classical kinetic functions or the previously developed multi-particle reaction function excluding the change in the average crystallite size during hydrogenation.

Formation of the oxyl's potential energy surface by the spectral kinetics of a vibrational mode.

One of the most reactive intermediates for oxidative reactions is the oxyl radical, an electron-deficient oxygen atom. The discovery of a new vibration upon photoexcitation of the oxygen evolution catalysis detected the oxyl radical at the SrTiO3 surface. The vibration was assigned to a motion of the sub-surface oxygen underneath the titanium oxyl (Ti-O●-) created upon hole transfer to (or electron extraction from) a hydroxylated surface site. Evidence for such an interfacial mode is derived from its spectral shape, which exhibited a Fano resonance-a coupling of a sharp normal mode to continuum excitations. Here, this Fano resonance is utilized to derive precise formation kinetics of the oxyl radical and its associated potential energy surface (PES). From the Fano lineshape, the formation kinetics are obtained from the anti-resonance (the kinetics of the coupling factor), the resonance (the kinetics of the coupled continuum excitations), and the frequency integrated spectrum (the kinetics of the normal mode's cross-section). All three perspectives yield logistic function growth with a half-rise of 2.3 ± 0.3ps and a time constant of 0.48 ± 0.09ps. A non-equilibrium transient associated with photoexcitation is separated from the rise of the equilibrated PES. The logistic function characterizes the oxyl coverage at the very initial stages (t ∼ 0) to have an exponential growth rate that quickly decreases toward zero as a limiting coverage is reached. Such time-dependent reaction kinetics identify a dynamic activation barrier associated with the formation of a PES and quantify it for oxyl radical coverage.

Simulation of the cancer cell growth and their invasion into healthy tissues using local radial basis function method

Applying mathematical models to simulate dynamic biological processes has been a common practice for a long time. In recent decades, cancer research has also adopted this approach to understand how cancer cell populations grow and spread. This study focuses on a mathematical model that uses a system of PDEs to explain the time-dependent reaction–diffusion interaction among cancer cells, extracellular matrix, and matrix degradation enzymes. We use a computational method that involves the discrete Galerkin technique by employing local radial basis functions (LRBFs) as its basis to approximate the behavior of cancer cells as they grow and invade neighboring healthy tissues. This novel approach employs a smaller set of nodes to approximate the solution, instead of considering all data in the given domain of the cancer growth model. Utilizing locally supported radial basis functions, this method significantly reduces the computational volume required, in contrast to globally supported radial basis functions. Finally, we provide experimental examples to validate and illustrate the effectiveness of this new scheme in modeling the growth and behavior of cancer cells at different stages.

Dual role of arsenite in hydrolysis and post-hydrolysis fluorescence sensing of selective pH-dependent probes.

In comparison to the sensing activity, the reactivity of arsenite (AsO2-) is less explored. Herein, we focused on AsO2- reactivity studies based on its pKa and compared the study with other common anions. All three pKa values of arsenite are >9.0, affording a flexible working pH range to design a probe for reactivity studies. We designed and synthesized six pH dependent benzothiazole-based Schiff bases, namely, 1-(((6-nitrobenzo[d]thiazol-2-yl)imino)methyl)naphthalen-2-ol (1), 5-(diethylamino)-2-(((6-nitrobenzo[d]thiazol-2-yl)imino)methyl)phenol (2), 9-(((6-nitrobenzo[d]thiazol-2-yl)imino)methyl)-2,3,6,7-tetrahydro-1H,5H-pyrido[3,2,1-ij]quinolin-8-ol (3), 5-methoxy-2-(((6-nitrobenzo[d]thiazol-2-yl)imino)methyl)phenol (4), 4-(((6-nitrobenzo[d]thiazol-2-yl)imino)methyl)benzene-1,3-diol (5), and 2-(((6-nitrobenzo[d]thiazol-2-yl)imino)methyl)phenol (6), as probes for hydrolysis studies containing 5% water in acetonitrile. In spite of the presence of water in the solution, no hydrolysis was observed for all the probes in the absence of a salt. In the presence of selected sodium salts of various anions in solution, intramolecular charge transfer (ICT) was observed after the deprotonation of an aromatic hydroxy group at the ortho position with respect to the imine groups within the probes. Among the studied anions, selective AsO2- induced imine hydrolysis was observed for probes 1 and 4. In the case of 5 with both o- and p-hydroxy groups, no hydrolysis was observed in the presence of AsO2-. Probe 6 with only the o-hydroxy group showed very fast hydrolysis with poor selectivity. The p-hydroxy group in 4-(((6-nitrobenzo[d]thiazol-2-yl)imino)methyl)phenol (7) resulted in poor AsO2- induced hydrolysis. The aldehyde, which was generated after hydrolysis of probe 1, showed selective emission at 450 nm in the presence of AsO2-. The time dependent hydrolysis reaction of probe 1 controls the emission intensity enhancement.

A kinetic non-steady state analysis of immobilized enzyme systems with external mass transfer resistance

<abstract><p>The goal of this paper is to utilize the homotopy perturbation method (HPM) and Laplace transform to provide an approximate analytical expression to the non-linear time-dependent reaction diffusion equation arising in a mathematical model of an immobilized enzyme system with external mass transfer resistance. This mathematical model is a non-steady, non-linear reaction diffusion equation based on Michaelis–Menten kinetics. Approximate analytical expressions are also provided for various geometries of the enzyme catalytic pellets, namely, planar, cylindrical, and spherical. Obtained semi-analytical expressions are proven to fit for all the parameters appearing in the system and for all the geometries of enzyme catalytic pellets. When comparing the numerical and approximate analytical solutions, satisfactory results are obtained. Also, approximate analytical expressions of the effectiveness factor (EF) of the immobilized system are presented, and the effect of parameters on the EF is also analyzed.</p></abstract>

Methylglyoxal-induced modification of myoglobin: An insight into glycation mediated protein aggregation.

Post-translational modification of proteins by Maillard reaction, known as glycation, is thought to be the root cause of different complications, particularly in diabetes mellitus and age-related disorders. Methylglyoxal (MG), a reactive α-oxoaldehyde, increases in diabetic condition and reacts with the proteins to form advanced glycation end products (AGEs) following a Maillard-like reaction. In a time-dependent reaction study of MG with the heme protein myoglobin (Mb), MG was found to induce significant structural alterations of the heme protein, such as heme loss, changes in tryptophan fluorescence, and decrease of α-helicity with increased β-sheet content. These changes were found to occur gradually with increasing period of incubation. Incubation of Mb with MG induced the formation of several AGE adducts, including, carboxyethyllysine at Lys-16, carboxymethyllysine at Lys-87, carboxyethyllysine or pyrraline-carboxymethyllysine at Lys-133, carboxyethyllysine at Lys-42 and hydroimidazolone or argpyrimidine at Arg-31 and Arg-139. MG induced amyloid-like aggregation of Mb was detected at a longer period of incubation. MG-derived AGEs, therefore, appear to have an important role as the precursors of protein aggregation, which, in turn, may be associated with pathophysiological complications.

Heat and Mass Transfer Analysis of an unsteady Non-Newtonian Magnetohydrodynamic Fluid Flow (Semi-Analytical Solution)

In the presence of a time-dependent chemical reaction, this work investigates unsteady squeezing Casson nanofluid flow and heat transfer between two parallel plates under the influence of a uniform magnetic field. Considering the effects of viscosity dissipation, heat generation from friction resulting from flow shear, Brownian motion, Joule heating, and thermodiffusion. The problem's nonlinear differential equations are solved using the Runge–Kutta (RK-4) technique and the Homotopy Perturbation technique. The excellent accuracy of the results is evident since they have been compared with other results from earlier research. In the form of graphs and tables, flow behavior under the many physical factors that are modified is also covered and well described. This work has shown that, by normalizing flow behavior, magnetic fields may be utilized to manage a variety of flows. Additionally, it is demonstrated that in every situation, the effects of positive and negative squeeze numbers on heat and mass transfer flow are opposite. Moreover, the thermophoresis parameter decreases as the concentration field increases. However, when the Brownian motion parameter is increased, the concentration profile gets better. Additionally, several other significant factors were examined. The results of this study can facilitate quicker and easier research and assist engineers.

Diversity in Proprotein Convertase Reactivity among Human Papillomavirus Types.

The cleavage of viral surface proteins by furin is associated with some viruses' high virulence and infectivity. The human papillomavirus (HPV) requires the proteolytic processing of its capsid proteins for activation before entry. Variability in reactivity with furin and other proprotein convertases (PCs) among HPV types was investigated. HPV16, the most prevalent and carcinogenic HPV type, reacted with PCs with the broadest selectivity compared to other types in reactions of pseudoviral particles with the recombinant PCs, furin, PC4, PC5, PACE4, and PC7. Proteolytic preactivation was assessed using a well-established entry assay into PC-inhibited cells based on the green fluorescent protein as a reporter. The inhibition of the target cell PC activity with serpin-based PC-selective inhibitors also showed a diversity of PC selectivity among HPV types. HPV16 reacted with furin at the highest rate compared to the other types in time-dependent preactivation reactions and produced the highest entry values standardized to pseudoviral particle concentration. The predominant expression of furin in keratinocytes and the high reactivity of HPV16 with this enzyme highlight the importance of selectively targeting furin as a potential antiviral therapeutic approach.

Laplace transform-homotopy perturbation method for fractional time diffusive predator–prey models in ecology

In this paper, we consider some reaction–diffusion systems arising from two-component predator–prey models with various kinetics ranging from prey-dependent, ratio-dependent functional responses and subdiffusion. The goal of the present work is to simulate the time-dependent predator–prey model of Lotka–Volterra. Analytical solutions of this model are performed using the Laplace transform-homotopy perturbation method. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that the proposed technique solves nonlinear problems without using Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method. We show all the possible equilibria and examine their stability in line with the ecological parameters. Numerical simulations of the diffusive predator–prey model in one-, two- and three-dimensions are given to compare and demonstrate the asymptotic behaviour of the time-dependent reaction–diffusion systems. The results show that proposed technique is a powerful tool to solve systems of nonlinear ordinary and partial differential equations of predator–prey models in ecology.

Electrochemical In Situ Hydrogen Peroxide Production Can Reduce Microbial Load in Bioponic Nutrient Solutions Derived from Organic Waste

Technological advancement in recent decades has allowed for crop cultivation in soilless controlled environments, known as hydroponics, and this is being employed in an increasing number of factories worldwide. With continued local and regional disruptions in the supply chain to provide mineral fertilizers, new pathways to generate nutrient solutions are being developed. One potential approach is the recovery of nutrients from organic waste and wastewater using bioponics. Bioponics refers to the biological mineralization of organic residues through processes such as anaerobic and aerobic digestion and the use of such organically produced nutrient solutions in hydroponic systems. However, without disinfection of the nutrient solution, the high microbial loads increase the risk of pathogens affecting plant and consumer health. In this work, electrochemical hydrogen peroxide (H2O2) demonstrated success in reducing microbial loads. Different scenarios of application were considered: (1) variation in the H2O2 concentration in the nutrient solution by dosing H2O2 from ex situ electrochemical production, (2) variation in the dosing time-dependent reaction between the nutrient solution and H2O2 produced ex situ, and (3) the in situ production of H2O2 of the organic nutrient solution. The highest tested H2O2 concentration of 200 mg L−1 showed a microbial load reduction of bacteria at 93.3% and of fungi at 81.2%. However, the in situ production showed the highest reduction rate for bacteria and fungi in bioponic nutrient solutions, where longer reaction times also impact microbial concentrations in situ. Final microbial reductions of 97.8% for bacteria and of 99.1% for fungi were determined after a H2O2 production time of 60 min. Overall, our results show that electrochemical H2O2 production can be used to disinfect bioponic nutrient solutions, and the production cell can be implemented in bioponic systems in situ.

Prolonged Door-to-Balloon Time Leads to Endothelial Glycocalyx Damage and Endothelial Dysfunction in Patients with ST-Elevation Myocardial Infarction.

Damage to the endothelial glycocalyx (eGC) has been reported during acute ischemic events like ST-elevation myocardial infarction (STEMI). In STEMI, a door-to-balloon time (D2B) of <60 min was shown to reduce mortality and nonfatal complications. Here, we hypothesize that eGC condition is associated with D2B duration and endothelial function during STEMI. One hundred and twenty-six individuals were analyzed in this study (STEMI patients vs. age-/sex-matched healthy volunteers). After stimulating endothelial cells with patient/control sera, the eGC's nanomechanical properties (i.e., height/stiffness) were analyzed using the atomic force microscopy-based nanoindentation technique. eGC components were determined via ELISA, and measurements of nitric oxide levels (NO) were based on chemiluminescence. eGC height/stiffness (both p < 0.001), as well as NO concentration (p < 0.001), were reduced during STEMI. Notably, the D2B had a strong impact on the endothelial condition: a D2B > 60 min led to significantly higher serum concentrations of eGC components (syndecan-1: p < 0.001/heparan sulfate: p < 0.001/hyaluronic acid: p < 0.0001). A D2B > 60 min led to the pronounced loss of eGC height/stiffness (both, p < 0.001) with reduced NO concentrations (p < 0.01), activated the complement system (p < 0.001), and prolonged the hospital stay (p < 0.01). An increased D2B led to severe eGC shedding, with endothelial dysfunction in a temporal context. eGC components and pro-inflammatory mediators correlated with a prolonged D2B, indicating a time-dependent immune reaction during STEMI, with a decreased NO concentration. Thus, D2B is a crucial factor for eGC damage during STEMI. Clinical evaluation of the eGC condition might serve as an important predictor for the endothelial function of STEMI patients in the future.

Experimental study on characterization of lime-based mineral carbonation reaction and CO2 sequestration.

This paper reports for the first time the use and application of a novel technique in the characterization of mineral carbonation reaction and CO2 sequestration in soil stabilization using flow meters. Soils based on SiO2 with two different sizes were tested. Lime (Ca(OH)2) was used as the reactant. Instant CO2 flow rate (L/min), total CO2 volume (L), temperature (°C), and absolute pressure (kPa) were monitored and recorded for 1h by flow meters connected to the mold inlet and outlet. It was determined that the mineral carbonation reaction started in the first seconds and ended before the 5th minute. The mineral carbonation is a short-term and potential reaction, and it is not a time-dependent reaction. It is separated from other carbonation reactions with these characteristics. The highest CO2 captured value was obtained in the soil mixed with 5% lime, where fines were not used. The second highest CO2 captured value was obtained in soil mixed with 1% lime, where fines were not used. CO2 captured with 1% lime is more than CO2 captured with 5% lime in the soil containing fines. Accordingly, 1-5% lime can be used in soil carbonation studies. According to the soil properties, the highest CO2 captured and the CO2 efficiency was achieved with the use of 6-7% water by weight.

Boron nitride nanosheets as precursors for 3D nano-configurations in titanium matrix composites: Interfacial evolution and mechanical behavior

Boron nitride nanosheets (BNNSs) have tremendous potential as reinforcements for titanium (Ti) due to their excellent strengthening and toughening efficiency from in-situ generated 3D nano-configurations. However, the effect of interfacial evolution on the mechanical properties of the BNNSs/Ti composite remains unexplored. To this end, in this study, the interfacial structure was regulated utilizing the time-dependent reaction of BNNSs/Ti system. Its effects on mechanical behavior were studied by combining experiments and molecular dynamic simulations. BNNSs were gradually converted to 3D nano-configurations over time and finally consumed to form coarsened TiB whiskers in the TC4 matrix. The composite with 3D nano-configurations exhibited a tensile strength of 1140.5 MPa and excellent toughness of 42.9 MJ/m3. Strength improvement stems primarily from nano-interlocking, which increases dislocation density under load and improves the interfacial shear strength. The considerable toughness results from the enhanced crack resistance brought by the 3D nano-configurations.

Solving forward and inverse problems involving a nonlinear three-dimensional partial differential equation via asymptotic expansions

Abstract This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction–diffusion–advection equation. By using an asymptotic expansion with the local coordinates in the transition-layer region, we prove the existence and uniqueness of a smooth solution with a sharp transition layer for a 3D partial differential equation. Moreover, with the help of asymptotic expansion, a simplified model is derived for the corresponding inverse source problem, which is close to the original inverse problem over the entire region except for a narrow transition layer. We show that such simplification does not reduce the accuracy of the inversion results when the measurement data contain noise. Based on this simpler inversion model, an asymptotic-expansion regularization algorithm is proposed for efficiently solving the inverse source problem in the 3D case. A model problem shows the feasibility of the proposed numerical approach.

Epitaxial growth of NixCo3-xS4 nanoflakes from co-based Prussian blue analog for high-performance pseudocapacitors

In this work, a NixCo3-xS4/PBA (Prussian blue analogue) heterostructure is obtained via a facile epitaxial growth method, forming a flower-like structure with NixCo3-xS4 nanoflakes standing independently on PBA. The 2D NixCo3-xS4 nanoflakes can provide sufficient reaction sites for charge storage, while the PBA core can facilitate quick ion transportation during charge/discharge process. Moreover, it has been shown that the growth of NixCo3-xS4 nanoflakes from PBA is a time-dependent reaction that could regulate the electronic state density of Co, Ni and S along the interface of NixCo3-xS4 and PBA. EELS and DFT calculations reveal that the formation of heterogeneous interface between NixCo3-xS4 nanoflakes and PBA results in an electron deficient region of NixCo3-xS4, which benefits the adsorption and reaction of OH– on NixCo3-xS4. With the structural and compositional merits, the NixCo3-xS4/PBA obtained with reacting for 7 h exhibits the superior specific capacitance and good rate capability with retaining 91.5 % of initial capacitance as well as quick charge response. The assembled NixCo3-xS4/PBA//AC asymmetric supercapacitor exhibit an energy density of 52.2 Wh kg−1, which could light 14 LED lamps with maintaining the brightness for 5 min. Therefore, the design of 3D NixCo3-xS4/PBA and the systematical investigation on the structural evolution as well as the concomitant electron configuration regulation may not only inspire the design of high-performance electrode materials for supercapacitors, but also be valuable for understanding the charge storage mechanism on heterostructures.

A numerical investigation of unsteady space–time dependent coefficients anisotropic-diffusion convection reaction equation

Two dimensional transient problems for anisotropic FGMs governed by a diffusion convection reaction (DCR) equation of time–space dependent coefficients are considered. Using a transformation, the space–time dependent coefficients equation is reduced to a time dependent coefficients equation. Then taking a Laplace transform will result in a constant coefficients equation which can be written in forms of boundary-only integral equations and solved using a standard BEM for the solutions. These BEM solutions are then numerically inverse transformed to get the solutions in the time variable. Some problems of trigonometrically, exponentially and quadratically graded materials with compressible or incompressible flow are solved. The numerical solutions obtained are quite accurate.