Spectral Quasi-linearization Method Research Articles

Numerical Analysis of Magnetohydrodynamic and Dissipated Hybrid Casson Nanofluid Flow Over an Unsteady Stretchable Rotating Disk with Cattaneo-Christov Heat Flux Model

The study scrutinized MHD and dissipated (SWCNTs-Fe3O4)/C2H6O2 hybrid Casson nanofluids flow over an unsteady stretchable rotating disk with a Cattaneo-Christov heat flux model. By means of proper similarity conversion, the boundary layer flow governing PDEs was changed into systems of dimensionless coupled nonlinear ordinary differential equations. Subsequently, the consequent nonlinear momentum and energy equations with their boundary conditions were worked out numerically employing the spectral quasilinearization method (SQLM). The convergence, stability, and accuracy of the SQLM were established as a computationally efficient method to solve a coupled system of boundary layer problems. It is specified that 5% of SWCNTs, 20% of Fe3O4, and 75% of C2H6O2 being taken for the preparation of (SWCNTs−Fe3O4)/C2H6O2 hybrid nanofluid with shape factor n1 = n2 = 3, and the values of the parameters used are fixed to M = 5, S = 0.5, β = 5, κ = 0.5, Ec = 2, Λ = 2, Pr = 7.3, α = 0.5, δ = 0. The effects of more perceptible parameters on velocity and thermal flow fields were considered and scrutinized carefully via graphs and tables. The results disclose that the momentum and thermal boundary layer thickness markedly declined with more value of the unsteady parameter. The local heat transfer rate improves nearly by 14% as 0.2 volume of Fe3O4 nanoparticles dispersed in 0.05 volume of SWCNTs and 0.75 volume of C2H6O2 nanofluid, hence, in realistic uses adding more values of nanoparticles in the hybrid nanofluids is useful to progress the heating process. The study is novel since to the best of the author’s knowledge, no paper has been published so far on the unsteady flow of (SWNT-Fe3O4)-Ethylene glycol hybrid Casson nanofluid with the effects of the Cattaneo-Christov heat flux model. As well, the model used for the thermophysical properties of the hybrid nanofluid is a new approach. Generally, hybrid nanofluids of (SWCNTs-Fe3O4)/C2H6O2 show better flow distributions with good stability of thermal properties than their mono counterparts.

Spectral simulation of hydromagnetic flow with dissipative and radiative heat transfer over an inclined rotating disk within a non‐Darcy porous medium

AbstractThe goal of the research presented in this paper is to examine how a magnetic field affects the unsteady flow of an incompressible nanofluid over a spinning disc that is inclined and stretched while the flow is embedded in a non‐Darcy porous medium. Furthermore, the heat transmission mechanism takes into account Joule heating and viscous dissipation. By imposing thermal radiation to enhance the heat transmission system under the effects of convection, the current article becomes more realistic. A set of nonlinear partial differential equations and associated boundary conditions defines the mathematical problem. Using an appropriate similarity transformation, the mathematical model is converted into a set of nonlinear ordinary differential equations with boundary conditions, which are then solved numerically by the Spectral Quasi Linearization Method (SQLM). Graphs and tables for various flow parameters illustrate the complete results for the exploration of dimensionless velocity and temperature. Regression analysis is used to statistically estimate the local Nusselt number and the skin friction coefficients. From the numerical results, it is found that when the magnetic parameter is increased, the flow velocity in the radial and tangential directions decreases due to the Lorentz force. With the variation of the Forchheimer number, the fluid flow in both directions decreases with increasing inertia coefficient. By increasing the magnetic parameter and Eckart number, the temperature of the fluid increases. The performed quadratic regression analysis reveals that the permeability of the medium and the generated Lorentz force are significant for the skin friction coefficient in the radial direction, whereas the stretching parameter and Forchheimer number are significant for the skin friction coefficient in the tangential direction. Thermal radiation and convective heating are found to significantly affect the heat transfer coefficient.

Entropy optimization in mixed convective boundary layer flow of CNTs Casson nanoliquid through a vertical cylinder moving with nonlinear velocity

This article inspects entropy generation and mixed convection boundary layer flow of carbon nanotubes (CNTs) Casson nanoliquid via semi-infinite vertical cylinder which moves with nonlinear velocity in Darcy-Forchheimer porous medium. Appropriate similarity variables have been employed to convert the original partial differential equations into ordinary differential equations that have been solved using overlapping grid spectral quasilinearisation method (SQLM). Comparison of accuracy, convergence and stability between the two methods is made. Rate of entropy generated, flow fields and engineering quantities are discussed for different embedding parameters. It is revealed that single-wall CNTs are more efficacious to improve heat transport features than multi-wall CNTs. The fluid flow and thermal dispersion processes improve with consideration of curved surface, CNTs, non-Newtonian fluid and injection of the fluid. The curvature surface and suction of the fluid contribute towards growth of skin friction factor and rate of thermal transference. Entropy generated expands by accounting for viscous nature of the fluid, strong nonlinearity, suction, non-Newtonian fluid, convective boundary condition and CNTs. The study finds applications in various processes, which are massively impacted by heat transport enhancement and high porosity. Boundary layer flow and heat transfer analysis through cylinders are relevant to various metallurgical and engineering solicitations.

Entropy Generation in a Magnetohydrodynamic Hybrid Nanofluid Flow over a Nonlinear Permeable Surface with Velocity Slip Effect

The current study is designed to model the hydrothermal feature of a hybrid nano liquid slip flows over a permeable expanding/contracting surface with entropy generation. The model incorporates Cu-Al2O3 nanoparticles with water as the host liquid to simulate the flow. Additional impacts incorporated into the novelty of the model are viscous dissipation and Joule heating. The model is transformed appropriately to its dimensionless form using similarity quantities and the solution is numerically obtained using the spectral quasi-linearization method (SQLM). The impact of pertinent factors on the flow characteristics is communicated through graphs for the hybrid nano-suspension to discuss the hydrothermal variations. The friction factor and the rate of heat transport are also discussed with sensible judgment through tables. To ensure the code validity, a comparison with earlier studies is conducted and excellent consensus is accomplished. The result explored that diminution in the irreversibility ratio is witnessed for rising magnetic field strength along the free stream, distance away from the permeable surface as the heat dissipation to the surrounding decelerates. Also, the augmented nonlinearity parameter intensified the heat transfer rate for about 2.79% of the hybrid nano-suspension.

Numerical and statistical analysis of hydromagnetic couple-stress hybrid nanofluid flow in a channel induced due to stretching of a wall

In this research paper, the authors wish to examine the effects of couple stress on hybrid nanofluid considering magnetohydrodynamic three-dimensional transient flow between two parallel plates. Stretching of the lower plate causes fluid flow in the channel. The fluid flow model is shown in mathematical form using a set of coupled nonlinear partial differential equations, which are then translated into coupled nonlinear ordinary differential equations using the proper transformation. The authors used the spectral quasi linearization method (SQLM), an effective numerical technique, to solve the updated equations and study the effects of various flow parameters on fluid temperature and velocity. The Nusselt number and skin friction coefficients were also investigated from an engineering standpoint. The generated solutions are verified using the residual analysis. Statistical analysis is performed on the skin-friction coefficients and the Nusselt number using quadratic regression models.

Magnetohydrodynamics Williamson Nanofluid Flow over an Exponentially Stretching Surface with a Chemical Reaction and Thermal Radiation

Presented in this current study is the numerical analysis of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface. The most important aspect of the investigation is that the effects of the magnetic field, chemical reaction and thermal radiation in the fluid flow are taken into account. The partial differential equations governing the present Williamson nanofluid flow problem were observed to be highly nonlinear and coupled. Suitable similarity transformations were used to transmute the coupled system of nonlinear partial differential equations governing the fluid flow into a linear system. The linear system was solved numerically using the spectral quasi-linearization method. The MATLAB bvp4c numerical technique and a comparison with existing results for the skin friction coefficient were used to confirm the appropriateness of the method in solving the current problem. The influence of some pertinent physical parameters on the fluid’s velocity, temperature and concentration profiles were displayed graphically. The effects of all the physical parameters on the skin friction coefficient, Nusselt number and Sherwood number were portrayed in a tabular form. It was noted that enhancing the thermal radiation parameter reduces the fluid’s temperature, Nusselt number and the skin friction coefficient, while the Sherwood number is improved.

Flow Analysis of Mixed Convective Nanofluid Flow in Presence of Magnetic Field with Thermal Radiation and Heat Source/Sink

This study discussed the mixed convection with thermal radiation on nanofluid flow with magnetic field and mass transfer with heat source over an inclined stretching cylinder in the presence of thermal conductivity. The governing equations in cylindrical form are transformed into the system of ODE and solved mathematically by spectral quasilinearization method (SQLM). The governing parameters velocity, temperature and concentration profile are derived using this new approach. Here it is mention that due to Hartman number (Ha) and relaxation to retardation time ratio (λ1), the velocity decreases but temperature enhanced in the boundary layer but in opposite effect on higher value of curvature parameter (γ) and thermal bouncy (λT) parameter. Here also observed convergence and accuracy in velocity and temperature profile. The SQLM is used to find out the solution of convergent series and various effect are shown graphically.

Effect of thermal radiation and nth order chemical reaction on non-Darcian mixed convective MHD nanofluid flow with non-uniform heat source/sink

The present perusal is to scrutinize the consequences of free-forced convective heat-mass transportation and n th order chemical reaction on MHD, non-Darcian, incompressible nanofluid fluid flow through an extended lamina, immersed in a permeable medium along with an external constant magnetic field. The fluid flow governing equations (PDEs) has been transformed into a system of nonlinear ODEs with the help of appropriate similarity transformation, and then solved numerically by using SQLM (Spectral quasilinearization method) method. Solution error for temperature and concentration profile against radiation parameter, Brownian motion parameter, and Hartman number also has been depicted diagrammatically. The graphical representation shows that the Hartman number, Brownian motion parameter, and chemical reaction parameter decline in velocity. While, the thermal boundary layer enhances with an enhancement of the Hartman number, Brownian motion parameter, radiation parameter, and chemical reaction parameter. Generation of entropy increases with the Brinkman number, Reynolds number, and Hartman number in the vicinity of the stretching lamina. Brinkman number and Reynolds number reduce the Bejan number. For the engineering interest Skin-friction, the local Nusselt number, and local Sherwood number also have been calculated. Impacts of pertinent parameters on the skin friction, Nusselt number, and Sherwood number are examined graphically and also numerically.

Entropy generation in magnetohydrodynamic radiative non-Darcy slip flow of a Casson nanofluid with Hall effects and activation energy

The present research work examines the entropy generation in the magnetohydrodynamic second-order slip flow of Casson nanofluid surpassing a horizontal stretching sheet inside a non-Darcy porous medium under the dominance of Hall current and nonlinear thermal radiation. The present model is made more realistic by taking second-order velocity slip flow. The energy field is pursued by incorporating the consequences of distinctive viscous dissipation and Joule heating. The chemical reaction incited by activation energy is comprised in the current exploration. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with second-order velocity slip and convective boundary conditions. A compatible similarity transformation comprised is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via the spectral quasi-linearization method. The present article deals with an in-depth exploration of the characteristics of diagnostic flow parameters against the-flow field and other efficient physical quantities with the help of distinctive graphs and tables. As per the regression analysis, the maximum relative error for the reduced Nusselt number ranging from .000090231% to .00015936% is less than that of the other physical quantities. Magnetic force, thermophoresis, and Brownian motion assist in lessening the heat transport rate, but it gets enriched under the Hall current effects. For the increasing Casson parameter, fluid movement tends to rise near the sheet’s surface and gets decelerated afterwards. The intense Hall current accelerates the Casson fluid’s motion. But the velocity components in xandz-directions become abated across the flow region due to increasing the first-order velocity slip parameter. Besides, the enhancement in the magnitude of the second-order velocity slip parameter undermines the velocity components in xandz-directions.

Analyses of entropy generation in micropolar liquid using overlapping multi-domain spectral quasilinearization method

In this article, entropy generation on Micropolar fluid through a perpendicular hot sheet is studied. The governing equations of the mathematical model of this article will transfer to non-dimensional system of ordinary differential equations by similarity transformations. This system of non-dimensional ODEs will be solved by a newly developed spectral collocation method. The dimensionless mathematical calculations are handled through utilizing the spectral quasilinearization method (SQLM) along with the concept of overlapping grids. Condition numbers, residual error and solution error norms estimations are provided to appraise accuracy, convergence and the stability of this numerical method. Using the overlapping multi-domain (M-D) approach has been found to produce most accurate, stable and convergent solutions when contrasted to the single-domain (S-D) technique. The outcomes are displayed and depicted graphically and through tabular forms. The effects of different non-dimensional parameters on flow, temperatures, concentration and entropy generation are studied. The accuracy of the numerical method has been checked through comparison with previously published articles and error analyses test.

Overlapping grid SQLM for third-grade modified nanofluid flow deformed by porous stretchable/shrinkable Riga plate

Abstract The improvement in thermal performance of fluid and the control of energy loss are equitably significant. Therefore, the purpose of this study is to analyze entropy generation, stagnation point flow, and thermal characteristics of non-Newtonian third-grade modified hybrid nanofluid generated by a stretchable/shrinkable Riga plate in a porous medium with varying flow viscosity. In this analysis, a modification of hybrid nanofluid is considered by using pure water as a base fluid and three various nanomaterials (aluminium oxide, copper, and nickel) as nanoparticles in the characterization of heat transfer. Furthermore, the contribution of heat source/sink and viscous dissipation are accounted for in the model. The suited transformations are enforced to remodel the governing mathematical equations to produce ordinary differential equations that are conveniently tackled via spectral quasilinearization method (SQLM) along with the overlapping grid idea to yield numerical solutions. The preference of this approach over others has been justified through discussion of error bound theorems, residual and solution errors, computational time, and conditioning of matrices. The physical significance of disparate governing parameters on flow variables, velocity gradient, thermal rate, and entropy generation are scrutinized through graphs and tables. Crucial findings of the study include that temperature of the modified hybrid nanofluid enhances quickly (better thermal conductor) than temperature of single nanofluid, hybrid nanofluid, and conventional third-grade fluid for higher Biot number, variable viscosity, and heat source parameters. Mass suction enhances fluid flow and physical quantities of interest, but suppresses the fluid temperature. An increase in variable fluid viscosity, modified Hartmann number, and third-grade parameters enhances the wall drag coefficient while lowering the rate of heat transfer, and the opposite is true for porous media. More entropy is generated in the system by high variable fluid viscosity, suction, viscous dissipation, modified Hartman number, and non-Newtonian parameters. Owing to high velocity and temperature associated with modified hybrid nanoparticles, modified hybrid technology is recommended in enhancing the physical attributes of the fluid with minimal cost effects. In engineering and industrial point of view, this study can contribute significantly in thermal improvement of the working fluid.

Axisymmetric boundary layer slip flow with heat transfer over an exponentially stretching bullet-shaped object: A numerical assessment

The slip flow and thermal transfer inside the boundary layer are extremely significant for various problems in aerodynamics, wing stall, skin friction drag on an entity, high-level velocity aircraft, etc. The current research investigated the effect of the slip factor and shape factor on the axisymmetric bullet-shaped object by taking the viscous dissipation parameter and location parameter. The analysis is conducted for both fixed and moving bullet-shaped objects due to thinner and thicker surfaces. The governing equations are transformed into a system of ordinary differential equations using suitable local axisymmetric similarity transformations and solved by applying the spectral quasi-linearization method. A new correlation analysis is made for velocity and temperature gradients. It is observed that the boundary layer structure has no defined shape due to a thicker bullet-shaped object instead it forms a steep angle with the axis which is contradictory to the formation of the boundary layer. A negative correlation is observed for the parameters M, Ec, Q*, and s but a positive correlation is observed for the parameters such as Pr, P, λ, and ε. The surface thickness and stretching ratio significantly affect the fluid flow and heat transfer processes. It is also noticed that the thinner bullet-shaped object performs as a better cooling conductor compared to a thicker one. The skin friction is reduced in the case of a thinner bullet-shaped object compared to a thicker one. The present analysis reveals that the heat transfer rate and the friction factor may be helpful in industrial sectors for controlling the cooling rate and quality of the final product. This research brings forward to increase in the rate of heat transfer inside the boundary layer region. The result may help to design the various types of moving objects in the automobile engineering sector when the objects pass through the fluid.

Entropy generation and thermal analyses of a Cross fluid flow through an inclined microchannel with non‐linear mixed convection

AbstractThe temperature difference of the various applications such as microchannel heat exchangers, microelectronics, solar collectors, automotive systems, micro fuel cells, and microelectromechanical systems (MEMS) is relatively large. The buoyancy force (mixed convection) modeled by the conventional Boussinesq approximation is inadequate since the density of the operating fluids fluctuates non‐linearly with the temperature difference. Therefore, the mixed non‐linear convective transport of the flow of Cross fluid through three different geometric aspects (horizontal, vertical, and inclined) of the microchannel under the non‐linear Boussinesq (NBA) approximation is investigated. Mechanisms of internal heat source, Rosseland radiative heat flux, and frictional heating are incorporated into the thermal analysis. The mathematical construction is proposed using the Cross fluid model for a steady‐state, and subsequent non‐linear differential equations are deciphered by the spectral quasi‐linearization method (SQLM). Graphical sketches were constructed and displayed that explore the stimulus of various key parameters on Bejan number, velocity, temperature, and entropy generation. It is found that the Bejan number and entropy production improved due to the non‐linear density temperature variation. The convective heating boundary conditions augment the entropy production. The pressure gradient accelerates the transport of fluid in a microchannel. Furthermore, among three different geometries, the velocity, entropy production, and temperature are the highest for the vertical microchannel.

Powell-Eyring Fluid Flow Over a Stretching Surface with Variable Properties

The objective of this study is to investigate the effect of temperature dependent viscosity and thermal conductivity on the stretching surface and heat transfer of a Powell-Eyring fluid with the effect of nonlinear thermal radiation. The Prandtl number is also considered to be varying within the boundary layer. The governing model which consists of a set of coupled non-linear partial differential equations is converted into a system of ordinary differential equations via suitable similarity transformations and then solved by a recent and reliable numerical method called the spectral quasi-linearization method is used in the computational analysis. The result shows that there is large variation in the value of the Nusselt number and skin friction co-efficient.

Spectral Quasilinearization Method for the Numerical Solution of the Non-standard Volterra Integral Equations

In this paper, an iterative scheme is proposed through quasilinearization and the Legendre spectral collocation method to approximate the solution of the non-standard Volterra integral equations (NVIEs). At first, the process of quasilinearization serves to turn a NVIE into a sequence of linear Volterra integral equations. Then, in each iteration, the linear problem is solved by the Legendre spectral collocation method. After that, a convergence analysis is performed. The efficiency and accuracy of the proposed scheme are also verified through several illustrative examples.

Entropy Generation and Regression Analysis of Magnetohydrodynamic Stagnation Point Flow of a Casson Fluid with Radiative and Dissipative Heat Transfer and Hall Effects

The phenomenon of heat transfer is prevalent in industries and has an extensive range of applications. However, mostly the discussion of heat transfer problems is limited to the study of the first law of thermodynamics, which deals with energy conservation. It is just restricted to the quantity of energy, not to its quality; i.e., there is no difference between the work (high‐grade energy) and the heat (low‐grade energy). A measurement of the degree of randomness of energy in a system is known as entropy. It is unavailable for doing useful work because work takes place only from ordered molecular motion. Even though many boundary layer models exist in the literature to investigate the flow and heat transfer of various fluids along a stretching surface, they have not yet been used at their maximum ability. The main motive of the current research is to discuss entropy generation or its minimization during heat transfer. This work presents an entropy generation analysis for the transient three‐dimensional stagnation point flow of a hydromagnetic Casson fluid flowing over a stretching surface in the existence of Hall current, viscous dissipation, and nonlinear radiation. The physical configuration of the present work is described in terms of partial differential equations (PDEs) of nonlinear nature. Furthermore, these PDEs are converted into ordinary differential equations by using some relevant similarity transformations. An efficient numerical method named as the spectral quasilinearization method (SQLM) is used to solve this model. The expression of the Bejan number and volumetric entropy generation rate is also computed. A parametric analysis, including the essential physical parameters, is performed to examine the influences of distinct flow parameters on the velocity profile, temperature profile, Bejan number, entropy generation number, and the coefficients of skin friction and the Nusselt number. In order to further insight into the emerging physical quantities of engineering interest, multiple quadratic regression models are used to estimate the coefficients of skin friction and heat transfer.

Analysis of entropy generation and activation energy on double diffusive magnetohydrodynamic Williamson nanofluid flow featuring nonlinear thermal radiation

In this article, we study the effects of the generation of entropy on the transfer of heat and mass by considering the activation energy in the Williamson nanofluid. The importance of Brownian motion and thermophoresis are analysed in various fields over a vertical stretching sheet. The mathematical governing basic equations are solved efficiently by using the spectral quasilinearisation (SQL) method. Numerous physical parameters are considered to plot profiles of nanofluid velocity, temperature, concentration and entropy generation fields. It is exhibited that the velocity profiles tend to reduce due to enhancement in magnetic and Williamson parameters. Furthermore, the entropy generation profile diminishes for the higher Williamson parameters, whereas it enhances due to higher values of the Brinkman numbers. Also, it is noticed that the temperature profile increases by enhancing the values of the activation parameter, whereas the entropy generation diminishes due to increasing the values of the activation parameter.

Numerical investigation of the non-Newtonian power-law fluid with convective boundary conditions in a non-Darcy porous medium

The boundary layer nanofluid flow over a horizontal plate embedded in a non-Darcy porous medium is investigated in this study. Non-Newtonian power-law fluid is considered the base fluid. The nanofluid model incorporated the effects of Brownian motion and thermophoresis. A mixed convective boundary condition that is more useful, in practice, is employed at the surface instead of Dirichlet or Neumann boundary conditions. The flow and convective heat transfer has engineering and industrial applications such as the thermal design of industrial equipment dealing with molten plastics and polymeric liquids and applications in nuclear plants and thermal energy storage processes. The main aim of this study is to use the spectral quasi-linearization method to study the effects of non-Newtonian nanofluid flow over a horizontal surface for a porous medium. The objective is to explore both the accuracy and the convergence of the method through the evaluation of residual errors and error norms and to investigate the impact of specific parameters on flow behavior and heat transfer characteristics. The velocity profile increases for higher values of the power law index and mixed convection parameter. The influence of the number of active variables on dimensionless temperature profiles increases for different values of the Biot number.

Spectral quasilinearization method for Sisko nanofluid past a stretching cylinder with activation energy and entropy generation effects subject to variable thermal conductivity

AbstractThis article focuses on how activation energy and entropy generation affect the parameters involved in Sisko nanofluid with the presence of a stretching cylinder. Spectral quasilinearization method is applied to solve the ordinary differential equations representing the flow equations to have a highly accurate solution. Furthermore, all the parameters involved are graphically analyzed to see the behavior of velocity, temperature, and concentration behavior under different circumstances. With the increment of heat generation parameter, Sisko nanofluid shows an increasing nature in concentration unlike base fluids. Thermophoresis and Brownian motion effects are observed to be different than usual, especially in nearby wall zones due to activation energy and entropy terms being introduced on a stretching cylinder medium.

Multi-domain multivariate spectral collocation method for (2+1) dimensional nonlinear partial differential equations

The novelty of this work rests upon the use of the domain partitioning technique in time variable when discretizing the domain of solution in spectral collocation algorithm. The single domain multivariate spectral collocation based methods have been proven to be effective in solving time-dependent partial differential equations (PDEs) defined over small time domains. However, there is a significant loss of accuracy as time computational domain proliferates and also when the number of grid nodes approaches a definite particular number. Therefore, the establishment of the new innovative multi-domain multivariate spectral quasilinearisation method (MDMV-SQLM) is described for the purpose of solving (2+1) dimensional nonlinear PDEs defined on large time intervals. The main output of this study is confirmation that minimizing the size of time computational domain at each subinterval assures sufficiently accurate results that are attained using minimal number of nodal points and less computational time. The solution algorithm involves partitioning the time domain into multiple non-overlapping sub-domains, simplification of the nonlinear PDEs using the quasilinearisation method and assumption of approximate solutions using triple Lagrange interpolating polynomials with Chebyshev–Gauss–Lobatto (CGL) points. The multi-domain spectral collocation procedure is executed on the linear systems of algebraic equations, where the subsequent matrix systems are solved separately in every time sub-interval with the continuity equation essentially used in obtaining initial conditions in the next subintervals. MATLAB software is used to implement the solution algorithm and numerical results are demonstrated graphically and in tabular form. To highlight the efficaciousness and accuracy of the MDMV-SQLM, error estimates, condition numbers and computational time are presented for well known (2+1) dimensional nonlinear initial-Dirichlet boundary value problems. The adoption of the domain decomposition technique is efficacious in suppressing the numerical challenges linked to large matrices and ill-conditioned nature of the resulting coefficient matrix. Also, the communicated results confirm that the numerical scheme is computationally cheap, fast and yield extremely accurate and stable results with the aid of fewer number of grid points for large time domains.