Dimensionless Partial Differential Equations Research Articles

Effects of vibration on natural convection in a square inclined porous enclosure filled with Cu-water nanofluid

PurposeThe purpose of this paper is to investigate the effects of gravitational modulation on natural convection in a square inclined porous cavity filled by a fluid containing copper nanoparticles.Design/methodology/approachThe present study uses a system of equations that couple hydrodynamics to heat transfer, representing the governing equations of fluid flow in a square domain. The Boussinesq–Darcy flow with Cu-water nanofluid is considered. The dimensionless partial differential equations are solved numerically using finite difference method based on alternating direction implicit scheme. The cavity is differentially heated by constant heat flux, while the top and bottom walls are insulated. The authors examined the effects of gravity amplitude (λ), vibration frequency (σ), tilt angle (α) and Rayleigh number (Ra) on flow and temperature.FindingsThe numerical simulations, in the form of streamlines, isotherms, Nusselt number and maximum stream function for different values of amplitude, frequency, tilt angle and Rayleigh number, have revealed an oscillatory behavior in the development of flow and temperature under gravity modulation. An increase of amplitude from 0.5 to 1 intensifies the flow stream (from |ψmax| = 21.415 to |ψmax| = 25.262) and improves heat transfer (from Nu¯ = 17.592 to Nu¯ = 20.421). Low-frequency vibration below 50 has a significant impact on the flow and thermal distributions. However, once this threshold is exceeded, the flow weakens, leading to a gradual decrease in heat transfer rate. The inclination angle is an effective parameter for controlling the flow and temperature characteristics. Thus, transitioning the tilt angle from 30° to 60° can increase the flow velocity (from 22.283 to 23.288) while reducing the Nusselt number (from 16.603 to 13.874). Therefore, by manipulating the combination of vibration and inclination, it is founded that for a fixed frequency value of σ = 100 and for increased amplitude (from 0.5 to 1), the flow intensity at inclination of 60° is boosted, and an increase of the heat transfer rate at inclination of 30° is also observed. Convective thermal instabilities may arise depending on the different key factors.Originality/valueTo the best of the authors’ knowledge, this study is original in its examination of the combined effects of modulated gravity and cavity inclination on free convection in nanofluid porous media. It highlights the crucial roles of these two important factors in influencing flow and heat transfer properties.

Analytical modeling of desublimation of a phase change material (PCM) in a porous medium with temperature-dependent volumetric heat sink and convection due to air-mixed vapor

The desublimation phase change heat and mass transfer process in a porous medium occurs during the conversion of vapor into solid form, which has several applications in chemical deposition and industrial coating. For economic feasibility, reducing the operating time of the conventional desublimation technique is of much interest. Toward this goal, current work presents a mathematical model for desublimation that accounts for a volumetric heat sink connected with temperature. A linear profile of the volumetric heat sink varying with temperature is modeled within the frozen region. Further, the rate of water vaporization (with mixed air) produces a convective term, which is also accounted for in the frozen region. Despite previous studies on desublimation phase change process, there is still insufficient mathematical modeling of this particular phenomena. The solution to the governing set of dimensionless partial differential equations is obtained analytically by employing the space-time transformation. Results indicate that the rate of desublimation process becomes faster with increasing the strength of the volumetric heat sink, which results in the reduction of the total operating time to desublimate of a phase change material. Higher values of the dimensionless temperature parameters also accelerate the desublimation process. On the other hand, a larger value of the convective term is found to slow down the desublimation process. The dimensionless moisture concentration profile in the vapor region increases with increasing the value of the Luikov number. Observations from this study are expected to aid in the fundamental design of processes including industrial coating, preservation of biological products, and evaporative deposition where desublimation plays a key role.

Enhanced Efficiency of MHD-Driven Double-Diffusive Natural Convection in Ternary Hybrid Nanofluid-Filled Quadrantal Enclosure: A Numerical Study

The study investigates the performance of fluid flow, thermal, and mass transport within a cavity, highlighting its application in various engineering sectors like nuclear reactors and solar collectors. Currently, the focus is on enhancing heat and mass transfer through the use of ternary hybrid nanofluid. Motivated by this, our research delves into the efficiency of double-diffusive natural convective (DDNC) flow, heat, and mass transfer of a ternary hybrid nanosuspension (a mixture of Cu-CuO-Al2O3 in water) in a quadrantal enclosure. The enclosure’s lower wall is set to high temperatures and concentrations (Th and Ch), while the vertical wall is kept at lower levels (Tc and Cc). The curved wall is thermally insulated, with no temperature or concentration gradients. We utilize the finite element method, a distinguished numerical approach, to solve the dimensionless partial differential equations governing the system. Our analysis examines the effects of nanoparticle volume fraction, Rayleigh number, Hartmann number, and Lewis number on flow and thermal patterns, assessed through Nusselt and Sherwood numbers using streamlines, isotherms, isoconcentration, and other appropriate representations. The results show that ternary hybrid nanofluid outperforms both nanofluid and hybrid nanofluid, exhibiting a more substantial enhancement in heat transfer efficiency with increasing volume concentration of nanoparticles.

Unsteady dynamical analysis of convective hydromagnetic thermal migration of chemically reacting tiny species with dissipation and radiation in an inclined porous plate

The essence of the current examination is to carry out thermofluid parametric sensitivity with time-varying thermal migration of chemically reactive tiny species across an oscillating infinite plate surface. The impact of thermal motile tiny particles under the influence of many other oscillating flow parameters has yet to be investigated; hence the results obtained in this research are novel. Using a suitable non-dimensional variable, the leading PDEs (partial differential equations) are transmuted into dimensionless PDEs, ensuring equations are numerically solved using the MAPLE built-in approach. The numerical values produced in a limited scenario are linked with the outcomes found in the literature to validate the precision of the numerical approach utilized. The fluctuations in the profiles of the velocity, temperature, and concentration, in addition to the wall friction and rate of thermal and solutal transport, are illustrated via graphs and tables due to the modification of the critical parameters. The endmost results of the study concede that increasing permeability quantity and thermal and solutal buoyancy impellers intensify the fluid velocity. In contrast, a converse tendency is perceived with magnetic parameter and also, wall friction acts opposite to the velocity. The fluid temperature attenuated with dilation of the Prandtl number and radiation parameter, whilst a contrary trend was perceived with Eckert number. The increasing thermo-diffusion helps to develop fluid concentration whilst the Schmidt number and chemical reaction displayed opposite trend. Further, we achieved a tremendous conformity between the current findings and genuine results in the literature.

Computational convection analysis of second grade MHD nanofluid flow through porous medium across a stretching surface

AbstractNanofluids significantly influence modern life due to their vast usages in the modern era. Transport analysis of non‐Newtonian fluids with nanoparticles (carbon nanotubes) over a stretching surface is the primary focus of the present investigation. Effects of viscous dissipation, porous medium, magnetic field, and heat source factors are also examined. Boundary layers approximation is used to simulate the underlying collection of partial differential equations (PDEs) that regulate the system. Using non‐similarity transformation, the basic PDEs of the model are converted into dimensionless nonlinear PDEs. Up to the second level of truncation PDEs that can be treated as ordinary differential equations (ODEs) are generated from dimensionless PDEs utilizing local non‐similarity approach. The resultant nonlinear differential equations are computationally solved using bvp4c code of MATLAB technique. In this study, we compile and compare the obtained findings with previous research. Graphs demonstrate how the velocity and temperature profiles depend entirely on a wide range of physical parameters. A rise in the second‐grade fluid parameter upsurges the velocity distribution, while an increment in porosity and magnetic parameter declines the velocity distribution. As magnetic values, Eckert number, porosity parameter, and heat source increase, so does the temperature profile of the nanofluid.

Heat and mass transfer characteristics of Al2O3/H2O and (Al2O3+Ag)/H2O nanofluids adjacent to a solid sphere: A theoretical study

A theoretical study is carried out to explore the heat and mass transfer features in the flow of two types nanofluid, i.e., A l 2 O 3 / H 2 O micropolar nanofluid and ( A l 2 O 3 + Ag ) / H 2 O hybrid nanofluid, adjacent to a solid sphere. Furthermore, simultaneous effects of linear thermal radiation and chemical reaction are also explored on the heat and mass transfer characteristics. In mathematical formulation basic conservation laws are utilized along with the Soret and Doufer effects as a coupling agents in the energy and mass concentration equations. The normalized variables are used to transform the governing system of non-linear partial differential equations into the system of dimensionless partial differential equations. Stream function reduces the number of dependent variables and the resulting system is solved numerically by Keller box method. Several plots are presented to explore the impact of involved parameters on the different profiles and engineering interest quantities for both types of fluids. The temperature profile and Nusselt number are large in magnitude for hybrid nanofluid as compared to A l 2 O 3 /water based nanofluid. The heat transfer and mass transfer rates rises with thermal radiation parameter and chemical reaction parameter, respectively.

Non-similar analysis of bioconvective stagnation-point flow toward a stretching surface in the presence of buoyancy force, viscous dissipation, and thermal radiation

Aim of this analysis is to investigate, bioconvective stagnation flow of an incompressible fluid across an expanding perpendicular surface in the existence of buoyancy force, viscous dissipation, and thermal radiation. The physical model is described in terms of nonlinear coupled partial differential equations (PDEs). The dimensional PDEs are transformed into dimensionless PDEs by using appropriate non-similar transformations. Local nonlinearity method (LNS) is used to generate high accuracy truncated ordinary differential equations (ODEs) that are used to approximate dimensionless PDEs. Using well-known techniques like finite-difference-based bvp4c, the ODEs are numerically formulated. This research also investigates how several physical, nondimensional parameters affect the profiles of velocity, temperature, and concentration, for both assisted and opposed flow cases. The comparison and range tables describe the validity and range of the presented results, respectively. The tabulated results indicate that enhancement in radiation parameter increases the local Nusselt number, Sherwood number, and the surface drag force.

Artificial neural network (ANN) analysis of non-similar solution of MHD nanofluid flow past a curved stretching surface

The objective of this study is to predict the non-similar solution of Magnetohydrodynamics (MHD) mixed convection transports of viscous nanofluids over a curved stretching surface by using numerical simulation with an artificial neural network (ANN) algorithm, namely the back-propagation Levenberg–Marquardt scheme. In this article, aluminum oxide and iron oxide are used as nanoparticles to enhance the thermal conductivity of the base fluid. Additionally, aluminum oxide and iron oxide nanoparticles are used in certain biomedical applications, including composite materials, photocatalysis, wastewater treatment, and nanofiltration membranes. The radiation, Joule heating, and viscous dissipation effects are studied along with the convective boundary condition. The flow problem is attained in the form of a system of Partial differential equations (PDEs) and converted into dimensionless PDEs via non-similarity transformation. These dimensionless systems of PDEs are converted into a system of Ordinary differential equations (ODEs) via local, non-similar techniques up to second-order truncations. The Bvp4c technique is used to simulate the numerical results. The data sets are collected using the Bv-p4c technique. These data sets are utilized for the validation, training, and testing phases of the developed Back-propagated Levenberg-Marquardt Scheme- Artificial Neural Network (BLMS-ANN) model to determine the solution of the problem for a variety of physical scenarios. The ANN model is utilized to choose data, construct and train a network, and evaluate the performance of the network through the use of mean square error and regression analysis. The ANN models are used to predict the performance of the Nusselt number for both nanofluids and the results demonstrated that ANN is capable of making accurate predictions of the local Nusselt number for both nanofluids. In the entire study, the ANN model predicts the result of the local Nusselt number of nanofluids with higher accuracy as compared to nanofluids.

Impact of thermal radiations, heat generation/absorption and porosity on MHD nanofluid flow towards an inclined stretching surface: Non‐similar analysis

AbstractObjective of this investigation is to provide a novel study of the flow of a magnetohydrodynamics (MHD) nanofluid over an inclined stretching surface in a permeable medium in a 2‐dimensional boundary layer. The convection model further incorporates heat radiation and heat sources/sinks. Nanomaterials include magnesium oxide and copper oxide . Using non‐similarity transformations, the set of governing equations is transformed into a set of dimensionless partial differential equations (PDEs). Using the local non‐similarity technique, the resulting system of dimensionless PDEs is treated as a set of ordinary differential equations (ODEs), and then solved with the help of the bvp4c MATLAB tools. This comprehensive research involves a thorough investigation of the significant starting physical characteristics and their impacts on the velocity and nanofluid temperature profiles. These profiles are shown using a set of graphical representations and numerical tables. It is worth noting that changes in the magnetic and porosity parameters result in a decrease in the velocity profile, but the Grashof number exhibits a reciprocal correlation. When we account for the effects of the Eckert number and the radiation parameters in a given flow regime, we also see an increase in the nanofluid's temperature profile. It has been shown that when the magnetic number and the Eckert number are augmented, the heat transmission rate decreases. The skin friction coefficient grows on a logarithmic scale when magnetic parameters and nanoparticle concentration are increased in estimation. The numerical calculations are checked for accuracy by comparing them to previously published findings, which guarantees an exact match in a constrained setting. Scientists investigating nanomaterials and their applications in manufacturing and thermal engineering may find this research instructive.

Peristaltic flow of bioconvective Ree–Eyring nanofluid through an inclined elastic channel with partial slip effects

Pharmaceutical fluid processing is a procedure of medication manufacturing, utilizing a particular kind of heat transfer in a biofluid designed to maintain the desired temperature for extended periods. Choosing a suitable fluid can have a positive effect on the operating efficacy of the system and lengthen the fluid’s and system’s life spans. As an outcome of this development, we investigate the influence of the partial slip and gyrotactic microorganisms on the peristaltic transport of a magnetohydrodynamic Ree–Eyring nanofluid via an aligned porous conduit with thermal radiation, energy generation, along with cross and double diffusion effects. By invoking suitable nondimensional parameters, the proposed dimensional governing equations are transformed into a system of dimensionless partial differential equations. The analytical solutions for the system of partial differential equations are obtained by incorporating the homotopy perturbation method. Further, tabular and graphical presentations are used to examine the characteristics of the various sundry parameters on the temperature, concentration, motile microorganism density, axial velocity, trapping, and other relevant flow quantities. The observations of this study indicate that the Darcy number and thermal Grashof number have the capability to enhance the velocity distribution of the Ree–Eyring nanofluid in the presence of bioconvection. The trapped bolus size and the skin friction coefficient increase noticeably because of an enhancement in the Ree–Eyring fluid parameter. Also, the Darcy number and the Hall current parameter increase the skin friction coefficient. Furthermore, validation of the results is carried out to examine the consistency between the current and the previous findings for some special cases and excellent agreements are found.

Numerical study of transient chemical reactive magnetized Casson fluid flow in the presence of Newtonian heating

ABSTRACT The numerical results of transient magnetohydrodynamic (MHD) Casson fluid flow under Soret-Dufour aspects are illustrated in this research. The governing dimensional equations of considered Casson fluids are first converted into dimensionless partial differential equations (PDEs) by utilizing the proper similar variables. The obtained system is then computed through the finite element method (FEM). The impact of dimensionless parameters is visualized on fluid velocity, skin friction, temperature, Nusselt number, concentration, and Sherwood number through the curves and tables. Both the temperature and velocity are risen against the higher Dufour number. It has been observed that the velocity profiles step up with the increment in various parameters. Comparisons are made with the available results in the open literature. These results are in good agreement with the previously published reports.

Non‐similar heat transfer analysis of magnetized flow of Ag‐Mgo/water hybrid nanofluid flow through darcy porous medium

AbstractThis study aims to examine the magnetized flow of Ag–MgO/water hybrid nanofluid over an extending sheet implanted in Darcy porous medium. Thermal radiations, Joule and viscous dissipations are incorporated into energy equation to account for heat transfer. The convective heat flux boundary condition is imposed at sheet surface. Using non‐similar conversions, governing equations are converted to a system of dimensionless partial differential equations (PDEs). These equations are transformed into ordinary ones by using local non‐similar method. MATLAB's bvp4c function is used to numerically simulate the ordinary differential equations (ODEs). The velocity and thermal profiles for positive variation of essential parameters are illustrated graphically. It was concluded that the velocity profile increases for the rising Darcy number. On the other hand, the temperature profile increased for the positive variation of magnetic number, volume fraction, radiation parameter, Eckert number and Biot number while decreasing for all other parameters. The skin friction coefficient and heat transfer rates are thoroughly investigated and findings are reported through tables. It was found that the magnitude of skin friction coefficient rises with an increase in volume fraction, suction and magnetic parameters while the heat transfer is enhanced by increases in Darcy number, suction parameter, radiation parameter, and Biot number. As per the author's knowledge, no work has previously been published on the current model using the local non‐similarity method. This work may provide insight to researchers interested in thermal systems and solar energy harvesting.

Unsteady mhd flow of tangent hyperbolic liquid past a vertical porous plate plate

The analysis in this communication addresses the unsteady MHD flow of tangent hyperbolic liquid through a vertical plate. The model on mass and heat transport is set up with Joule heating, heat generation, viscous dissipation, thermal radiation, chemical reaction and Soret-Dufour in the form of partial differential equations (PDEs). The PDEs are simplified into a dimensionless PDEs by utilizing a suitable quantities. The simplified equations are solved by utilizing the spectral relaxation method (SRM). The outcomes shows that increase in the Weissenberg and the magnetic field degenerates the velocity profile. The thermal radiation is found to elevate the velocity and temperature profiles as its values increases. The impact of Soret and Dufour on the flow is found to alternate each other. The computational outcomes for concentration, temperature and velocity are illustrated graphically for all encountered flow parameters. The present outcomes are compared with previous outcomes and are found to correlate.

Numerical Solution of Stagnation Point Flow of Non-Newtonian Fluid and Heat Transfer over a Porous Medium under Effect of Thermal Radiation and Magnetic Field

We study three key topics in this article, including Casson fluid flow at its stagnation point, heat transfer in the current magnetic field, and thermal radiation. Several equations related to coupled mass, momentum, and energy are controlled by the mathematical model. This is accomplished by using appropriate transformations to study dimensionless partial differential equations of motion, energy, and continuity. The Adam-Bashforth method is used to solve several nonlinear dimensionless partial differential equations. The analysis is based both on analytic and numerical representations of the impact of parameters which are relevant to the analysis, such as the Casson parameter β, porosity parameter K, magnetic field M, mixed convection parameter γ, and thermal radiation R. Finally, using the Adam-Bashforth approach, we are able to determine velocity profiles as well as temperature profiles.

Biomedical applications of gold nanoparticles in thermofluids flow through a porous medium

Gold nanoparticles have a variety of applications in medical sciences, including photothermal (PT), gene transfection agents, radiosensitizing, drug delivery, therapeutic etc. Especially in a lab, gold metallic nanoparticles are commonly utilized as a tracer to indicate the existence of certain proteins or DNA in a sample and identify the different antibiotics. They are biocompatible and can deliver heat energy to tumor cells via various therapeutic techniques. Because cancer cells are microscopic, appropriately, nanosized gold nanoparticles were infused into the bloodstream for infiltration and found very effective. Keeping in mind the applications of gold nanoparticles, this paper aims to consider the Magnetohydrodynamics thermofluids flow of blood containing gold nanoparticles. More precisely, the couple stress Casson fluid flow is taken as blood flow through a porous medium. This flow regime is modeled in terms of classical partial differential equations. These equations are nondimensionalized using suitable non-dimensional variables. The dimensionless partial differential equations are fractionalized using Caputo’s fractional derivatives definition with the application of Fick’s and Fourier’s laws. Laplace and Fourier’s transforms are used to accomplish exact solutions for temperature, concentration, and velocity profiles. The skin friction, Nusselt and Sherwood numbers are calculated and displayed in tabular form. The impact of several physical parameters on temperature, concentration and velocity profiles of thermofluids are shown graphically. The obtained results show that the blood velocity is a decreasing function of the couple stress parameter (λ) and the Casson parameter (β), which is very useful for controlling blood flow during magnetic therapy for treating pain in the back and foot and bleeding during surgeries. It is observed that the heat transfer rate of blood using gold nanoparticles increases up to 36%, which is very useful in hyperthermic tumor treatment.

Nonsimilar forced convection analysis of maxwell nanofluid flow over an exponentially stretching sheet with convective boundary conditions

AbstractThis proposed work aims to describe nonsimilar forced convection analysis for the flow of Maxwell nanofluids. The forced flow is commenced due to the stretching surface (SS) at an exponential rate. Heat and mass transmission is tackled with convective and zero mass flux at the surface. The fundamental laws of conservation governing the present flow problem are expressed mathematically in the form of a nonlinear partial differential system. The differential system is then remodeled into a system of nonlinear dimensionless partial differential equations (PDEs) under the implementation of suitable nonsimilar transformations. The resulting nonsimilar system is analytically approximated by applying local nonsimilarity (LNS) and then using the finite‐difference based bvp4c algorithm, it is numerically simulated to ascertain the influences of the various parameters—including the; Deborah number, Biot number, Schmidt number, Brownian diffusion parameter, Prandtl number, and thermophoresis diffusion parameters, on velocity and temperature. The reduced Nusselt numbers and the conduct of velocity and thermal distribution for varying parameters are illustrated graphically. The reduction of the boundary layer (BL) thickness is measured because‐of the Biot number while an increase is observed with an elevation in Deborah number. The velocity configuration is reduced with expanding Deborah number. It is remarked that as the values of the thermophoresis and Brownian motion parameter rise, the thermal BL thickness expands, and at the surface, the temperature gradient demises. An excellent comparison is noticed between present works with the already published article. The novelty of this article is that most of realworld BL flow problems are nonsimilar in nature, while many research have neglected this fact and treated the problem as similar. Therefore, we talked about the Maxwell problem's nonsimilar analysis here. The author's observations indicate that the analysis of the topic under discussion has not yet been declared in published literature.

Heat transfer analysis in a longitudinal porous trapezoidal fin by non-Fourier heat conduction model: An application of artificial neural network with Levenberg–Marquardt approach

Thermal critical issues commonly occur in advanced electrical devices as a response to excessive heat generation or a loss in efficient surface area for heat exclusion. This issue can be addressed by utilizing the extended surface to improve the heat transfer performance of the devices. Thus, the present analysis is devoted to scrutinizing the non-Fourier unsteady heat transference of a trapezoidal porous fin. Levenberg–Marquardt technique of backpropagation artificial neural network (LMT-BANN) is employed here to analyze the thermal variation in the fin. The developed governing equation is the hyperbolic heat conduction equation (HHCE), which is transformed into a dimensionless partial differential equation (PDE) using dimensionless variables. LMT-BANN is employed on thermal numerical data and is developed to trace numerical approximation of fin problem using a methodology that includes testing, training, and validation. A graphical visualization of the consequences of thermal variables on the temperature field is presented. The notable evidence of this study reveals that as the magnitude of the convection factor increases, thermal dissipation through the fin gradually decreases. Further, the LMT-BANN technique has been determined to be an effective, reliable, and rapidly convergent stochastic computational solver that can be used effectively for examining the thermal model.

Nonlinear Oscillations of a Composite Stepped Piezoelectric Cantilever Plate with Aerodynamic Force and External Excitation

Axially moving wing aircraft can better adapt to the flight environment, improve flight performance, reduce flight resistance, and improve flight distance. This paper simplifies the fully unfolded axially moving wing into a stepped cantilever plate model, analyzes the structural nonlinearity of the system, and studies the influence of aerodynamic nonlinearity on system vibration. The model is affected by aerodynamic forces, piezoelectric excitation, and in-plane excitation. Due to Hamilton’s principle of least action, the mathematical model is established based on Reddy’s higher-order shear deformation theory, and using Galerkin’s method, the governing dimensionless partial differential equations of the system are simplified to two nonlinear ordinary differential equations, and then a study of the influence of the various engineering parameters on the nonlinear oscillations and frequency responses of this model is conducted by the method of multiple scales. It was found that the different values of a5, a6, b6 and b8 can change the shape of the amplitude–frequency response curve and size of the plate, while different symbols a7 and b7 can change the rigidity of the model. The excitations greatly impact the nonlinear dynamic responses of the plate.

Three-dimensional MHD flow of hybrid material between rotating disks with heat generation

In this study, we investigate the flow of electrically conducting hybrid nanofluid (Ag+Cu/H2O), due to rotating disks, along with thermal slip, heat generation, and viscous dissipation. The nonlinear differential system is modelled and transformed into dimensionless partial differential equations using suitable dimensionless variables. To obtain solutions for the considered model, a finite difference toolkit is implemented, and numerical solutions are achieved. Graphical results are presented to display the influences of different dimensionless variables on flow velocity and temperature. This research contributes to a better understanding of hybrid nanofluid flows and can inform the design of cooling systems and other practical applications.

Non-similar investigation of magnetized boundary layer flow of nanofluid with the effects of Joule heating, viscous dissipation and heat source/sink

The main objective of this numerical study is to investigate the steady, incompressible and two-dimensional magnetohydrodynamic convection flow of a nanofluid across a stretched sheet with the influence of viscous dissipation, Joule heating, and slip condition. Also, the effects of convective boundary condition, mass flux and heat source are considered. The nanofluid under consideration is a combination of water and copper nanoparticles. In this analysis, appropriate non-similar transmutations are applied to transform partial differential equations (PDEs) into dimensionless PDEs. The dimensionless PDEs are converted into ordinary differential equations (ODEs) using the local non-similarity method. ODEs are solved through the use of well-known method (MATLAB-based bvp4c). The different results of velocity profile and temperature profile are conferred through graphs for several dimensionless parameters including Hartmann number, slip parameter, porosity parameter, Biot number and Eckert number. Physical quantities like Nusselt number and surface drag force are also estimated in tabular form. From the obtained results, it is noted that enhancing the values of volume fraction, slip parameter cause an increment in the values of skin friction coefficient while enhancing the values of Hartman number, porosity parameter causes a reduction in the values of skin friction coefficient. Also, by increasing the values of volume fraction, slip parameter, Eckert number causes a reduction in the values of local Nusselt number while the values of Nusselt number enhances by increasing the values of Hartman number, porosity parameter and heat source parameter.