Differential Equations Of Energy Research Articles

Dynamic simulation of roll bond PVT solar collector under Simulink/Matlab

Abstract This paper presents an innovative methodology to investigate dynamic roll bond PVT solar systems under real-world operational weather conditions using the Simulink/Matlab environment. The method is based on the MPPT electrical model of the solar cell and the differential energy equations of PVT at each of its layers. The effect of PV operating temperature, mass flow rate, and insulation medium on overall PVT thermal performance are all thoroughly examined. Results reveal that the annual average power delivered, in terms of both heat and electricity, is 352.8 W and 34.08 W, respectively. Furthermore, the addition of an insulating layer could lead to a significant improvement in PVT overall effectiveness. The present work offers a simple and flexible integration tool for roll bond PVT system simulation.

Analytical simulation of Darcy–Forchheimer nanofluid flow over a curved expanding permeable surface

Abstract This research paper presents an analytical simulation of Darcy–Forchheimer flow over a porous curve stretching surface. In fluid dynamics, the Darcy–Forchheimer model combines Forchheimer adjustment and high-velocity effects with Darcy’s formula for porous media flow: two nanofluid particles, molybdenum disulphide, and graphene oxide, form nanofluid with the base fluid blood. The governing partial differential equations for momentum and energy are converted into a nonlinear ordinary differential equations system by applying the appropriate similarity transformations. The homotopy analysis method is used to solve the transform equations analytically. The impact of essential factors includes the Forchheimer parameter, porosity parameter, slip parameter, Eckert number, nanoparticle volume friction, magnetic field parameter, and curvature parameter. The results have applications in the design of sophisticated cooling systems, where effective thermal control is essential.

Assisting and opposing mixed convective flow over a solid sphere at its bottom stagnation point with a constant surface heat, mass and motile microorganism flux

This study examined the laminar mixed convective flow around the lower point of stagnation for a solid sphere with a steady flux of gyrotactic microbial motility, mass and temperature. Biological convection phenomena have been considered in this study due to their intermixing traits and capacity in order to enhance mass transit in numerous biotechnology and biological systems. The first objective of this study is to examine and establish the mathematical formulation comprising partial differential equations for energy, momentum, mass conservation and mobile microorganism conservation balances. To do numerical calculations, the controlling partial differential equations are initially transformed by similarity transformations into a collection of interconnected non-linear ordinary differential equations. These equations are then solved by using the MATLAB Bvp4c scheme. The results indicate that several controlling parameters, particularly bioconvection parameters such as the Lewis number ( Le ), Bioconvection Lewis parameter ( Lb ) and Bioconvection Peclet number ( Pe ), have significant effects on flow transfer rates. A dual solution is observed in a certain region of mixed convection λ , where the mixed convection parameter is within the range of 0.41–0.65. The findings reveal significant results from dual solution analysis, highlighting the occurrence of unstable and stable phenomena for specific values of bioconvection parameters exclusively in the case of opposing flow. The assisting flow demonstrates only a single solution that is physically stable and unique. Observing lower stagnation point flow is essential for predicting and analysing complex fluid–microorganism interactions in various scientific and engineering applications such as designing spherical-shaped microbial fuel cell. Optimising flow conditions can enhance the efficiency of processes like wastewater treatment, where microorganisms play a crucial role in breaking down pollutants.

Viscoelasticity of maxell fluid in a permeable porous channel

This study examines the flow dynamics and heat transfer characteristics of Maxwell fluid in a channel influenced by magnetohydrodynamics (MHD), Joule heating, thermal radiation, and boundary layer suction/blowing effects. The governing partial differential equations (PDEs) for momentum, energy, and concentration are transformed into ordinary differential equations (ODEs) using similarity transformations. The boundary value problem (BVP) is solved numerically using the bvp4c solver in MATLAB, yielding accurate solutions for velocity, temperature, and concentration profiles under various parameters. Key findings reveal that the porous parameter decreases the velocity profile but increases the temperature profile for both suction and blowing effects. Additionally, the MHD, Deborah, and Eckert numbers significantly influence the velocity and temperature profiles differently under these conditions. This study highlights the crucial role of integrating MHD, thermal, and boundary control effects to optimize performance and efficiency in engineering systems involving Maxwell fluids, with applications in polymer processing, biomedical engineering, electronics cooling, oil recovery, and chemical processing.

Computation of SWCNT/MWCNT-doped thermo-magnetic nano-blood boundary layer flow with non-Darcy, chemical reaction, viscous heating and Joule dissipation effects

CNTs have been shown to exhibit exceptional electrical and thermal conductivities, chemical and mechanical stability and physiochemical reliability in wide-ranging applications covering biomedicine, energy and aerospace. Motivated by emerging applications in nano-drug delivery in medicine and radiative ablation therapy, a steady-state mathematical model is established for magnetohydrodynamic boundary-layer transport of chemically reactive carbon nanotubes (CNTs)-doped electrically conducting blood along a porous stretching wall of a blood vessel. Multiple and single walls CNTs are considered using the model developed by Xue (2005). Heat generation, radiative flux, wall mass (concentration) slip, viscous heating and Joule magnetic dissipation are incorporated. Chemical reaction effects are addressed utilizing homogenous first-order model. The Darcy-Forchheimer drag force model is utilized for bulk matrix and inertial drag effects in the porous medium. Radiative heat-transport is studied considering Rosseland's diffusion model. The governing partial differential conservation equations for mass, momentum, energy and species are formulated in a two-dimensional Cartesian coordinate system with allied wall and free-stream boundary conditions. Via scaling transformations, a nonlinear boundary value problem is derived. Numerical computations are achieved through bvp4c scheme. The impact of selected parameters on dimensionless quantities (velocity, temperature, concentration, skin friction, local Nusselt and Sherwood numbers) are computed and elaborated through tables and graphs. A good correlation of the numerical solutions with earlier simpler models from the literature is included. The simulations show that with augmentation in Hartmann magnetic number and Forchheimer inertial drag number, significant damping in the nano-doped blood flow is produced for both SWCNTs and MWCNTs. Temperature is elevated with increment in dissipation effect i. e. Eckert number. Higher values of mass (solutal) slip parameter induce a depletion in the concentration. Nusselt number i. e. heat transfer rate to the blood vessel wall is improved with greater values of solid volume fraction for both CNTs. The present model is relevant to radiative ablation therapy combined with nano-medical treatments in blood vessels wherein constant mechanical loading via blood pressure and flow can elevate internal stresses (circumferential wall stress and endothelial shear stress) and induce morphological alterations in blood vessel wall (stretching) and endothelium in conjunction with biochemical reactions.

Analytical solution for MHD nanofluid flow over a porous wedge with melting heat transfer

This study employs the Hybrid Analytical-Numerical (HAN) method to investigate steady two-dimensional magnetohydrodynamic (MHD) nanofluid flow over a permeable wedge. Analyzing hyperbolic tangent nanofluid flow, the governing time-independent partial differential equations (PDEs) for continuity, momentum, energy, and concentration transform into a set of nonlinear third-order coupled ordinary differential equations (ODEs) through similarity transformations. These ODEs encompass critical parameters such as Lewis and Prandtl numbers, Brownian diffusion, Weissenberg number, thermophoresis, Dufour and Soret numbers, magnetic field strength, thermal radiation, power law index, and medium permeability. The study explores how variations in these parameters impact the velocity field, skin friction coefficient, Nusselt, and Sherwood numbers. Noteworthy findings include the sensitivity of fluid velocity to parameters like Weissenberg number, power law index, wedge angle, magnetic field strength, permeability, and melting heat transfer. The skin friction coefficient experiences a significant increase with specific parameter changes, while Nusselt and Sherwood numbers remain relatively constant. The local Reynolds number significantly affects Nusselt and Sherwood numbers, with a less pronounced impact on the skin friction coefficient. The study's uniqueness lies in employing the analytical HAN method and extracting recent insights from the results.

Analyzing the impact of convective boundary conditions on fluid–particle mixture flow in a ciliated walled horizontal tube filled with Rabinowitsch fluid

This study investigates the impact of convective boundary conditions, thermal radiation, and viscous dissipation on the flow of fluid–particle mixture in a ciliated walled horizontal tube filled with Rabinowitsch fluid. A mathematical model is developed using partial differential equations of continuity, motion, and energy, which are solved using the symbolic software MATHEMATICA 12.0 with convective boundary conditions. Exact solutions for velocity, temperature distribution, pressure gradient, pressure rise, stream function, and heat transfer rate are obtained and analyzed for dilatant, Newtonian, and pseudoplastic fluids. Computational results reveal that the velocity and temperature profiles are highest at the center of the tube for pseudoplastic and Newtonian fluids compared to dilatant fluid. Additionally, pressure gradient fluctuates near the tube walls. The study also explores special cases where the Rabinowitsch fluid model is reduced to dilatant, Newtonian, and pseudoplastic fluids. The findings have potential applications in medical treatments for respiratory system tumors, airway cleaning, physiological fluids, and manufacturing processes involving peristaltic flow. This original research contributes to the understanding of fluid dynamics in complex systems and has implications for various practical applications.

Energy and reserve procurement in integrated electricity and heating system: A high-dimensional covariance matrix approach based on stochastic differential equations

The integration of stochastic renewable energy sources into energy systems presents challenges due to flexibility insufficiency and uncertainty modeling inaccuracy. To address these challenges, this paper explores a high-dimensional covariance matrix approach based on stochastic differential equations (SDEs) for energy and reserve co-dispatch in integrated electricity and heating systems. By capturing the long-term correlation of wind power forecast errors, the SDE model simultaneously models point forecasts and high-dimensional positive-definite covariance matrices, resulting in a compact uncertainty set. To ensure computational efficiency, we employ duality theory to transform the stochastic co-dispatch problem with the high-dimensional uncertainty set into deterministic convex programming. Additionally, a virtual heat storage model is introduced for the district heating network, leveraging the thermal inertia of the network to enhance reserve capacity. Simulations validate the calibration and sharpness of the proposed high-dimensional uncertainty set. The results demonstrate that co-dispatch using the SDE-based uncertainty set reduces operational costs by 4.9% compared to a set that does not consider the long-term correlation of wind power, under a 95% coverage rate. Moreover, the storage capabilities of district heating pipelines and smart buildings provide cost-free reserves, saving the operational costs of the two test systems by 2.8% and 1.3%, respectively.

Modeling of artificial neural network to analyze heat and mass transfer of ternary hybrid nanofluid between two parallel plates with inclined magnetic field

The applications of the artificial neural network (ANN) have become the focus of interest of researchers due to their convenience for accurate modeling, simulation, and efficiency of evaluation. The primary objective of this study is to investigate the characteristics of heat and mass transfer of the ternary hybrid nanofluid flow (THNF), which is squeezed between two parallel plates, using ANN. The plate which lies on x-axis is stretching while the upper plate (UP) can move in upward and downward direction. An inclined magnetic field (MF) is also applied to the lower plate (LP). A system of partial differential equations of flow, energy, and mass transfer is used to simulate the THNF, which is then condensed using similarity substitution to a collection of ordinary differential equations (ODEs). Using the differential transform method (DTM), the resultant nonlinear ODEs in dimensionless form are further solved. The influence of the different varying physical parameters on velocity, temperature, and concentration is graphically presented and discussed. It becomes apparent that the velocity, heat, and mass transfer in squeezing flows are significantly impacted by the inclination angle of the applied MF. To demonstrate the validity of the study, the numerical findings of the Nusselt and the Sherwood numbers are provided. For the accuracy of the used approach, DTM results are compared with results from the numerical approach. The novelty of the current work is to train the neural network with the Levenberg–Marquardt algorithm in the model. To get the estimated output of the model, different scenarios are set for training, testing, and validation. The analysis is done by mean square error (MSE), histogram, fitness curve, and regression (RG). The created ANN model is shown to be reliable due to its exceptional accuracy throughout the training, validation, and testing stages.

Design and simulation of a novel reactor for the H2 storage mechanism in methylcyclohexane

The present study addresses the modeling and simulation of an intensified dehydrogenation reactor-heat exchanger system designed for a H2-based 2.0 MW mobile power plant. The reactor consisted of a multiple triple-tube system where the catalyst was packed in the middle tube while hot exhaust gases passed through the innermost and outermost tubes. A basecase design was defined and the reactor was simulated using the rigorous kinetics developed elsewhere for the MCH dehydrogenation. The parabolic differential equations of mass and heat energy were solved and the axial and radial conversion and temperature profiles were computed. Moreover, the effects of the number of longitudinal fins on the reactor tubes as well as the flow direction were also studied. With 12 number of fins on the reactor tube, the MCH conversion increased from 70.8% to 81.8%, with a corresponding increase in the average bed temperature from 569.3 K to 577.6 K and hydrogen yield from 37.05 kmol h−1 to 42.79 kmol h−1.

Holographic massive plasma state in Friedman universe: cosmological fine-tuning and coincidence problems

Massive particle and antiparticle pair production andoscillation on the horizon form a holographic and massive pair plasma state in the Friedman Universe. Via this state, the Einsteincosmology term (dark energy) interacts with matter and radiation and is time-varying Λ̃ in the Universe's evolution.It is determined by a close set of ordinary differential equations for dark energy, matter, and radiation energy densities. The solutions are unique, provided the initial conditions given by observations.In inflation and reheating, dark energy density decreases from the inflation scale, converting to matter and radiation energy densities.In standard cosmology, matter and radiation energy densities convert to dark energy density, reaching the present Universe. By comparing with ΛCDM, quintessence and dark energy interacting models, we show thatthese results can be the possible solutions for cosmological fine-tuning and coincidence problems.

Evaluation of the effect of rotational speed and rheological nature on heat transfer of complex fluid between two cylinders

This paper presents numerical results for flow behavior between a cold inner cylinder and a hot outer cylinder. Both cyl-inders are placed horizontally. The space separating the two compartments is completely filled with a fluid of a complex rheological nature. In addition, the outer container is subjected to a constant and uniform rotational speed. The results of this work were obtained after solving the differential equations for momentum and energy. The parameters studied in this research are: the intensity of thermal buoyancy, the speed of rotation of the outer container and the rheological nature of the fluid. These elements are expressed mathematically by the following values: Richardson number (Ri = 0 and 1), Reyn-olds number (Re = 1 to 40), power-law number (n = 0.8, 1 and 1.4) and Prandtl number (Pr = 50). The results showed that the speed of rotation of the cylinder and the rheological nature of the fluids have an effective role in the process of heat transfer. For example, increasing the rotational speed of the enclosure and/or changing the nature of fluid from shear-thickening into shear-thinning fluid improves the thermal transfer rate.

Analysis of chemical reactive nanofluid flow on stretching surface using numerical soft computing approach for thermal enhancement

ABSTRACT In this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem’s consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10−06–10−08, 10−05–10−10 and 10−06 05–10−09. In order to reduce mean square error, the nonlinear fluid dynamics system’s numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified.

Flow field and heat transfer characteristics in dimple pipe with different shape of dimples

In this work, a numerical study of a thermal performance of water flow inside a dimpled pipe. The effect of three types of dimples (circular, square and rhombus) studied in the numerical simulation. A commercial program called ANSYS was used to model the flow through a circular pipe .The three-dimensional governing differential equations of mass, momentum, and energy were used together with the (K − ε ) model to evaluate the impact of dimples on a turbulent flow and the velocity field. The study was carried out in the Reynolds number (Re) range (2500–15000). The research results demonstrate that the presence of a dimple on the pipe surface greatly increases the rate of heat transmission and the friction factor compared to a normal smooth pipe. Also, the numerical study demonstrated that the Nusselt number (Nu) in case of circular dimples at diameter (4 , 6 and 8) mm was (22, 28 and 43) % greater than the smooth surface. It is discovered that the improved pipe with circular dimples have a benefit for increased heat transmission efficiency compared with the square and rhombus dimples. Additionally , circular dimples have the ability to supply the lowest friction factor (f) when compared to other types of dimple. The pipe with circular dimples with D= 4mm , at Reynolds number 2500 provided the largest thermal performance criterion (PEC) value about 1.44.

Insight into the peristaltic motion through a tapered channel with Newton’s cooling subject to viscous dissipation, Lorentz force, and velocity slip

Peristalsis has gained significant attention due to its numerous applications in the medical field, engineering, and manufacturing industries. Therefore, the current work intends to look into the effects of variable liquid properties on the magnetohydrodynamics of peristaltic flow exhibited by viscous fluid through a tapered channel. The viscosity of the liquid differs over the thickness of the channel, and temperature-dependent thermal conductivity is considered. The constitutive relation for energy is formulated with the addition of viscous dissipation and heat generation/absorption. The assumption of velocity slip along with the convective boundary condition energizes the thermal system as well as the flow phenomena. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution were obtained for the resulting non-linear differential equations of momentum and energy for small values of variable viscosity and variable thermal conductivity. The effects of various relevant parameters on flow properties were investigated through graphical analysis. The results show that the maximum velocity does not occur in the middle of the tapered channel, but moves toward the upper wall with the increase in the variable viscosity difference between the walls. The application of viscosity is essential in many engineering and industrial processes.

Entropy analysis of electromagnetic trihybrid nanofluid flow with temperature-dependent viscosity in a Darcy-Forchheimer porous medium over a stretching sheet under convective conditions

This study introduces a novel theoretical model known as the trihybrid nanofluid (THNF), which demonstrates remarkable thermal conductivity properties to enhance heat transfer in liquids. The base liquid (H2O) was employed to immerse nanoparticles of Cu, Al2O3, and TiO2, thereby resulting in the creation of a THNF (Cu + Al2O3 + TiO2/H2O). This research focuses on the entropy generation of electromagnetic THNF flow in a Darcy-Forchheimer porous medium over a stretching sheet under convective conditions. The analysis considers the intricate interplay between various factors, including convection, radiation, heat source, chemical processes, and cross-diffusion effects. Complex partial differential equations for flow, energy, and concentration are transformed into nonlinear ordinary differential equations using similarity transformations. The Runge–Kutta–Fehlberg method with a shooting mechanism is used to solve these ODEs. The comprehensive graphical analysis visually exemplifies the impact of significant parameters on the profiles of velocity, temperature, and concentration, in conjunction with skin friction, Nusselt, and Sherwood numbers. The flow velocity decreased by 8.89 % in NFs with higher viscosity and Darcy-Forchheimer porous medium values, but it accelerated by 13.64 % in THNF with more convection. Electric fields boost THNF velocity and temperature by 20.94 % and 14.27 % respectively, while stronger magnetic fields reduce NF velocity by 15.34 % and elevate THNF temperature by 7.52 %. THNFs show the largest temperature increase of 18.67 % due to radiation, while it decreases by more than 7.51 % for NFs with an increasing Prandtl number. NP concentration drops by 10.19 % when Schmidt and chemical reactions increase. Elevating electric and magnetic fields can reduce heat transfer by 4.78 % and entropy generation by at least 6.45 % in NFs, while increasing the Bejan number by up to 18.83 % in THNFs. Radiation and diffusion increase the entropy generation by 6.71 % and decrease the Bejan number by 7.98 %.

Analysis of the Exothermic Reaction of Flame Ignition in the Combustion Chamber of a Gas Turbine Unit

This article analyses the exothermic reaction of flame ignition in the combustion chamber of a gas turbine unit, which is characteristic of combustion chambers operating on traditional hydrocarbon fuels. The combustion of gases as an explosive process in confined and semi-enclosed areas remains a poorly understood section of thermal physics. Without a detailed review of the physical and chemical processes taking place in the combustion chamber, it cannot be said whether the gas turbine unit will run sustainably. It is also important to know what combustion modes are in principle possible after a loss of stability in the combustion chamber in order to take action against this in advance. To describe flame ignition and quenching in the flow of the fuel–air mixture through a combustion chamber, a system of differential conservation equations of energy and reactive species supplemented with the equation of state is used. Nonstationary combustion processes in gas-turbine engines were studied, and flame ignition and blow-off were determined by the heat balance and by the continuity of chemical processes. Calculation methodologies for various operating modes of the combustion chamber of a gas turbine unit are developed and realized. The results of the calculations that were carried out are presented with graphical interpretation and with their analysis provided in sufficient detail. Based on this analysis, recommendations are then provided. From the graphs, it can be observed that the combustion chamber of a gas turbine unit reaches its maximum limit of stable operation at the optimum value of the reduced flow velocity in the openings of the air supply to the combustion and the mixing zones of the flame tube (λOC)opt = 0.22 when the fuel–air mixture is at maximum depletion, ensuring that combustion does not stop and flame failure does not occur. The topic of this article relates to the intensification of hydrocarbon fuel combustion and the technological improvement of combustion chambers in gas turbine units. This topic is of exceptional importance and relevance, emphasizing its significance. The purpose of this work is to develop and implement a methodology for calculating various modes of operation of the combustion chamber of a gas turbine unit.

Heat and mass transfer correlations of supercritical n-decane considering the influence of pyrolysis reaction by simplifying internal heat and mass sources as pseudo-wall fluxes

The convective heat and mass transfer characteristics of the supercritical pressure (SCP) fuel in the regenerative cooling channel of hypersonic vehicles are significantly affected by pyrolysis reactions. In this study, we proposed a novel method to develop the Nusselt number (Nu) and Sherwood number (Sh) correlation of SCP fuel that considers the influence of pyrolysis reaction by simplifying internal heat and mass sources as pseudo-wall fluxes based on the differential global reaction (DGR) model of pyrolysis. The convective heat and mass transfer and pyrolysis characteristics of n-decane were investigated experimentally and numerically in a vertical downward-flow heated tube at pressures of 3-7 MPa. Theoretical analysis of the experimental conditions was conducted sequentially according to the partial differential equations (PDEs) of species continuity and energy, in which the internal source terms of heat and mass due to pyrolysis reactions were simplified and predicted using the DGR model of n-decane pyrolysis. A semi-empirical Sh correlation for predicting the radial distribution of fuel conversion was proposed associated with computational fluid dynamics (CFD) data by equivalently simplifying the internal mass source as pseudo-wall mass flux. A Nu correlation for convective heat transfer was proposed using the same methodology considering the influences of pyrolysis. The correction terms consider pyrolysis endothermicity and thermophysical property variation due to the conversion differences between the pipe wall and the bulk flow. Finally, the Nu correlation was compared to the experimental data, and the influence of heat transfer deterioration (HTD) due to pyrolysis coking was also analyzed quantitatively and empirically.

Computational method for energy transport of MHD nanofluids flow near non-aligned stagnation point with non-linear thermal radiation and interface slip

Haemodialysis, nuclear reactors, cooling and heating systems, and heat exchangers are glimpses of applications where thermal problems are considered as a fundamental for flow over aligned stagnation points with heat and mass transfer components. The purpose of this study is to present steady dual solutions for non-aligned stagnation point flow of nanofluid over a linearly contracting/expanding surface under temperature and velocity slips. The mathematical model is established using boundary layer assumption. The authors acknowledge from prior investigations and studies that the non-aligned stagnation point flow across a contracting/expanding surface is highly rare in the field of engineering and fluid dynamics research. In the backdrop of non-linear thermal radiation, the problem of oblique hydromagnetic stagnation point flow of an electrically conducting optically dense viscous incompressible nanofluid across a convectively heated stretching sheet is formulated. The effects of Brownian motion and thermophoresis are incorporated into the nanofluid model. With the use of appropriate similarity transformations, the governing nonlinear partial differential equations for momentum, energy, and nanoparticle concentration are converted into a set of nonlinear ordinary differential equations. Using the BVP4c approach, the modified equations are numerically solved. It is discovered that when the strength of the magnetic field increases, the non-alignment of the re-attachment point on the sheet surface becomes less pronounced. The thickness of the thermal boundary layer grows as the magnetic and Biot parameters expand. The extent of the skin friction factor ascends with increasing magnetic field and suction variable inputs. The heat transfer rate detract with radiative parameter.

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.