Dissipative Effects Research Articles

Targeted Energy Transfer Evaluation for Nonlinear Vibrations of Elastic Medium-Finite Length Beam System Using Nonlinear Energy Sink Theory

The elastic medium can usually reduce the vibration of supporting structure, and the impact of the interaction on the vibration characteristics of the structure is similar to the characteristic of nonlinear energy sink. At present, the dynamic research of beam on elastic foundation considering soil motion has been paid more and more attention. According to the modified Winkler model, the finite-depth elastic medium can be considered to the nonlinear energy sink mass, and the vibration energy dissipation capacity and parameter optimization of the elastic medium supporting finite-length beam under half sine pulse are studied. The Galerkin truncation is applied to the discretization of the governing equations. The numerical solution of the beam coupling system with simple support on the elastic medium is obtained by applying the fourth-order Runge–Kutta method. Based on this, the input energy ratio of the elastic medium dissipation is investigated. Furthermore, through the analysis and optimization of targeted energy transfer and dissipation, the dissipation effect of the finite range elastic medium on the vibration energy of its supporting beam is revealed, and the optimal parameter range of the elastic medium is proved. The results show that after adjusting the elastic medium parameters by technical means, the nonlinear energy sink can absorb most of the vibration energy of the beam quickly and effectively, and the optimal energy dissipation ratio can reach 95.16[Formula: see text]. The quantitative evaluation of the energy dissipation in elastic medium within soil–structure interaction effect is realized.

Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle

Abstract The thermo-diffusion applications of nanofluid subject to variable thermal sources have been presented. The significance of Darcy–Forchheimer effects is attributed. The flow comprises the mixed convection and viscous dissipation effects. Furthermore, the variable influence of viscosity, thermal conductivity, and mass diffusivity is treated to analyze the flow. The analysis of problem is referred to convective mass and thermal constraints. The analytical simulations are proceeded with homotopy analysis method. The convergence region is highlighted. Novel physical contribution of parameters is visualized and treated graphically. It is noted that larger Brinkman number leads to improvement in heat transfer. The concentration pattern boosted due to Soret number. The wall shear force enhances with Hartmann number and variable thermal conductivity coefficient.

Nonlinearly induced entanglement in dissipatively coupled optomechanical system

Nonlinearly induced steady-state photon–phonon entanglement of a dissipative coupled system is studied in the bistable regime. Quantum dynamical characteristics are analysed by solving the mean-field and fluctuation equations of the system. It is shown that dissipative coupling can induce bistable behaviour for the effective dissipation of the system. Under suitable parameters, one of the steady states significantly reduces the dissipative effect of the system. Consequently, a larger steady-state entanglement can be achieved compared to linear dynamics. Furthermore, the experimental feasibility of the parameters is analysed. Our results provide a new perspective for the implementation of steady-state optomechanical entanglement.

Analytical analysis of water and engine oil base nanofluid flow with the influence of viscous dissipation and variable viscosity on stretching surface

AbstractIn this study, we will look at the analytical characterization of water and motor oil‐based nanofluid flow and the effects of viscous dissipation and variable viscosity on stretching surfaces. The primary goal of this research is to improve heat transfer efficiency in a range of systems, including cooling applications, refrigeration systems, and heat exchangers. The addition of nanoparticles to the base fluid increases its thermal conductivity, which boosts heat transfer rates. The flow system considers the impact of viscous dissipation. In addition, this methodology accounts for temperature and velocity slips during stretching. We utilized the proper transformations to convert a set of PDEs to NLODEs. To solve this system of equations, we use hybrid nanofluid. The impact of different parameters obtained from temperature and velocity equations involving the porosity parameter, power law number, ratio velocity, dynamic viscosity, Forchheimer parameter, and Eckert number input factors are shown in the form of graphs.

Numerical insights of fractal–fractional modeling of magnetohydrodynamic Casson hybrid nanofluid with heat transfer enhancement

Fractional calculus expands the idea of differentiation to fractional/non‐integer orders of the derivatives. It includes the memory‐dependent and non‐local system's behaviors while fractal–fractional derivatives is the generalization of fractional‐order derivatives which refers to a combination of fractional calculus and fractal geometry. In this article, we have considered the magnetohydrodynamic (MHD) flow of Casson hybrid nanofluid through a vertical open channel with the effect of viscous dissipation and Newtonian heating. The problem is modeled in terms of non‐linear and coupled integer‐order PDEs which is further generalized through fractal–fractional derivative of power law kernel. Due to non‐linearity and complexities, we have adopted the numerical procedure as it is used when the analytical solutions of PDEs are frequently difficult or impossible for complicated situations. We have established the numerical algorithms for both the classical and fractal–fractional‐order model and compared the results. The existence and uniqueness of the model's solution has been shown theoretically. The effect of various embedded parameters on the heat transfer and fluid flow has been simulated and presented through various figures while skin friction and Nusselt number are tabulated. The effect of fractional and fractal parameter is also shown. As the present model is taken for the hybrid nanofluid flow and for the heat transfer applications, we have considered mineral transformer oil as a base fluid while titania and cadmium telluride nanoparticles are dispersed in it. From the results, it is observed that hybrid nanofluid have a better heat transfer enhancement up to 19.71% while the unitary nanofluids are only capable to enhance the heat transfer up to 9%.

Effects of thermal boundary conditions on Stokes' second problem

In this investigation, an infinite flat plate is employed to examine the flow behavior of Casson fluid and the associated heat transfer phenomena. The plate undergoes an initial acceleration with a constant velocity until it eventually decelerates to rest. The energy equation incorporates the effects of viscous dissipation. An appropriate similarity transformation transforms the governing equations into coupled nonlinear ordinary differential equations (ODEs). A closed-form solution for the velocity profile is obtained, while the energy equation is solved using the built-in function NDSOLVE in Mathematica. The study investigates the influence of governing parameters on dimensionless velocity, temperature, skin friction, and local heat transfer rate under two thermal boundary conditions: Newtonian heating and convective boundary conditions. The fluid's thermophysical properties remain constant throughout the study, with the surface temperature of the plate assumed to be fixed at a constant value. A graphical analysis examines the flow behavior and temperature distribution, revealing the impact of non-dimensional parameters. This study reveals that thermal boundary conditions significantly influence heat transfer rates, with Newtonian heating leading to an increase and convective heating causing a decrease. This is attributed to the direct application of heat at the boundary in Newtonian heating, which enhances thermal energy transfer. In contrast, convective heating disperses heat through fluid motion, limiting transfer rates.

Viscous dissipation and Joule heating effects of Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk

In this piece of communication, a theoretical investigation of two dimensional boundary layer flow of Magnetohydrodynamics (MHD) Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk is made. The investigation includes the effects of viscous dissipation, Joule heating, thermal radiation, suction/injection, Darcy–Forchheimer porosity model and binary chemical reaction with activation energy, etc. To examine the impacts of the aforementioned effects, the conservation laws are formulated with strongly nonlinear partial differential equations (PDEs), which are then transformed into a system of initial value problems (IVPs) using appropriate similarity transformations and techniques. The 5th order Runge–Kutta with the shooting technique is used to find numerical solutions aided by Python programming with built in program “fsolve”. The method is validated with other published articles under common assumptions and it agrees nicely. The impacts of the pertinent parameters on velocity, temperature, concentration, skin friction coefficient and the rates of mass and heat transfers with in the flow regime are displayed using graphs and tables. The main outcomes include the motivation of local Nusselt and Sherwood numbers for shear thickening (n=1.5) than shear thinning (n=0.5) cases of the Carreau nanofluid. The momentum boundary layer of the Carreau nanofluid gets thinner with an increase in Forchheimer number, unsteady and suction parameters. A dual nature is observed for concentration of the Carreau nanofluid with a rise in Eckert number, i.e increasing in concentration around the wall and decreasing far away from the wall. The rise in destructive and constructive chemical reaction parameters disperse and accumulate the concentration of the system, respectively.

Modeling viscous dissipation in MHD boundary layer flow: A two-stage in time and compact in space finite difference approach

It is suggested that an explicit-implicit third-order in-time numerical scheme be used to solve time-dependent partial differential equations (PDEs). A fourth-order compact scheme in space is adopted for discretizing space variables. The work creatively blends a third-order explicit-implicit numerical scheme in time with a fourth-order compact scheme in space to solve time-dependent PDEs. Notably, the proposed numerical scheme demonstrates stability for scalar PDEs and exhibits convergence for both linear and nonlinear PDE systems. In addition, a mathematical model is given for the heat transfer of magnetohydrodynamic (MHD) flow over flat and oscillatory sheets, and the effect of viscous dissipation is also considered. For various governing parameters, features of the flow and heat transfer characteristics are discussed and examined. Some results are verified using an exact solution. We use an explicit-implicit finite difference method guaranteed to be stable and convergent under all conditions to solve the coupled nonlinear partial differential equations that describe this problem. Physical aspects of the problem are discussed in light of the system’s embedded parameters, and numerical and graphical results are presented. To sum up, progress in our knowledge of such systems relies heavily on creating an accurate and efficient numerical scheme for modeling MHD boundary layer flows while considering the influence of viscous dissipation. This study aims to improve the current state of MHD flow simulations and provide a useful resource for engineers and scientists engaged in developing and improving MHD-based technologies.

Time-dependent hydromagnetic convective transport upon a vertical perforated sheet with heat production and viscous dissipation effects

This research analysed the theoretical influences of viscous dissipation and heat production on an unstable hydromagnetic free convective transference upon a vertical porous sheet. The converted conservation equations are resolved numerically with suitable boundary conditions by exerting the similarity techniques. Then the coupled ODEs is resolved by inserting the finite difference method (FDM). The influences of the working dimensionless numbers or parameters on the flow, concentration and temperature fields, the mass transmission rate, the coefficient of local skin friction, and the heat transmission rate examined and discussed quantitatively with the aid of graphs. The findings show that as the Eckert number rises, the temperature and fluid velocity both advance along with the heat generation parameter. The f ′ ( 0 ) increases by around 8% and 12% due to uprising amounts of the heat generation parameter from 1.0 to 2.0, and the Eckert number from 0.5 to 2.5, respectively. Growing amounts of the heat generation parameter from 1.0 to 2.0 and Eckert number from 0.5 to 2.5, the heat transmission rate lessens by around 63% and 52%, respectively. The comparable outcomes are good coincided with a published article.

Structural Design and Strategy Optimization of PEMFC in Thermal Management

Due to growing energy and environmental issues, clean energy technology has gained recognition around the world. Because of its great energy transfer efficiency, outstanding power density, low operational temperatures, and environmental protection, PEMFC has been employed extensively in a variety of fields. But the thermal management of PEMFC has been a great challenge limiting its commercialization. Ineffective heat management strategies can shorten the fuel cell battery's lifespan in addition to affecting its performance. Therefore, this study provides an overview of how fuel cell bipolar plate structure and thermal management techniques have improved fuel cell performance. The results show that the tree-shaped fractal fuel cell bipolar plate, novel tapered dual serpentine channel and so on can enhance the heat dissipation effect of the bipolar plate and the temperature uniformity of the MEA, and form a uniform temperature distribution and pressure. Process strategies such as the new thermal management system with a thermal peak regulator can efficiently regulate the peak temperature and the average temperature of the fuel cell system to improve its starting performance. Most importantly, this research can help to alleviate the energy tension and reduce the environmental pressure.

Entropy generation on MHD motion of hybrid nanofluid with porous medium in presence of thermo-radiation and ohmic viscous dissipation

Hybrid nanotechnology has significantly contributed to enhancing energy efficiency and reducing heat loss. This study addresses entropy analysis in the motion of hybrid nanofluids incorporating magnetohydrodynamic effects, thermal radiation, and ohmic viscous dissipation phenomena. The implementation of magnetohydrodynamic, thermal radiation, and dissipation effects allows for a second law of thermodynamics analysis. The hybrid nanoparticles considered are Graphene Oxide (GO) and Molybdenum Disulphide (MoS2), with water serving as the base liquid. Entropy generation analysis, a thermodynamic approach, quantifies irreversibility and inefficiencies within the system, aiding in understanding losses and identifying areas for improvement. Additionally, a comparative study is conducted. The BVP4C algorithm, implemented using MATLAB, is employed to address this study and obtain solutions. The key findings indicate that heat transfer rates are higher for blade-shaped nanoparticles, and entropy is minimized by controlling parameters such as the radiation parameter, Brinkman parameter, and temperature difference.

Entropy generation due to MHD Falkner–Skan flow of Casson fluid over a wedge: A numerical study

AbstractThis study highlights the significance of entropy generation in the Falkner–Skan flow of Casson fluid past a wedge. To investigate the energy analysis, the governing equations include the heat transport equation in the presence of internal heat source, and the energy transport accounts for heat dissipation using viscous dissipation and Joule heating effect. The mathematical formulation of the problem leads to a set of nonlinear coupled partial differential equations. To obtain a similarity solution, similarity variables are introduced. The resulting differential equations are solved numerically using the shooting technique in conjunction with the Runge–Kutta–Fehlberg 45 (RKF‐45) method. Graphical representations are utilized to demonstrate the physical significance of the relevant parameters. The study analyzes the impact of various parameters on the velocity, temperature, and entropy distributions for three wedge positions: stationary, forward‐moving, and backward‐moving. The results show that an increase in the wedge angle parameter and Casson parameter leads to an increase in fluid velocity, while fluid entropy increases rapidly with an increase in the Brinkmann number, power law Falkner–Skan parameter, and Reynolds number. Moreover, with an increment in the Prandtl and Eckert number, the Nusselt number coefficient decelerates for both static and moving wedge.

Linear stability analysis of MHD mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation

PurposeThis paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel.Design/methodology/approachThe treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method.FindingsAnalysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances.Originality/valueLinear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation.

Significance of shape factor on magnetohydrodynamic buoyancy thin film flow of nanofluid over inclined sheet with slip condition: Irreversibility analysis

This work aims to examine the entropy production, heat transport, and dynamics of the unsteady thin film magnetohydrodynamic (MHD) flow of a nanofluid composed of alumina (Al2O3) and water. The fluid flow is seen to pass over an inclined sheet, taking into account the effects of buoyancy force, viscous dissipation, and joule heating. The system of partial differential equations (PDEs) is optimized under the boundary layer assumptions. Appropriate transformations are used to convert the governing partial differential equations (PDEs) and boundary conditions into dimensionless forms. Using MATLAB’s bvp4c code and a local non-similarity technique with up to second-degree truncation, we can obtain the findings of the enhanced model. The effect of multi-shape Al2O3 nanoparticles on flow, heat, and entropy-generating features is also investigated after the calculated results have been successfully aligned with published data. Mixed convection, nanoparticle volume percent, inclination angle, magnetic field intensity, mass suction, Eckert number, and Biot number are only a few of the governing parameters whose effects are graphically shown for selected values. As a result, the local Nusselt number and skin friction coefficient may be calculated. The skin friction and Nusselt number profiles exhibit a decreasing trend as the values of nanoparticle volume fraction ([Formula: see text]) magnetic [Formula: see text] and unsteadiness (A) increase toward mixed convection ([Formula: see text]). On the other hand, Nusselt number profile increases with increasing values of mass suction parameter [Formula: see text] The profiles of entropy generation and Bejan number show an upsurge as the values of the magnetic parameter [Formula: see text] and Brinkman number (Br) increase. Conversely, the entropy generation reduces with an increase in the temperature difference parameter [Formula: see text] and Bejan number increases.

Influence of thermal radiation and shape factor on a hybrid nanofluid flow over a permeable flat plate with cross-diffusion effects: An irreversibility analysis

Understanding and controlling the shape factors of nanoparticles in fluid flow problems is crucial for optimizing heat transfer, fluid dynamics, and various applications such as nanofluids, drug delivery systems, catalysis, and nanocomposites. By tailoring the shape of nanoparticles, researchers can manipulate their behavior, dispersion, and interaction with the fluid, thereby optimizing the desired outcomes in various fluid flow problems. The meticulous investigation uncovers the integration of entropy analysis in the investigation of the flow of convective magnetohydrodynamic hybrid nanofluid via a permeable flat surface, by considering the effects of Dufour, viscous dissipation, Soret, and thermal radiation. The governing equations are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved using the bvp4c solver, a MATLAB in-built function. We display the outcomes for three different shape factors: platelet, cylinder, and brick. The skin friction coefficient increases at a rate of 1.5089 for the brick shape, 1.5163 for the cylindrical shape, and 1.5212 for the platelet shape when the mixed convection parameter lies between 1 and 5. In this regard, it is important to point out that there is a direct connection between the increase in temperature transmission rate and a decline in the Dufour number ( Du ). It has been found that when 1 ≤ Du ≤ 2.4 , the Nusselt number decreases by 0.4786, 0.4618, and 0.4512 for brick, cylinder, and platelet shapes, respectively. A decline in the Sherwood number is noticed with an upsurge in the Soret number ( Sr ). There is a noticeable increase of 0.0442 in the Sherwood number for brick shape, 0.0438 for cylinder form, and 0.0435 for platelet form when 1 ≤ Du ≤ 2.4 . Furthermore, we have detected that an increase in the radiation parameter amplifies both the Bejan number and the profiles of entropy formation.

Parametric simulations of fractal-fractional non-linear viscoelastic fluid model with finite difference scheme

Fractal-fractional derivatives are more general than the fractional derivative and classical derivative in terms of order. Fractal-fractional derivative is used in those models where the classical continuum hypothesis theory fails. More precisely, these derivative operators are used where the surface or space is discontinuous, e.g., porous medium. Fractal-fractional derivative is considered advance tool to analyze the fluid dynamic model more than fractional and classical model. Given the extensive applicability of fractal-fractional derivatives, the current analysis focuses on investigating the behavior of a non-linear Walter’s-B fluid model under the influence of time-varying temperature and concentration During the simulation process, we have also taken into account the effects of first-order chemical reactions, Soret numbers, thermal radiation, Joule heating, and viscous dissipation of energy. A magnetic field with a strength of B0 was applied to the left plate in the transverse direction. The classical mathematical model was first developed using relative constitutive equations and later generalized with the fractal-fractional derivative operator. Numerical solutions to the generalized model have been obtained using the finite difference method. Various graphs are drawn from the obtained numerical solutions to study the influence of physical parameters on the rheology of Walter’s-B fluid. It has been observed that by varying the fractional and fractal order of the generalized model, one can easily derive fractal, fractional, and classical models.

Transition Threshold for the 3D Couette Flow in a Finite Channel

In this paper, we study nonlinear stability of the 3D plane Couette flow ( y , 0 , 0 ) (y,0,0) at high Reynolds number R e {Re} in a finite channel T × [ − 1 , 1 ] × T \mathbb {T}\times [-1,1]\times \mathbb {T} . It is well known that the plane Couette flow is linearly stable for any Reynolds number. However, it could become nonlinearly unstable and transition to turbulence for small but finite perturbations at high Reynolds number. This is so-called Sommerfeld paradox. One resolution of this paradox is to study the transition threshold problem, which is concerned with how much disturbance will lead to the instability of the flow and the dependence of disturbance on the Reynolds number. This work shows that if the initial velocity v 0 v_0 satisfies ‖ v 0 − ( y , 0 , 0 ) ‖ H 2 ≤ c 0 R e − 1 \|v_0-(y,0,0)\|_{H^2}\le c_0{Re}^{-1} for some c 0 > 0 c_0>0 independent of R e Re , then the solution of the 3D Navier-Stokes equations is global in time and does not transit away from the Couette flow in the L ∞ L^\infty sense, and rapidly converges to a streak solution for t ≫ R e 1 3 t\gg Re^{\frac 13} due to the mixing-enhanced dissipation effect. This result confirms the threshold result obtained by Chapman via an asymptotic analysis(JFM 2002). The most key ingredient of the proof is the resolvent estimates for the full linearized 3D Navier-Stokes system around the flow ( V ( y , z ) , 0 , 0 ) (V(y,z), 0,0) , where V ( y , z ) V(y,z) is a small perturbation(but independent of R e Re ) of y y .

Effects of Hall, ion slip, viscous dissipation and nonlinear thermal radiation on MHD Williamson nanofluid flow past a stretching sheet

This work aims to explore the effects of ion slip and Hall current on the flow of MHD Williamson nanofluid over a stretching plate in the presence of chemical reaction, viscous dissipation, ohmic (Joule) heating, nonlinear thermal radiation, and heat generation/absorption. After using appropriate similarity transformations, the highly nonlinear governing partial differential equations are transformed to a system of ordinary differential equations. The subsequent non-linear problems are treated to numerical results by reducing the converted nonlinear ODE in to first order. The fifth-order Runge–Kutta method along with the shooting approach is implemented using the python programming tool to analyze the problem. Graphical representations have been used to investigate the impacts of the derived physical parameters on the temperature, velocity, and concentration distributions of nanoparticles with the goal of giving each parameter a physical interpretation. The study of the effects of various physical parameters on the skin friction coefficient, the local Nusselt number and the Sherwood number was finally explained with the help of graphs and tables. It is discovered that when the Williamson parameter increases, both the principal and secondary velocity profiles decline but the temperature and concentration profiles rise. Both the Hall parameter and ion slip effect produce similar results with increasing principal velocity profile and decreasing secondary velocity, temperature and concentration profiles. Furthermore, it is seen that the temperature and concentration profiles increase in response to an increase in the nonlinear thermal radiation parameter. The increment in Eckert number (viscous dissipation term) also showed enhancements in temperature and concentration profiles. Additionally, the primary skin friction coefficient and rate of mass transfer are accelerated by raising the magnetic field parameter, Williamson parameter, or Darcy number, but the heat transfer rates are slowed down in the boundary layer. Lastly, the obtained results were cross-referenced with earlier findings, considering specific assumptions, to establish the credibility of the results. The comparison revealed that the new results provided valuable and profound insights into the studied phenomenon.

Mathematical modeling of Cross‐fluid model in a peristaltic channel with viscous dissipation and MHD effects

AbstractIn this analysis, Cross‐fluid model along wall properties is investigated. Impact of the magneto‐hydrodynamic on the non‐Newtonian model is also considered. Numerical algorithm MATLAB bvp4c function is adopted for the solution of coupled nonlinear equations along long‐wavelength and low Reynolds number approximations. Viscous dissipation phenomena are counter to discuss the energy possession during flow. Fluid velocity and stream lines for the flow are also precisely determined in this analysis. The various parameters that influence the physical characteristics of flow are plotted through the graph, and their effects are discussed in detail. From the conclusions, the consequence of the flow model parameters is found to be substantial and also noted that the present model has the potential applications to comprehend the bile conduit drive via bladder, gallstones, and blood flow features in living organisms in a much better way than prior.

Effects of viscous dissipation, gravity modulation and Joule heating on MHD Casson fluid flow over a vertically moving plate with second-order slip velocity

The study of magnetohydrodynamic flow problems for non-Newtonian fluids is significant in many engineering problems. The current inquiry is concerned with a time-dependent, incompressible magnetohydrodynamic Casson fluid flow in a vertically moving plate. The aim of this study is to analyse the effect of viscous dissipation, gravity modulation, heat source and Joule heating with second-order slip velocity. Governing equations are converted to non-dimensional ones using appropriate similarity transformations. To solve the altered equations, the perturbation method is applied, together with MATLAB software. The important physical outcome of this research is that the gravity modulation parameter increases the temperature and velocity of fluid inside the boundary layer. The Eckert number enhances the fluid velocity, concentration boundary layer, skin friction and Nusselt number, whereas the temperature boundary layer reduces for heat sink parameter. The permeability of the porous parameter raises the fluid’s concentration. The work of Kodi et al. [2021. “Investigation of MHD Casson Fluid Flow Past a Vertical Porous Plate Under the Influence of Thermal Diffusion and Chemical Reaction.” Heat Transfer 51 (1): 377–394] has been expanded in this study by adding the novel effects of gravity modulation, Joule heating and viscous dissipation. In addition, the boundary condition includes second-order slip velocity. The obtained results are compared with Kodi et al. [2021. “Investigation of MHD Casson Fluid Flow Past a Vertical Porous Plate Under the Influence of Thermal Diffusion and Chemical Reaction.” Heat Transfer 51 (1): 377–394] and it shows an excellent agreement when added effects are neglected.