Impacts of variable viscosity and chemical reaction on Ohmic dissipative fluid flow in a porous medium over a stretching sheet with thermal radiation

This study investigates the chemical reaction influence on heat transfer flow of viscous Newtonian fluid over a moving surface under the intensity of nonuniform heat source/sink. Variable fluid viscosity and ohmic heating effects are considered in the model equation. The uniqueness of the present investigation is to scrutinize the significance of nonuniform heat source/sink and ohmic heating on the heat transfer flow of optically thin radiative fluid in a permeable medium. The flow equations of continuity, momentum, thermal and solutal fields are converted by invoking relevant dimensionless variables. Also, the converted nonlinear equations are analyzed numerically by using the fourth order Runge–Kutta Fehlberg approach. The significance of model parameters are scrutinized and discussed in detail via graphs and tables. The important findings of this study are the effects of Joule heating $J$, viscous dissipation parameter $B_r$, variable fluid property parameter $ϵ$ and radiation parameter $R_a$ on fluid flow, energy profile and solutal field. The results show that the thermal field depreciates as the Prandtl number increases but escalates against higher values of Joule heating parameter and Brinkman number. Also, the outcome of this study reveals that an enhancement in the values of variable viscosity parameter declines velocity distribution. Concentration distributions behave as a growing function of the Soret number and diminishing function of the Schmidt number. Furthermore, contrasting this study with existing results reveals excellent agreement.     

Heat and mass transfer effects on fluid past an exponentially accelerated vertical plate due to time-fractional MHD-free convection

This article focuses on the study of heat and mass transfer (HMT) fluid flow over an exponentially accelerated vertical plate, which is subjected to an applied magnetic field and viscous dissipation. The research has applications in various manufacturing processes such as wire/fiber drawing, hot rolling, continuous casting, and hot extrusion, where heat transfer to the ambient medium and the hot moving material are of utmost importance. The findings could also be relevant to aerospace engineering applications. The study investigates the time-fractional natural convection phenomenon and utilizes conservation laws to derive the flow guiding equations, which are then made nondimensional. Finite difference discretization is utilized to solve the dimensionless equations implicitly. Then the flow simulation results such as concentration, temperature, and velocity profiles are discussed based on the variation in parameters such as Prandtl number ($Pr$), thermal/mass Grashof number ($\mathit{Gr}/\mathit{Gc}$), Eckert number ($\mathit{Ec}$), magnetic parameter ($M$), time-fractional order ($\lambda$), and Schmidt number $\left(\mathit{Sc}\right)$. Also, the HMT rate is depicted using the Nusselt number and skin friction plots. It is noted that HMT increases when $\mathit{Sc}$ increases and $\lambda$ decreases. The change in time-fractional order affects the velocity profiles adjacent to the wall and is more significant in the case of lower values of the Prandtl number.     

Unsteady problem of magnetohydrodynamic heat plus mass transfer convective flow over a moveable plate with effects of thermophoresis and thermal radiation

This paper investigates the problem of unsteady magnetohydrodynamic heat plus mass transfer convective flow over a moveable vertical plate with the influence of thermophoresis and thermal radiation. The physical problem is governed by a set of partial differential equations. These sets of equations are coupled and are nonlinear. They were transformed into a dimensionless form of equations by introducing appropriate nondimensional quantities. An iterative method called the spectral relaxation method was used to linearize and decouple the set of dimensionless equations. Results were presented both in graphs and tables. It was found out that thermophoresis parameter has a significant effect on velocity and concentration fields. The thermal radiation is seen to have a significant effect on velocity and temperature fields. The skin friction is seen to increase the moment thermal Grashof number is increased. The model of Newtonian fluid flow over a moveable vertical plate is considered. The plate was considered moving toward the $y^{?}$‐direction and the radiative heat flux is only with respect to $y^{?}$. This study considered effects of viscous dissipation, thermophoresis, and radiation on heat plus mass transfer. This, to the best of our knowledge, has not been considered in the literature.     

Multiple slip impacts on unsteady MHD micropolar fluid past a stretching sheet with non-Darcy porous medium and uneven heat source/sink

The major scope of this research is to scrutinize the effects of multiple slips on unstable magnetohydrodynamic micropolar fluid past a stretched sheet with a non-Darcy porous medium. In the momentum equation, the non-Darcy porous medium effect is also taken into consideration. The effects of uneven heat source/sink and thermal radiation in the energy equation are also analyzed. By implementing the similarity transmission, the mathematical modeling of the set of managing partial differential equations is reframed into nonlinear ordinary differential equations. These equations are numerically solved by applying Matlab built-in solver bvp5c. The implications of foremost parameters such as micropolar parameter, magnetic parameter, permeability parameter, Prandtl, Eckert, and Schmidt numbers, Chemical reaction, slip parameters on velocity, microrotation, temperature as well as concentration profiles are displayed pictorially and explained. It is worthwhile to mention that the improving values of micropolar parameter $K$ escalate the velocity as well as microrotation profiles. However, the upsurge in non-Darcy porous medium $F_s$ will cause a declining nature in the velocity profile. Also, an enhancement in the unsteadiness parameter $A$ brings about a lessening in all the profiles. Increment in all the three usual slip parameters will bring a declining nature in the respective profiles. An increase in Schmidt number will give a deduction nature in velocity as well as concentration profile. Moreover, the physical quantities are defined and Nusselt numbers are formulated in the table, and it enlarges while boosting up $Pr$ and $R$, whilst a reverse nature is noticed for others. This present study compared with the earlier studies in special cases holds a better agreement.     

Effect of arc-shaped vertical control plate on heat and mass transfer in uniform flow past an isothermally heated circular cylinder

The current work investigates the effect of an arc-shaped vertical control plate on the heat and mass transfer in uniform flow past an isothermally heated circular cylinder. The control plate is positioned downstream at various distances from the circular cylinder's surface. The governing equations are discretized by the higher order compact (HOC) finite difference scheme, and then this system of discretized equations is solved by using a bi-conjugate gradient stabilized iterative method for Prandtl number $Pr=0.7$, Reynolds number $Re=150$. To investigate the effect of an arc-shaped control plate on heat and mass transfer, we consider a range of nondimensional distances between the circular cylinder and the control plate, $0.5\le d∕R_0\le 8$, where $d$ is the control plate's distance and $R_0$ is the cylinder's radius. The exact timing and location of the bifurcation points are calculated by using topological aspect-based structural bifurcation analysis. Significant effects of various locations of the control plate on periodic wake and heat transfer are observed. It is found that the increasing distance of the control plate from the cylinder delays the occurrence of the structural bifurcation and shifts the bifurcation points upwards in the upper half and downwards in the lower half of the cylinder. Our study shows that the specific location of the control plate can fully suppress the vortex shedding. Time-averaged total Nusselt number can be drastically reduced by increasing the distance between the control plate and the cylinder. With proper positioning, the vertical control plate can lessen the time-averaged drag force by up to $22.5\%$ when compared to a cylinder without a control plate. Overall, this work presents many new phenomena that have not been reported before.     

Investigation of Oldroyd-B fluid flow and heat transfer over a stretching sheet with nonlinear radiation and heat source

The given investigation concerns the study of non-Newtonian Oldroyd-B fluid flow across a permeable surface along with nonlinear thermal radiation, chemical reactions, and heat sources. Equations modified are thus numerically evaluated by employing bvp4c-technique. Obtained outcomes are exhibited graphically. Pictorial notations are used to investigate the consequences of necessary parameters of velocity, energy, and mass. Acquired outcomes provide promising agreement with already established consequences provided in the open literature. The obtained results guided that magnetic field parameter ($M$), porosity parameter ($Kp$), Deborah number ${\beta }_1$ reduce momentum boundary layer thickness, furthermore, growth in the relevant Deborah number ${\beta }_2$ improves the corresponding momentum boundary layer.     

Non-Newtonian laminar pulsating heat and fluid flow in plane duct

In the present study, laminar pulsating power-law momentum and heat transfer in a uniformly heated plane duct is studied analytically. Assuming that fully developed conditions exist both hydrodynamically and thermally, a perturbation series method is utilized to derive analytical solutions for the momentum and energy balance equations, and the amplitude is prescribed as the perturbation parameter. For varying values of the power-law index ( $n$), representing pseudoplastic, Newtonian, and dilatant fluids, effects of dimensionless amplitude ( $ϵ$) and frequency ( $F$) on periodic and period-averaged friction factor and Nusselt number are obtained. The results obtained for Newtonian fluid are shown to be in good harmony with the corresponding findings in the open literature.     

Unsteady thermally radiative and chemically reactive viscoelastic fluid flow past a vertical porous plate with a heat source

An analytical study is performed to investigate the thermal radiation effect on the unsteady two-dimensional magnetohydrodynamic flow of a viscoelastic incompressible fluid (Walters $B\prime$ fluid model) along an infinite hot vertical sheet embedded in a porous medium. Further, the addition of a heat source in the energy equation as well as a chemical reaction in the concentration equation renders the present analysis realistic in the field of engineering and technology. The governing equations of mass, momentum, energy, and concentration are solved with successive perturbation techniques. The effects of pertinent parameters on fluid velocity, temperature, concentration, and bounding surface coefficients are shown graphically and in tabular form. The salient feature of the present study is to impose control on magnetic field strength vis-à-vis electromagnetic force by regulating voltage in the electric circuit. The important findings are: the elasticity property of the fluid is more sensitive to heated bounding surface consequently free convection current in enhancing the velocity near the plate than the inherent property viscosity. This outcome contributes to the design requirement to control the flow near the heated surface, higher values of frequency parameters contribute to the attainment of a free stream state in temperature distribution. Besides the aforesaid outcome, the present model is conducive to thinning of boundary layer as the elasticity, magnetic as well as free convection parameters enhance the force coefficients at the bounding surface.     

Heat transfer characteristics in non-Newtonian fluid flow due to a naturally permeable curved surface and chemical reaction

In this research endeavor, Casson fluid flow and melting heat transfer due to a curved nonlinearly stretching sheet are investigated. The sheet is naturally permeable and the flow is considered in a porous medium. For flow in a porous medium, a modified Darcy's resistance term for Casson fluid is considered in the momentum equation. In the energy equation, heat transport characteristics, including viscous dissipation, are taken into account. Mass transport is also studied together with the impact of chemical reaction of higher order. The governing nonlinear partial differential equations of flow, heat, and mass transport are reduced to nondimensional ordinary differential equations using adequate similarity transformations and then solved numerically employing the bvp4c technique and Runge–Kutta fourth-order method on MATLAB. The impacts of numerous occurring parameters on relevant fields (velocity field, temperature field, and concentration field) are depicted and discussed by plotting graphs. We concluded the curvature parameter, $K$ reduces the pace of the flow. The impacts of the stretching index, $m$ and melting parameter, $Me$ are also found to reduce flow and temperature field. Furthermore, we noted that the reaction parameter, $K_n$ and its order, $n$ exhibit opposite impacts on the concentration field. Moreover, the numerical values of skin-friction coefficient and Nusselt number calculated employing bvp4c and Runge–Kutta fourth-order technique are expressed in tabular mode, and these are found in an excellent match. For validation of the results, skin-friction coefficient values were computed using the Runge–Kutta fourth-order technique and bvp4c solver, compared with the existing results, and a good agreement was found.     

Thermophoretic movement,heat source,and sink influence on the Williamson fluid past a Riga surface with positive and negative Soret-Dufour mechanism

This study investigates the boundary layer motion of Williamson fluid over an electromagnetic with thermophoretic movement, variable thermal conductivity and viscosity, nonlinear radiation, and $\pm$Soret-Dufour influences. The real prediction of regional movement and temperature-dependent properties of the non-Newtonian fluids in real space (three-dimensional [3D]) becomes imperative due to their numerous industrial, engineering, and biomedical use. This flow motion is induced as a result of the introduced mechanism (Riga plate) capable of controlling a weakly hydromagnetic flow. To actualize the aim of this study, the formulated governing partial differential equations conveying the flow model of Williamson fluid in a 3D sense are transformed to systems of ordinary differential equations (ODEs) via applicable similarity variables. The reduced systems of ODEs are solved numerically by the collocation approach. Therein, the Riga surface is seen preventing the heat source/sink impact on the flow fields, the thermophoretic impact indicates a more accumulation of Williamson fluid particles in the cold region thus resulting in higher fluid concentration. Thermal variability energizes the energy field positively, momentum boundary layer reduction prevails for higher Williamson number while heat source dominates the temperature field and heat sink showcases its ability to enhance the fluid concentration in contrast to the heat source.     

Three-dimensional numerical simulation of free convection and entropy generation in a cubic cavity containing a heat source

The present article provides a three-dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (${10}^3\le \mathit{Ra}\le {10}^7$). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from $\mathit{Ra}={10}^3$ to ${10}^7$. The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient $\mathit{\phi }={10}^{-4}$, the analysis of the results showed that for low values of the Rayleigh number ($\mathit{Ra}={10}^3$), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of $\mathit{Ra}={10}^4$ and ${10}^5$, entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large ($\mathit{Ra}{\ge 10}^6$), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications.     

Convection of 3D MHD non-Newtonian couple stress nanofluid flow via stretching surface

This study involvesthe numerical modeling of steady thermal radiation and chemical reaction on non-Newtonian fluid motion via a bidirectional stretching surface. We have taken convective boundary conditions, and heat sources on the stretching surface. The working fluid of the present study is Casson fluid (“non-Newtonian”) with couple stress. The self-similarity forms of the nonlinear thermal radiative flow model are obtained by using similarity variables. Furthermore, the numerical results are computed with the help of fourth-order Runge–Kutta–Fehlberg method with a shooting algorithm after reducing nonlinear partial differential equations have been translated into strong ordinary differential equations (ODEs). Impacts of the various flow physical parameters especially Biot number, nonlinear thermal radiation, and heat source parameters containing nonlinear ODEs are discussed in detail for distinct numerical values. A comparison of calculated results with the known numerical results made with the previously published literature is mentioned and obtained a good agreement. Finally, we found that the $R{e}_x^{1/2}{C}_{fx}$ (“coefficient of skin friction”) declines along $x*,y*$ directions, respectively, with $\beta$ via $\lambda$ while the opposite direction follows $M$ with respect to $\lambda$ and the $R{e}_x^{-1/2}N{u}_x$ (“heat transfer rate”), $R{e}_x^{-1/2}Sh$ (“mass transfer rate”) increase with $\Gamma$ via ${\gamma }_1$ while opposite direction follows ${\gamma }_1$ with respect to ${\gamma }_2$.     

Parametric studies of mixed convective fluid flow around cylinders of different cross-sections

A numerical study of mixed convective heat transfer in a lid-driven square enclosure containing a hot elliptic cylinder is conducted. The impacts of the Grashof number $({10}^3\le \mathit{Gr}\le 10^6)$, Reynolds number $(1.0\le Re\le 100)$, cylinder tilt angle $(0^{°}\le \varphi \le {90}^{°})$, and aspect ratio $(1.0\le AR\le 3.0)$ have been examined for a fluid of $Pr$ of 0.71. The horizontal enclosure walls are insulated, while its vertical walls are restricted to a nonvarying temperature T_c, whereas a sinusoidal temperature of $T_h+∆T\sin (\pi x/L)$ is imposed on the wall of the elliptical cylinder. The governing equations are solved using COMSOL Multiphysics 5.6 software. The fluid dynamic and the heat transport profiles between the enclosure and the elliptical cylinder walls are represented by the stream function, isothermal contours, and average Nusselt number. Results established that for all the considered aspect ratios, the thermal heating range of ${10}^3\le \mathit{Gr}\le 10^4$ is predominantly a conduction mechanism. The critical position of the ellipse where the inclination effect becomes insignificant is determined by the Grashof number and aspect ratio when the Re = 100. The strength of vortices and cell numbers are significantly influenced by the aspect ratio, particularly when the $\mathit{Gr}=10^4$. When $AR=1.0$, the average heat transfer from the cylinder remains the same regardless of the cylinder's orientation. The impact of cylinder orientation on heat transfer from the cylinder wall is minimal for $1.5\le AR\le 2.0$. For AR values of $2.5\le AR\le 3.0$, increasing the inclination angle does not result in improved heat transfer. The influence of the increasing inclination angle on the right wall diminishes as the angle increases, except when the Grashof number is greater than 10⁵, where the rate of heat transfer is enhanced for inclination angles beyond 45°.     

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon  and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.     

Natural convection coupled to surface radiation in an air-filled square cavity containing two heat-generating bodies

The present numerical study focuses on the cooling by natural convection and surface radiation of two electronic components generating two different and uniform volumetric powers. These components are modeled by two square bodies placed inside a closed square cavity with a cold straight wall. Two configurations are analyzed based on the position of the two heat-generating bodies. In the first one (horizontal position configuration), the two bodies are located at the same height of the cavity, while they are placed at different heights in the second case (vertical position configuration). The effects of two Rayleigh numbers ($0\le ({\mathit{Ra}}_1,{\mathit{Ra}}_2)\le {10}^6$), the conductivity ratio ($0.01\le K\le 100$), and the emissivity ($0\le \epsilon \le 1$) on the heat transfer characteristics and the flow structure are analyzed. The data is displayed as streamlines, isotherms, velocity, and maximum temperature profiles, and local heat transfer on the active wall. The obtained results indicate that the choice of the appropriate configuration depends mainly on the deviation between the two Rayleigh numbers. Furthermore, the maximum temperature of a specific block decreases as the quantity of heat generated by the other block rises. We can also see that the maximum temperature of the two blocks decreases by about $50\%$ with the increase in the emissivity (from $0$ to $1$) or the conductivity ratio (from $0.1$ to $1$).     

Influence of chemically reactive species and a volumetric heat source or sink on mixed convection over an exponentially decreasing mainstream

In this paper, we investigate mixed convection flow over an exponentially decreasing freestream velocity in presence of nonlinear chemically reactive species and a volumetric heat source or sink. Nonsimilar transformations are used to reduce the boundary layer equations into dimensionless equations and are further solved by the implicit finite difference scheme in combination with the quasi‐linearization technique. The influence of various governing parameters such as the volumetric heat source/sink parameter (Q), the ratio of buoyancy forces (N), the Richardson number (Ri), and the chemical reaction parameter (Δ) on the flow, thermal and species concentration fields are discussed and presented in terms of graphs. The numerical investigation reveals that the increase in volumetric heat source/sink parameter Q increases the temperature profile about 69% in presence of injection and the concentration profile decreases about 56% for and increases around 53% for as n increases from 1 to 2.     

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

In this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are , , , , , , and . It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number, whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.     

Dual solution of heat transfer in hydromagnetic micropolar fluid flow over a stretching sheet in a porous media: A numerical approach

In this study, the researcher looks at the heat transmission of an incompressible magnetohydrodynamics micropolar fluid across a moving stretched surface in a Darcian permeable medium. The proper boundary conditions are used to facilitate the numerical solution (bvp4c) of the transformed governing equations. Graphical discussions have been made of the influence of the physical parameters on the velocity, angular velocity (microrotation), and temperature, and the distributions are accentuated on the plots via MATLAB. The study is validated by the previous work and it is found appropriate for investigation, where the absolute difference between the previous work and the present investigation by adopting the finite difference scheme is smaller than which implies that the scheme is stable and convergent. The microrotation has a great impact on the micropolar fluid with the influences of buoyancy forces, source, and suction over the stretching surface in a Darcian regime. With a rise in the heat source parameter, both velocity and microrotational profiles lessen, but the opposite is true for temperature. Eringen number () rises with the flow velocity, whereas temperature and microrotational profiles show the reverse relationship. The current study focused on particular applications in non-Newtonian fluid mechanics, polymer flows in filtration systems and metallurgical procedures that included cooling unbroken strips or filaments via a static fluid.     

Natural convective flow past a suddenly started vertical plate with uniform mass and heat flux in the presence of radiation,thermal diffusion

An attempt has been made to investigate the problem of a natural convective radiative flow past an impulsively moving vertical plate with uniform mass and heat flux in the existence of the thermal diffusion effect. The resulting governing equations are solved by the Laplace transform technique in closed form. Effects of radiation, Prandtl number, Soret number, Grashof number, modified Grashof number, and Schmidt number are studied on temperature field, concentration field, velocity field, plate temperature, plate concentration, skin friction, and are demonstrated through graphs. The present study reveals that an intensification of the thermal radiation effect causes a downfall in the fluid temperature, plate temperature, and skin friction, but a contradictory outcome is spotted for plate concentration. One of the significant findings of this study includes that the increasing thermo-diffusion effect hikes the concentration and frictional resistance of the field.