Narrow Results

This research discusses the investigation of heat and mass transfer in a magnetohydrodynamic (MHD) Casson fluid (CF) flow over an exponentially porous stretching sheet. The analysis takes into account the existence of thermal radiation, viscous dissipation, chemical reactions, and the influence of velocity and thermal slips. A recognized Casson model is taken into account in order to distinguish the characteristics of Casson fluid from those of Newtonian fluids. Using the geometry under consideration, the current physical problem is modeled. Appropriate similarity conversions are implemented to reduce the resultant set of coupled nonlinear PDEs to a set of nonlinear ODEs. By implementing the Keller-Box technique, numerical solutions to these reduced non-dimensional governing flow field equations are obtained. Tables and diagrams are utilized to illustrate the physical behavior of various control parameters. The temperature profile is enhanced and velocity profile diminished as the CF parameter value increased, according to this study. An increase in the velocity slip factor resulted in a diminution in the velocity field, while a gain in the thermal and concentration contours. With growing amounts of the chemical reaction factor, the concentration profile exhibited a decline. Indeed, the similar outcomes elucidated in this paper exhibit a remarkable correspondence with solutions that have been previously documented in the academic literature. This research may be motivated by a desire to improve the comprehension of fluid flow in different engineering and environmental situations, where these conditions are common, such as geothermal energy extraction, thermal management, chemical processing industries, and environmental control technologies.

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

This study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity $\mathrm{\Omega }$. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation.

A stagnation-point flow in a two-dimensional (2D) geometry across a nonlinear stretchable surface with varying viscosity and bioconvection is considered. The prominent feature of mass and heat transport is further explained by the instantaneous influences of variable mass diffusivity, chemical reaction, changing thermal conductivity and magnetohydrodynamics. The mathematical model for the above problem is developed in the form of partial differential equations. After applying the proper similarity variables, the PArtial Differential Equation (PDE) are converted to a system of Ordinary Differential Equation (ODE) and are numerically targeted by utilizing a built-in BVP4C technique in MATLAB software. The discussion regarding the problem focuses on determining the crucial values that correspond to the suction and stretching parameters. A parametric analysis of the temperature field, concentration distribution, and axial velocity has been carried out. The numerically produced outcomes show a good fit with results in existing literature. The study underscores the importance of understanding the interplay between various physical parameters in nanofluid flow systems involving bioconvection. Magnetic parameters contribute to an increased axial velocity profile on the other hand diffusive constant parameters $\lambda$ initially reduce but eventually enhance velocity. Additionally by fixing the values of parameters as $0.1\le \mathrm{\text{Ha}}\le 0.7$, $0.3\le \alpha \le 1.3$, $0.4\le \lambda \le 0.8$, $0.2\le \mathrm{\text{Pr}}\le 0.8$, $0.1\le \mathrm{\text{Rd}}\le 1.0$, $0.1\le {\theta }_r\le 1.1$, $0.5\le \mathrm{\text{Sc}}\le 1.2$, and $0.1\le \delta \le 0.4$, it is observed that the higher Prandtl numbers reduce thermal conductivity, leading to a lower temperature profile. Variable viscosity introduces circular streamline patterns, indicating vortex formation and a gradual change in flow curvature from lower to higher viscosity regions. The magnetic field enhances flow stability, producing smoother streamlines and effectively controlling heat distribution in magnetohydrodynamic systems.

Swirling flows are important in rheological devices, spin coatings and lubrication, so we set out to investigate what makes chemically reactive non-Newtonian spinning flows across a disk with a radially applied magnetic field so interesting. Nanofluids are thermally enhanced working fluids with many interesting physical properties. This study takes its inspiration from rotating disk oxidations used in the medical techno industry and builds a mathematical model of a continuous convective von Kármán swirling flow including Jeffrey, magnetic, Joule/ohmic and chemical reactions. The wall anisotropy slips and the concentration-induced blowing effects are included. By using the bvp4c approach, the transformed boundary conditions (BCs) are addressed. Graphical representations of the effects of involved parameters on the density distribution of motile microorganisms, concentration, temperature and dimensionless velocity components are shown. Supporting evidence from prior research is included. Novel bioreactors, membrane oxygenators, bio-chromatography and food processing should take note of the study’s findings. As Jeffrey’s parameter upsurges, there is a decrease in radial velocity. As the Jeffrey parameter increases, there is a decrease in the circumferential velocity. Radial flow is significantly enhanced near the wall as the radial slip parameter ($\delta u)$ increases. As the Eckert number grows, the quantity of temperature increases. Concentration distribution closer to the disk to grow as Le increases. The concentration and diffusivity of microorganisms drop as the number of motile microorganisms thickens.

This study focuses on examining the magnetized bioconvection flow of Casson ternary nanofluid. The mathematical modeling is developed considering Cattaneo–Christov double diffusion (CCDD), Joule heating, and viscous dissipative effects. The Cattaneo–Christov heat flux model is employed to account for finite thermal relaxation time, which addresses limitations of the conventional Fourier’s law by capturing non-instantaneous heat propagation and magnetic responsive boundary conditions considered. The transformation of the governing equations is done using a group of similarity variables. The reduced nonlinear differential equations flow model is numerically solved using the pseudo-spectral collocating integration method. MAPLE develops a graphical illustration of the involved flow parameters. The obtained outcomes are validated by comparing them to recent investigations in the same field. The most important outcome of the work is that growing the Casson variable improves microorganism fluxing at the wall, whereas increasing the mixed convective parameter decreases it. As the thermal relaxation coefficient grows, the Nusselt numbers fall. Conversely, as the thermophoretic parameter increases, the Nusselt number improves. The Brownian diffusion factor and chemical reactive rate reduce the Sherwood numbers and mass transference in a hybrid ternary nanofluid. The findings provide critical insights into optimizing heat transfer mechanisms in industrial cooling, microfluidic devices, and energy storage systems, where precise control over fluid properties and heat flux is essential.

In this paper, we thoroughly examine the influences of slip effects and stagnation point flows in the context of an upper-convected non-Newtonian Maxwell nanofluid interacting with a stretching sheet. The existence of a heat generation, transverse magnetic field, and thermal radiation induces a flow resulting from a linearly stretched sheet. The application of the shooting method involves deriving nonlinear ordinary differential equations from the governing partial differential equations, followed by their solution. The effects of dimensionless governing parameters, including velocity ratio, Brownian motion parameter, thermophoresis parameter, velocity slip parameter, Lewis numbers, solutal slip parameter, Maxwell parameter, magnetic number, Eckert number, thermal slip parameter, chemical reactions parameter, and heat source parameter, are examined. The outcomes are illustrated and discussed through graphical representations, showcasing their impact on the velocity field, as well as heat and mass transfer characteristics. Tabular data are generated to display numerical values for physical parameters, including the skin-friction coefficient, local Sherwood number, and the reduced local Nusselt number. The findings suggest that an increase in the velocity slip parameter results in a reduction of both the local Sherwood number and the local Nusselt number. Furthermore, an increase in the strength of the magnetic field leads to a decrease in velocity profiles while simultaneously elevating temperature and concentration profiles.

To govern the complex rheological dynamics of fluid simulations, numerous mathematical approaches are being developed. The examination of such mathematical frameworks employs theoretical, iterative, empirical, and analytical methodologies. This work analyzes and evaluates the Laplace transforms to estimate the time-dependent mixed convective flow of hybrid nanofluid in a porous material. A hybrid nanofluid is produced through dispersing molybdenum disulfide (${\mathrm{\text{MoS}}}_2$) and silicone dioxide (${\mathrm{\text{SiO}}}_2$) nanoparticles in carboxymethyl cellulose ($\mathrm{\text{CMC }}-\mathrm{\text{water}}$). The objective of this study is to examine the heat transfer properties of a hybrid nanofluid (${\mathrm{\text{MoS}}}_2-{\mathrm{\text{SiO}}}_2)$/$(\mathrm{\text{CMC }}-\mathrm{\text{water}}$) flowing over a vertical sheet while being subjected to a thermal radiation and heat source and sink. The Laplace transform approach has been used in closed form to solve the resulting partial differential equations governing the flow. This study examines how hybrid nanofluids influence time-dependent flow and heat transmission in the presence of porous medium, heat radiation, and rate of heat generation. The computer program MATHEMATICA is used to emphasize the impact of each flow parameter. Graphs are used to analyze the results of radiation, heat source, magnetic, and nanoparticle volume fraction obtained using the Laplace transform technique for engineering variables like fraction and rate of heat, as well as velocity and thermal distribution. The velocity distribution is an increasing function of mixed convective parameter. Larger values of porosity variable and mixed convection variable result in accelerating the velocity of the fluid. Additionally, we conducted research with various ratios of nanoparticles and discovered several intriguing outcomes that can be used to solve various technical issues, particularly in the cooling process.

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme.

This study investigates the mixed convection on a vertically oriented exponentially stretching surface, considering the exponential distributions of velocity, concentration and temperature. The governing highly nonlinear partial differential equations (PDEs) are transmuted into highly nonlinear ordinary differential equations (ODEs) by considering appropriate similarity variables. The highly nonlinear differential equations are solved numerically using the Hermite wavelet method (HWM) in MATHEMATICA 12. The obtained results show excellent agreement with previous studies focusing on different special cases of the problem. A parametric analysis of the physical parameters is shown and illustrative numerical results are presented graphically. The analysis incorporates the radiation, chemical reaction and cross-diffusion effects. The interaction between radiation and chemical reaction is particularly relevant in high-temperature systems, such as combustion, industrial furnaces, photochemistry, polymerization and certain chemical reactions. The results indicate that an increase in radiation enhances the temperature profile in the momentum boundary layer. Higher reaction rate values lead to a decrease in the concentration profile, while an increase in the Dufour value results in increased velocity and temperature and decreased concentration.

In this work, chemically reactive and mixed convective magnetized AuNF flow in a saturated porous medium inclined channel due to radiative heat transfer and thermo-diffusion/Soret effects is investigated. The prototype is designed and nondimensional partial differential equations are formulated and solved systematically. Also, the heat transfer rate for cylindrical-shaped gold nanoparticles (AuNPs) is evaluated and comparative analysis is done with other shapes (platelet, brick and blade) and previous studies. It is evaluated that the cylindrical shape of AuNPs within base fluid kerosene (C${}_{12}$H${}_{26}$C${}_{15}$H${}_{32})$ enhances the heat transfer capacity of conventional fluids. The transient velocity and concentration profile of AuNF also increased due to a rise in the thermo-diffusion effect, whereas an increase in magnetic field, volume fraction, inclination angle and chemical reaction suppressed the AuNF velocity profile. The elucidated prototype and found results are prominently useful in engineering applications, such as microchannel heat exchangers, advanced cooling in electronic devices, solar thermal systems, aerospace applications and various chemical processes in chemical industries.

In this paper we consider a chemical process, for which the reagent of interest decays shortly after it is created. For such a system the standard theory of nonequilibrium spatial correlations in the density fluctuations, which leads to Ornstein–Zernike type of expression, does not work. We compare results of molecular simulations with another theoretical description based on the assumption that the lifetime of the reagent is short enough to treat its motion as a ballistic rather than diffusive one.

Computational studies have been widely applied for the thermal evaluation of the nanomaterial thermal feature in different industrial and scientific issues. The squeezed flow and heat transfer features for Al₂O₃-water nanofluid among analogous plates are investigated using the GOHAM and its validity is verified by comparison with existing numerical results. Novel aspects of Brownian motion and thermal force were accounted in the simulation of nanomaterial flow within parallel plate. Analytical investigation has been done for diverse governing factors namely: the squeeze, chemical reaction factors and Eckert number. The obtained outcomes show that $|C_f|$ has direct relationship with absolute values of squeeze factor. Nu increases for large Eckert number and absolute values of squeeze number.

The aim of this paper is to study the combined effects of induced magnetic field and chemical reaction on MHD nonlinear mixed convective flow of Casson fluid over an inclined vertical porous plate embedded in a porous medium. The influence of viscous dissipation, heat source/ sink, and slip phenomena is taken into consideration. The effect of thermal radiation is also considered in the energy equation. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. The main objective here is to analyze the induced magnetic field in a nonlinear mixed convective flow. At first, the appropriate similarity transformation is used to transform the governing nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations. The nonlinear ordinary differential equations are solved by a shooting technique with the help of bvp4c Matlab package. For the validation of the obtained results through the bvp4c Matlab solver, we have also solved this problem via R-K fourth-order method in Matlab and a good agreement is noted in both the results. The results of different physical parameters involved in the problem on the velocity, temperature, induced magnetic field and concentration are discussed by using graphs. It is noticed that the increasing values of the inclination angle cause rising of the induced magnetic field while induced magnetic field has opposite nature with magnetic parameter and magnetic Prandtl number. With increasing values of the thermal radiation parameter, the temperature profile diminishes. Apart from this, the numerical values of skin friction coefficient, Nusselt number and Sherwood number for the various values of parameters are displayed in tabular form.

This study explores heat and mass transport in natural convection of Casson fluid in a vertical annulus via porous medium. Impacts of thermal radiation, heat source and chemical reaction are taken into consideration. The equations representing the model reduced into nondimensional ordinary differential equations under adequate transformations are solved analytically. Closed form solutions are obtained for the problem in terms of Bessel’s functions. Influences of various arising parameters such as porous medium parameter, heat generation, thermal radiation, thermal Grashof number, solutal Grashof number, etc. on flow, temperature and concentration fields are exhibited by graphs and discussed. Also, we have solved the problem numerically on MATLAB software employing the bvp4c technique along with shooting technique. The exact and numerical solutions compared found a good match. Moreover, the effects of numerous parameters on quantities of physical importance such as skin-friction coefficient, Nusselt number and Sherwood number are also portrayed and discussed. Heat exchangers, energy storage systems such as batteries and inverters, thermal storage and thermal protection systems are some examples of applications of the study.

A hot spot model, involving interaction of pulse laser with nanoparticles where heat diffusion and exothermic chemical reaction are considered and spread out of heat and chemical reaction, is developed to model the thermal reaction dynamic process of Al/NC (nitrocellulose) nanothermites excited by pulse laser for the purpose of verifying the experimental ablation criterion proposed recently and providing a microscopic insight into different physical pathways leading to ablation. In this model, the spatial position and conversion of matters taking place in chemical reactions are regarded as the functions of time, space, and temperature. An exact expression of power density absorbed by nanoparticles in matrix is incorporated to calculate the diameters of chemical reaction region. Calculation results justify experimental ablation criterion, and show that thermal decomposition mechanism predominates the nanosecond pulse-excited process before ablation but it is not suitable for the 100 ps regime which is qualitatively attributed to shock pressure. The effects of pulse duration and nanoparticle size on ablation threshold are examined.

This paper examines nonlinear thermal radiative stagnation point flow of Walter-B nanofluid. The characteristics of nanofluid are explored using Brownian motion and thermophoresis effects. In the presence of uniform magnetic field, fluid is conducting electrically. Furthermore, phenomena of mass and heat transfer are studied by implementing the effects of chemical reaction, Joule heating and activation energy. Outcomes of distinct variables such as induced magnetic parameter, Eckert number, thermal radiation parameter, Weissenberg number, ratio of rate constant, heat capacity ratio, thermal Biot number, solutal Biot number, Prandtl number, heat generation parameter, Schmidt number on concentration, temperature and velocity distributions are explored. The numerical method is implemented to solve the governing flow expression. Further, Sherwood number, Nusselt number and skin friction coefficient are analyzed and discussed in tables. Weissenberg number have opposite behavior on velocity field while it increases for larger values of mixed convection parameter. Temperature of the fluid rises for higher values of thermal Biot number, thermophoresis diffusion coefficient, heat generation parameter and Eckert number Activation energy parameter and Weissenberg number have direct relation with concentration field.

In this study, we investigated dual solutions for the influence of chemical reaction and radiation effect on axisymmetric flow of magneto-Cross nanomaterial towards a radially shrinking disk on taking account of stagnation point. The governing expressions which describe the assumed flow are reduced to ordinary differential equations by opting suitable similarity variables. The dual solutions on the performance of dimensionless velocity, thermal, concentration gradients, skin friction, rate of heat and mass transfer with the impact of relevant parameters are studied using suitable graphs. Result outcomes reveal that, upsurge in Brownian motion parameter improves the thermal gradient in case of both the solution but, converse trend is detected in concentration gradient. The uplift of thermophoresis parameter boosts up the concentration gradient in both branch solution but reverse trend is noticed in concentration profile for inclined values of Schmidt number. Further, dual nature of solutions exists only for certain range of shrinking parameter.

This paper numerically simulates the nanofluid flow over a thermally expanding Riga plate. Buongiorno model for nanofluid is employed to investigate the contribution of Brownian motion and thermophoretic force on the nanoflow. Magnetohydrodynamics (MHD) of viscous nanofluid through a porous medium is characterized with the help of Darcy–Forchheimer’s model. In addition, the simultaneous effects of activation energy and chemical reaction have been incorporated. Moreover, highly nonlinear coupled differential equations are formulated which highlight the influence of viscous dissipation and heat generation. A numerical solution is achieved with the help of the Range–Kutta fourth-order (RK4) method combined with the shooting technique. Finally, the role of emerging parameters is studied via performing the numerical simulation which reveals that the momentum boundary layer of nanofluid shrinks due to the porous medium. Whereas, thermal boundary layer expands for all variables, except for the Prandtl number. Finally, mass transfer rated suffers due to Schmidt number.

In the recent years, nanotechnologies have been widely used in several fields regarding their rapid developments which creates a lot of prospects for researchers and engineers. More specifically, replacement of conventional liquids with nanoliquids is considered as an innovative solution to heat transfer problems. Keeping the aforesaid pragmatism of nanofluid in view, we have considered a time-dependent mathematical model to formulate the heat sink–source-based Sutterby liquid under thermophoretic and Brownian movements with wedge geometry. Additionally, convective condition, heat sink/source and chemical reaction properties are considered. Appropriate similarity transformations are used to obtain ordinary differential equations (ODEs) from the corresponding PDEs. Furthermore, coupled ODEs are tackled numerically by technique bvp4c in MATLAB. Discussion for thermal and concentration distribution is also presented graphically. Moreover, the temperature field enhance for Brownian parameter and decays for concentration field in this study. A similar impact has been examined for unsteadiness and chemical reaction parameters on concentration plot. Thermal distribution declines for boosted Prandtl number.