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The aim of this study is to present forced convective nanofluid flow over a moving plate embedded in an absorbent medium. Following Darcy law's for porous medium, the flow analysis is explored in attendance of warmth basis/drop. The main objective of this study is to explore the effects of Brownian motion and thermophoresis. The plate is considered to move in both directions: in the way of movement of fluid and in the opposite route of fluid movement. Similarity alterations have been applied to alter the leading partial differential equations (PDEs) to ordinary differential equations (ODEs). Numerical solutions have been obtained with the help of MATHEMATICA software. Dual solutions have been obtained when the plate and liquid go in reverse ways. Wall shear stress, Nusselt and Sherwood numbers all are found to rise with the rising permeability parameter of absorbent medium. For Nusselt and Sherwood numbers, ranges of dual solutions diminish by the mounting values of permeability parameter K. The critical values for porosity parameter K = 0. 0 1 , 0.02, 0.03 are R c 1 = 1. 8 7 2 9 0 9 , R c 2 = 1. 9 2 7 2 1 1 , R c 3 = 1. 9 8 2 4 2 8 4 , respectively. For decreasing values of s, range of dual solutions decreases. For s = − 0. 4 5 , dual solutions exist in the range (1. 1 9 , 1. 2 0). [ABSTRACT FROM AUTHOR]

The combined impacts of Thompson‐Troian slip and Stefan blowing on flow of nanoliquid over a vertical plate in attendance of shear flow have been studied. Nanofluid is generally used to enhance the thermal properties as well as heat transport of liquid. Moreover, Stefan blowing can enhance the heat transfer coefficient by lessening the thermal resistance which is widely used in different types of cooling system. For this, such type of problem has its significant importance in various technological sectors and it attracts the attention of the researchers. The forced convection flow was considered by the authors whereas the mixed convection flow in this aspect is new and fills the gap in the literature as we have addressed this issue in this article. Here lies the novelty of our work. Using proper “similarity transformations”, the principal (partial differential equations) PDEs are altered to (ordinary differential equations) ODEs, and abridged ODEs are numerically solved with the support of Runge‐Kutta method and shooting technique. The outcomes of this investigation have significant impression on the physical appearance for flow, heat and mass transports. Fluid velocity reduces due to rise of Stefan blowing parameter but temperature is experienced to diminish. For growing slip speed and the critical shear speed, the liquid speed augments, while the hotness reduces for growing velocity slip. Compared to no‐slip case, rate of heat transfer increases 73.73% and 17.95% rise in concentration gradient at the wall is noted whereas 5.35% reduction in wall shear stress is observed for δ=0.2$\delta = 0.2$. The outcomes of this learning will be of immense help to the engineers and scientists to acquire superior flow and warmth convey features. [ABSTRACT FROM AUTHOR]

Combined impacts of prescribed surface heat and mass fluxes on nanoliquid flow over a vertical plate with shear flow have been inspected. A two‐phase model for nanofluid has been considered. By means of similarity alterations, partial differential equations which govern the problem under consideration are changed to ordinary ones and nonlinear equations are solved numerically by shooting technique and Runge–Kutta method. The related effects of appropriate parameters on streamwise velocity, velocity, velocity gradient, temperature, and concentrations are analyzed elaborately. The importance of unlike factors on heat and mass transport as well as fluid flow phenomena are detected and analyzed physically as far as practicable. Fluid velocity rises but temperature and concentration are noted to diminish due to mixed convection. Velocity gradient at the wall rises with the rise in mixed convection parameter but wall temperature and wall concentration are found to diminish with the growing values of mixed convection parameter. As Brownian motion parameter and thermophoresis parameter increase, the wall velocity gradient declines until a certain point and from that point it starts to behave in the opposite way. Additionally, the temperature at the wall increases as these parameters grow, but temperature at the wall decreases with the rising values of the mixed convection parameter. On the other hand, the wall concentration increases with the increasing values of the thermophoresis parameter, but wall concentration decreases with the swelling values of the Brownian motion parameter and mixed convection parameter. The results of this study will be of immense help to the engineers and scientists to obtain superior flow phenomenon and heat, mass transport features. [ABSTRACT FROM AUTHOR]

The unsteady three-dimensional flow of nanofluid over a stretching surface in the presence of a magnetic field and thermal radiation are investigated. Zero nanoparticle flux at the wall has been considered. Buongiorno's model for nanofluid has been used in this study. Employing similarity transformations, the governing partial differential equations are transformed to ordinary ones and the transformed equations are then solved numerically by using the shooting technique with the help of Runge–Kutta method. The computed results are compared with previously reported work and found in excellent agreement. Fluid velocity initially decreases with the increase of the unsteadiness parameter. Temperature and nanoparticle volume fraction both increase with the increase of unsteadiness parameter. Due to the increase of thermal radiation temperature increases, nanoparticle volume fraction decreases initially but increases away from the surface. The effect of the other governing parameters on velocity, temperature and concentration fields are discussed through their graphical representations. Besides, the local skin friction coefficient, local Nusselt number and local Sherwood number are presented through graphs. [ABSTRACT FROM AUTHOR]

An investigation is carried out to analyze the flow, heat and mass transport phenomena of nanofluids over a disk stretched radially in a porous medium. Besides nonlinear radiative heat flux and Arrhenius activation energy, multiple slips are considered in this model. This ensures the novelty of the present research. The main goal of the current investigation is to explore the mutual impacts of nonlinear radiative heat flux, various slip factors and Arrhenius activation energy on flow, heat and mass transfers. The highly nonlinear central equations which are partial differential equations (PDEs) are transformed into nonlinear ordinary ones (ODEs) by employing suitable similarity alterations and then for finding the approximate numerical solutions, shooting technique with 4th order "Runge–Kutta method" are applied. The impact of a variety of parameters on "skin friction coefficient," "Nusselt number," "Sherwood number," velocity of the fluid, heat and mass transfers are computed and presented graphically. It is interesting to observe that fluid velocity diminishes with the growing porosity, suction and velocity slip parameters. Nanofluid's temperature reduces for enhanced values of thermal slip parameter but for rising thermal radiation parameter, temperature is boosted up. Also, nanoparticle concentration diminishes for increasing values of mass slip parameter. [ABSTRACT FROM AUTHOR]

An expanding sheet problem is more relevant when the thickness of the sheet is variable and it bears frequent applications in polymer press, paper production, metallic plate cooling, etc. On the other hand, activation energy is an important phenomenon of chemical reaction in flow dynamics of Newtonian and non-Newtonian fluids. The activation energy and chemical reaction have vital applications in food preparing, the mechanism of water and oil emulsions, chemical engineering, and more. So in this project, the impacts of activation energy and binary chemical reaction on MHD two-dimensional boundary layer flow of Williamson nanofluid on an expanding surface of variable thickness embedded in Darcy–Forchheimer porous medium are investigated. Using suitable transformations, the governing equations are transformed into a set of non-linear ordinary differential equations (ODEs). Later, numerical solutions have been achieved by well-known MATLAB inbuilt function 'bvp4c'. Several vital results are explored for variations of involved physical parameters and those are presented in graphical and tabular modes. The achieved results suggest that when wall thickness parameter increases, there is a contrast in behaviors of velocity, temperature and nanoparticle concentration if there is a condition that the shape parameter is greater than or less than unity. For the former case, the above flow properties reduce with wall thickness parameter, whereas, for the latter case, those are showing significant growth. The Brownian motion of nanoparticles causes an increase in temperature and a reduction in nanoparticle concentration, whereas due to thermophoretic force, both temperature and nanoparticle concentration rise. Due to the presence of activation energy in chemical reaction, the nanoparticle concentration enhances, while, temperature decreases(increases) near(away from) the sheet. With increasing reaction rate parameters, nanoparticle concentration diminishes, but temperature increases near the sheet. The surface drag force decreases with Williamson fluid parameter, while it increases with the magnetic parameter, inverse Darcy number, and Forchheimer parameter. On the other hand, the surface heat flux and surface mass flux are decreasing functions of Williamson fluid parameter, magnetic parameter, inverse Darcy number, and Forchheimer parameter. It also reveals that surface heat flux reduces with increasing reaction rate parameters, whereas surface mass flux increases. Finally, for the growth of activation energy parameter, initially surface heat flux rises and surface mass flux declines, but for its larger values, the quantities turn out to be constants. Also, the surface heat and mass fluxes are decreasing functions of thermophoresis parameter. [ABSTRACT FROM AUTHOR]

A numerical analysis has been presented for stream of a mixture nanoliquid over a slendering stretched sheet in company of an external magnetic meadow under boundary layer approximations. This investigation is performed to look at the impacts of variable thickness on balanced two-dimensional (2D) flow of a hybrid nanofluid under border-level approximations as it has wider technological applications in various industries. A variable magnetic field has been considered here. An effort has been taken in this piece to report the joint impacts of variable thickness and MHD on hybrid nanoliquid flow over a slendering stretched sheet as no one has reported such effects. Here lies the novelty of the work. By applying appropriate similarity transformations, the leading partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) and the solutions of the nonlinear equations are subsequently obtained numerically using shooting technique. To hold up the soundness of the statistical outcomes, an assessment is completed with the accessible known outcomes for a few meticulous cases of this study. The consequences of a variety of parameters on motion of fluid and heat transport are analyzed and talked about exhaustively with the help of tabular and graphical representations. It is found that Lorentz force slows down the border-level flow and thickens the momentum border level width. Skin-friction coefficient reduces with the decreasing values of m for m > 0 which is obvious as superior values of m help the liquid to move faster over the exterior and the thickness of the boundary layer augments with the mounting values of m (m > 0). Thus, it can be concluded that the fluid motion is controlled by the power-law index m (m < 1) since the motion slows down for m < 1 and goes faster for m > 1. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the combined effects of unsteadiness and thermal radiation on the flow of a mixture nanoliquid due to a shrinking disk. Investigation of flow near a stagnation-point naturally arises in several industrial sectors and is useful owing to its significance in thermal enhancement. The motion is persuaded by a radially stretched/shrinked exterior of the disk in adding to the flow near a stagnation point. As a result, this research examines the thermophysical belongings of the unsteady flow near a stagnation-point past a stretching/shrinking disk by using twin-kind nanoelements, viz. a mixture nanoliquid. Cu and Al2O3 nanoparticles have been considered in water to produce hybrid nanofluid. The numerous uses like electronic cooling system, heat exchangers and radiators are available. Using similarity transformations, self-similar equations have been obtained which are then solved numerically using MATHEMATICA software. Comparisons have been made with the available data in the literature and found a complete agreement for some special case of the problem. Double solutions subsist for equally stretched and shrinked disks, whereas a unique solution exists for the static disk. For flow past a stretching or a shrinking disk, a 27.79% of increase in warmth transport speed is noted for mixture nanofluid, contrasted to the nanoliquid. Hence, this study will be of interest to several scientists and engineers, owing its capability to augment the speed of heat transport in contrast to the regular nanofluids. [ABSTRACT FROM AUTHOR]

The squeezing flow bears a major importance in everyday phenomena and has vast industrial and biomedical applications. The current study looks at the nanofluid flow among two infinite "parallel plates" that are squeezed. The velocity slip and first‐order compound response have been considered in this problem for a clear understanding of their consequences in the flow of nanofluid and heat transport mechanism. This fluid replica thinks about "Brownian motion" and the influences of "thermophoresis" of nanofluid. The novelty of this work lies in exploring the combined effects of first‐order chemical reaction and the velocity slip on unsteady squeezing flow of nanofluid between two parallel plates as one has not yet reported such effects. The prevailing equations are altered into simplified forms by deploying suitable similarity transformations. Then "numerical solutions" of these equations are obtained by applying the fourth‐order "Runge–Kutta method" with the help of the shooting technique. The accuracy is verified by using two different methods and also comparing our data with the available existing literature. The main goal is to study heat and mass transfer through unsteady squeezing plates by the influence of velocity slip and chemical reaction. The consequences of diverse pertinent parameters on fluid flow, thermal, and concentration fields have been explored in this study. With the rise in "velocity slip parameter" from 0 to 1, 81.37% decrease in skin friction coefficient, 15.81% increase in Nusselt number, and 29.13% increase in Sherwood number are observed. Rising values of the chemical reaction parameter from 0.3 to 0.5, the mass transfer coefficient increases by 66.94%. [ABSTRACT FROM AUTHOR]

Nanofluid bioconvective channel flow is an essential aspect of the recent healthcare industry applications, such as biomedical processing systems. Thus, the present work examined the influence of nth order chemical reaction in an unsteady nanofluid bioconvective channel flow in a horizontal microchannel with expanding/contracting walls. The suitable form of the similarity transformation is exercised to transform the governing boundary layer equations into a more straightforward form of system to ease the computation process. The Runge–Kutta method of fifth-order integration technique solved the reduced boundary layer system and generated the numerical results as the governing parameters vary. It is found that the destructive second-order chemical reaction enhances the mass transfer rate at the lower wall but deteriorates the mass transfer rate at the upper wall. The upper channel wall has a better heat transfer rate than the lower wall when the Reynolds number increases.

In this article, the three-dimensional Magnetohydrodynamics flow of a nanofluid over a horizontal non-linearly stretching sheet in bilateral directions under boundary layer approximation is addressed. A two-phase model has been used for the nanofluid. The influences of thermophoresis, Brownian motion and thermal radiation on heat and mass transfers are considered. Two different cases for the heat and mass transfers are studied. In the first case, uniform wall temperature and zero nanoparticles flux due to thermophoresis are considered. In the second case, prescribed heat and mass fluxes at the boundary are considered. By using the appropriate transformations, a system of non-linear partial differential equations along with the boundary conditions is transformed into coupled non-linear ordinary differential equations. Numerical solutions of the self-similar equations are obtained using a Runge–Kutta method with a shooting technique. Our results for special cases are compared with the available results in the literature, and the results are found to be in good agreement. It is observed that the pertaining parameters have significant effects on the characteristics of flow, heat and mass transfer. The results are presented and discussed in detail through illustrations.

An exploration is carried out to examine mass diffusion of unsteady 'boundary layer' (bl) motion of viscous liquid passed a stretched leaky piece with variable mass flux. For several engineering applications, moving free stream is considered here. This makes this research unique. The leading 'partial differential equations' (PDEs) accompanied by the 'boundary conditions' are converted to 'ordinary differential equations' (ODEs) with the help of 'similarity transformations' and 'numerical solutions' are attained by MATLAB software. The effect of pertinent 'parameters' on fluid 'flow, concentration, skin friction coefficient' and wall concentration are discussed 'graphically' and numerically. When suction/blowing parameter increases from -0.2 to 0.2, skin friction coefficient decreases 18.235%. Fluid concentration reduces with growing values of velocity ratio parameter X for all cases considered. Compared to the case for static free stream, fluid velocity is higher when the free stream moves. Also higher concentration is noted in presence of moving free stream. The presence of moving free stream causes to diminish the effect of suction/blowing on flow and concentration fields. The increasing strength of suction causes to decrease the fluid velocity more significantly than that for blowing. [ABSTRACT FROM AUTHOR]