Heat and mass transfer analysis of MWCNT‐kerosene nanofluid flow over a wedge with thermal radiation

A comparison between the unsteady and steady magnetohydrodynamics Tiwari‐Das model Williamson nanofluid flow through a wedge occupied by carbon nanotubes of multiwalled type nanoparticles and kerosene as base fluid is presented in this analysis. A suitable similarity variable technique is adopted to transmute the governing partial differential equations into a set of nonlinear ordinary differential equations (ODEs). To solve these ODEs together along with boundary conditions, we have utilized finite element analysis. The behavior of concentration, temperature, and velocity sketches for diverse values of the pertinent parameters is plotted through graphs. The impact on the above parameters on the rates of velocity, heat, and concentration is also evaluated and depicted through tables. It is noted that as the values of nanoparticle volume fraction parameter rises, the rates of temperature increase in both the unsteady and steady cases.     

Interaction of Cu and Ag nanoparticles on MHD water‐based nanofluids past a stretching sheet

The study explores the MHD flow of water‐based nanofluids past a stretching sheet that melts at a constant rate. Cu and Ag nanoparticles are considered to merge into the base fluid to discuss the flow, heat and mass transfer characteristics. Suitable transformation is employed to transform the governing partial differential equations to a system of nonlinear coupled ordinary differential equations (ODEs). A semi‐analytical technique, that is, in particular, the Adomian decomposition method is implemented to tackle this system of ODEs. The influences of characterizing parameters for the flow phenomena are determined via graphs and displayed. Furthermore, the computed values of the quantities of engineering interest are exhibited through tables and discussed. The main findings of the results are laid down as follows: the Cu‐water nanofluid momentum is more pronounced than that of Ag‐water due to the heavier density of the Ag nanoparticles and an increasing melting parameter is favorable to decrease the fluid temperature, which is useful for the cooling of the substances at the final stage of production in industries.     

Magnetohydrodynamic micropolar slip flow due to an exponentially stretching sheet with chemical reaction and nonuniform heat generation

The main focus of the current study is to examine the impact of melting heat transfer and chemical reaction on magnetohydrodynamic micropolar fluid flow over a sheet that is exponentially stretching and immersed in a porous medium. A nonuniform heat source is placed within this flow system. Other impacts like slip phenomena and thermal radiation are also taken into consideration. The governing partial differential equations are converted to a system of ordinary differential equations (ODEs) via similarity transformation and we also get the corresponding necessary boundary conditions. These nonlinear ODEs are resolved with the help of shooting technique and an Runge-Kutta fourth order (RK-4) iterative strategy. Also, we solve this problem using the Bvp4c approach for validating the results of the RK-4 method. Both outcomes are consistent with previously published data. With the help of tables and graphs, we examine the influence of multiple physical parameters on velocity, thermal, microrotation, concentration, Nusselt number, Sherwood number, coefficient of skin friction, and wall couple stress. We see that the temperature distribution and velocity profiles decrease when the melting parameter increases. The temperature profile boosts when the heat source parameter is increased.     

Magnetized impacts of Brownian motion and thermophoresis on unsteady squeezing flow of nanofluid between two parallel plates with chemical reaction and Joule heating

Present research article investigate the heat and mass transfer characteristics of unsteady magnetohydrodynamic Casson nanofluid flow between two parallel plates under the influence of viscous dissipation and first order homogeneous chemical reaction effects. The impacts of thermophoresis and Brownian motion are accounted in the nanofluid model to disclose the salient features of heat and mass transport phenomena. The present physical problem is examined under the presence of Lorentz forces to investigate the effects of magnetic field. Further, the viscous and Joule dissipation effects are considered to describe the heat transfer process. The non‐Newtonian behaviour of Casson nanofluid is distinguished from those of Newtonian fluids by considering the well‐established rheological Casson fluid model. The two‐dimensional partial differential equations governing the unsteady squeezing flow of Casson nanofluid are coupled and highly nonlinear in nature. Thus, similarity transformations are imposed on the conservation laws to obtain the nonlinear ordinary differential equations. Runge‐Kutta fourth order integration scheme with shooting method and bvp4c techniques have been used to solve the resulting nonlinear flow equations. Numerical results have been obtained and presented in the form of graphs and tables for various values of physical parameters. It is noticed from present investigation that, the concentration field is a decreasing function of thermophoresis parameter. Also, concentration profile enhances with raising Brownian motion parameter. Further, the present numerical results are compared with the analytical and semianalytical results and found to be in good agreement.     

Magnetically driven chemically reactive Casson nanofluid flow over curved surface with thermal radiation

During this exploration, Casson nanofluid is taken over a sheet that is curved and stretching in nature and its flow equations are analyzed. Radiation and slip provisions are also taken into consideration. A magnetic field of uniform rate is provided. Convective heat and mass transference extract dominant conclusions from the system. The Brownian migration together with thermophoresis is also included in the flow structure. Moreover, the chemical reaction of higher-order within the nanoingredients also generates interest. Guiding equations furnished by the selected model are resettled to ordinary differential equations of nonlinear type by significant similarity transformation. We have worked on MAPLE-19 software to work out this with a suitable accuracy rate. Upshots are shown with diagrams and tables. Corresponding physical consignment such as Nusselt number has been analyzed. Determination of skin friction and moreover Sherwood's number is also in the area of interest. Magnificent advancement in heat sifting is dealt with by magnetic and Brownian motion specification. The graphs prescribed the upshots of thermophoresis and slip parameters. Outcomes convey that temperature together with concentration are reduced for stretching parameters but velocity lines are enhanced. Heat transport goes up for magnetic and Brownian motion framework but elevated outcomes are spotted for radiative flow in contrast to nonradiative flow. Mass transfer is reduced for chemical reaction components but the rate of augmentation is elevated for higher-order chemically reactive flow. Mass Biot number and temperature Biot number both increase the concentration and temperature transport, respectively.     

Thermochemistry and viscous heat dissipative effects on unsteady upper-convected Maxwell fluid flow past a stretching vertical plate with thermophysical variables

In this paper, unsteady upper-convected Maxwell fluid flow with variability in viscosity, thermal conductivity, and mass diffusivity is presented. The effects of chemical reaction, internal heat generation, and viscous dissipation with respect to variability properties were explored. The governing partial differential equations were transformed with the appropriate similarity transformation variables into nonlinear coupled ordinary differential equations. The spectral collocation method was used to solve the resulting ordinary differential equations. Hence, the effects of various parameters such as temperature-dependent viscosity and thermal conductivity, mass diffusivity parameters among others on velocity, temperature, concentration, skin friction, local heat and mass transfers were presented in graphs and tables. It is seen that heat and molecules of the fluid disperse faster as a result of destructive chemical reaction, while, the temperature-dependent viscosity and thermal conductivity gave increasing profiles of the momentum and thermal boundary layer. The viscous dissipative parameter generates heat and yields a buoyancy force in consequence.     

Heat and mass transfer characteristics of radiative hybrid nanofluid flow over a stretching sheet with chemical reaction

Unsteady magnetohydrodynamic heat and mass transfer analysis of hybrid nanoliquid flow over a stretching surface with chemical reaction, suction, slip effects, and thermal radiation is analyzed in this study. A combination of alumina (Al₂O₃) and titanium oxide (TiO₂) nanoparticles are taken as hybrid nanoparticles and water is considered as the basefluid. Using the similarity transformation method, the governing equations are changed into a system of ordinary differential equations. These equations together with boundary conditions are numerically evaluated by using the Finite element method. The influence of various pertinent parameters on the profiles of fluids concentration, temperature, and velocity is calculated and the outcomes are plotted through graphs. The values of nondimensional rates of heat transfer, mass transfer, and velocity are also analyzed and the results are depicted in tables. Temperature sketches of hybrid nanoliquid intensified in both the steady and unsteady cases as the volume fraction of both nanoparticles rises.     

Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

The unsteady magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid across a vertical stretching surface with second‐order velocity slip is the main concern of the present paper. The influence of electrical energy, temperature‐dependent thermal conductivity, thermal radiation, Joule heating, and heat sink/source is investigated. The basic partial differential equations are changed into ordinary differential equations with the help of appropriate similarity variables and then solved by the fourth‐order Runge‐Kutta–based shooting technique. The impact of physical parameters on the velocity, microrotation, and temperature as well as friction factor, couple stress, and local Nusselt number is thoroughly explained with the support of graphs and tables. The results divulge that the heat source/sink and thermal radiation parameters have a propensity to enhance the fluid temperature. The distribution of velocity is an increasing function of an electric field and unsteadiness parameter. The numerical results are also compared with the results available in the literature.     

Influence of heat transfer on the nonorthogonal stagnation point flow of a third‐order fluid towards a stretching surface

The present article looks at the theoretical analysis of a steady stagnation‐point flow with heat transfer of a third‐order fluid towards a stretching surface. The formulation of the problem has been carried out for a third order fluid and constructed partial differential equations are rehabilitated into ordinary differential equations. The consequential ordinary differential equations are solved analytically using the homotopy analysis method (HAM). Graphical illustrations are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients and heat flux are computed and presented through tables. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21042     

MHD Mixed Convection and Mass Transfer Due to Unsteady Stretching Sheet

Heat and mass transfer in the flow of a viscous incompressible fluid along a vertical isothermal unsteady stretching sheet in the presence of heat generation and a transverse magnetic field is investigated. The governing equations of continuity, momentum, energy, and species concentration are transformed into a system of nonlinear ordinary differential equations and solved numerically by using the Runge–Kutta fourth‐order method with shooting technique. The velocity, temperature, and concentration distributions are discussed numerically and shown through graphs. The expressions of skin‐friction coefficient, Nusselt number, and Sherwood number at the sheet are discussed numerically and their variations are presented through tables. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 447–458, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21088     

A generalized perspective of magnetized radiative squeezed flow of viscous fluid between two parallel disks with suction and blowing

In this research article, the electrically conducting magnetized radiative squeezed flow of two‐dimensional time‐dependent viscous incompressible flow between two parallel disks with heat source/sink and Joule heating effects under the presence of an unsteady homogeneous first order chemical reaction is demonstrated numerically. The considered physical problem is studied under the influence of Lorentz forces to describe the effect of an applied magnetic field. Heat dissipation due to viscosity and Joule heating are considered in the energy equation to demonstrate the behavior of the thermal profile. Also, the thermodynamic behavior of temperature field is described by considering the concept of heat source/sink in the energy equation. The mass transport characteristics of a viscous fluid are described through the time‐dependent chemical reaction of first order type with homogenous behavior. Thus, the considered physical problem gives the time‐dependent, highly nonlinear coupled partial differential equations, which are reduced to a system of ordinary differential equations by invoking the suitable similarity transformations. The discretized first order ordinary differential equations are solved by using the Runge‐Kutta fourth order integration scheme with the shooting technique (RK‐SM) and bvp4c Matlab function. Flow sensitivity of various emerging control parameters are described with the help of tables and graphs. The axial velocity field enhanced for the suction case and suppressed for the blowing case for the increasing values of suction/injection parameter. Also, an excellent comparison between the present solutions and previously published results shows the accuracy and validity of the present similarity solutions and used numerical methods.     

Stefan Blowing and Slip Effects on Unsteady Nanofluid Transport Past a Shrinking Sheet: Multiple Solutions

The aim of a present article is to investigate the laminar unsteady two‐dimensional boundary layer flow of a nanofluid with Stefan blowing and slip effect. First, governing boundary layer equations are converted in the ordinary form of the differential equations (ODEs) from partial differential equations using appropriate coordinate transformations. The obtained ODEs are then solved by applying a shooting method with the Runge‐Kutta fourth order method by implementation of the Maple software. The influences of different controlling dimensionless parameters over the dimensionless velocity, temperature, concentration, friction factor, local heat as well as mass transfer have been discussed and represented by plots. It is found that there exist dual solutions for the different applied nanofluid parameters along with the blowing parameter. The results reveal that by increasing the values of the Brownian motion (Nb), thermophoresis (Nt) and blowing parameters (fw), the skin friction increases (decreases) in the first (second) solution.     

Approximate Analytical Solution of Stagnation Point Flow and Heat Transfer over an Exponential Stretching Sheet with Convective Boundary Condition

This study is concerned with the stagnation point flow and heat transfer over an exponential stretching sheet via an approximate analytical method known as optimal homotopy asymptotic method (OHAM). The governing partial differential equations are converted into ordinary nonlinear differential equations using similarity transformations available in the literature. The heat transfer problem is modeled using two‐point convective boundary condition. These equations are then solved using the OHAM approach. The effects of controlling parameters on the dimensionless velocity, temperature, friction factor, and heat transfer rate are analyzed and discussed through graphs and tables. It is found that the OHAM results match well with numerical results obtained by Runge–Kutta Fehlberg fourth‐fifth order method for different assigned values of parameters. The rate of heat transfer increases with the stretching parameter. It is also found that the stretching parameter reduces the hydrodynamic boundary layer thickness whereas the Prandtl number reduces the thermal boundary layer thickness.     

Symmetry analysis of MHD Casson fluid flow for heat and mass transfer near a stagnation point over a linearly stretching sheet with variable viscosity and thermal conductivity

In this article, the impacts of variable viscosity and thermal conductivity on magnetohydrodynamic, heat transfer, and mass transfer flow of a Casson fluid are analyzed on a linearly stretching sheet inserted in a permeable medium along with heat source/sink and viscous dissipation. To reduce the ascendant partial differential equations into ordinary differential equations, Lie group transformation is utilized. Further, the fourth-order Runge–Kutta strategy is utilized to solve the ordinary differential equations numerically. The numerical results obtained for various parameters by employing coding in MATLAB programming are investigated and considered through graphical representation and tables. We anatomize the impacts of distinctive parameters on velocity, temperature, and concentration distributions.     

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge-Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.     

Velocity slip,chemical reaction,and suction/injection effects on two-dimensional unsteady MHD mass transfer flow over a stretching surface in the presence of thermal radiation and viscous dissipation

The purpose of this study is to analyze the impact of velocity slip, chemical reaction, and suction/injection on two-dimensional mass transfer effects on unsteady MHD flow over a stretching surface in the presence of thermal radiation and viscous dissipation. The governing time-dependent nonlinear partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformations. The converted equations are solved using the numerical technique with the help of Keller-Box method. The effect of nondimensional variables is studied and graphically illustrated on velocity, temperature, concentration, friction factor, Nusselt number, and Sherwood number. Concentration and temperature profiles are enhanced and the contrasting pattern for velocity profiles as increasing the velocity slip and magnetic parameter. The concentration profile is diminished as the Schmidt number (Sc) and chemical reaction (C_r) increase. The concentration, velocity, and temperature profiles display a reversal pattern, as the suction and unsteady parameter (A) increase. The findings of this study are very well-acknowledged with current research.     

Impact of slip effects on unsteady Sisko nanoliquid heat and mass transfer characteristics over stretching sheet filled with gold nanoparticles

We have presented a comparison between steady and unsteady magnetohydrodynamic boundary layer flow, heat transfer features of Au–kerosene‐based nanoliquid over a stretching surface by taking variable viscosity, variable thermal conductivity, and slip boundary conditions in this study. Appropriate similarity translations are engaged to reduce nonlinear partial differential equations into a set of ordinary differential equations. These equations along with boundary conditions are elucidated numerically by finite‐element technique. Influence of several pertinent parameters on velocity, temperature, and concentration scatterings, in addition to that, the values of Nusselt number, skin‐friction coefficient, and Sherwood number are scrutinized in detail and the outcomes are exhibited through plots and tables. It is perceived that the values of Nusselt number, skin‐friction coefficient, and Sherwood number intensify in both steady–unsteady cases as the values of volume fraction parameter $\left(\mathrm{?}\right)$ rise.     

The effect of Joule heating and viscous dissipation on the boundary layer flow of a magnetohydrodynamics micropolar-nanofluid over a stretching vertical Riga plate

Joule heating and viscous dissipation effects on the behavior of the boundary layer flow of a micropolar nanofluid over a stretching vertical Riga plate (electro magnetize plate) are considered. The flow is disturbed by an external electric magnetic field. The problem is formulated mathematically by nonlinear system of partial differential equations (PDEs). By using suitable variables transformations, this system is transformed onto a system of nonlinear ordinary differential equations (ODEs). The Parametric NDsolve package of the commercial software Mathematica is used to solve the obtained ODEs as well as the considered numerical results for different physical parameters with appropriate boundary conditions. Novel results are obtained by studying the stream lines flow around the plate in two and three dimensions. Moreover, the effects of the pertinent parameters on the skin friction coefficient, couple stress, local Nusselt, and Sherwood number are discussed. Special cases of the obtained results show excellent agreements with previous works. The results showed that as the magnetic field parameter increases the velocity of the boundary layer adjacent to the stretching sheet decreases. Also, for a productive chemical reaction near the sheet surface, the angular velocity decreases but opposite trend is observed far from the sheet surface. The importance of this study comes from its significant applications in many scientific fields, such as nuclear reactors, industry, medicine, and geophysics.     

Aspects of second-order velocity slip and radiation absorption on hydromagnetic stagnation point flow of Jeffrey fluid with chemical reaction

The present article describes the magnetohydrodynamic flow of a moving Jeffrey fluid along a convectively heated porous stretching surface with second-order velocity slip and radiation absorption effects. Furthermore, chemical reactions and viscous dissipation impacts are also taken into account. The governing equations are converted into dimensionless ordinary differential equations (ODEs) using appropriate similarity transformations. The highly nonlinear ODEs are solved numerically by employing a shooting technique based on the Runge–Kutta Cash–Karp formula. The figures are used to study the variations in temperature, velocity, and concentration profiles for several physical factors. The numerical values of the local skin friction, Sherwood number, and Nusselt number are explained and shown in tables. The analysis reveals that the velocity profile is enhanced for amplifying values of velocity ratio parameter and first-order velocity slip parameter. However, the temperature profile of Jeffrey nanofluid is highlighted w.r.t. Eckert number and radiation absorption parameter. This study may find significant applications in polymer production, food processing, instrumentation, combustion modeling, catalytic chemical reactors, and so on.