Dissipative heat for the Casson fluid flow past an expanding cylindrical surface

A non-Newtonian model is developed by considering the flow of non-Newtonian Casson fluid past an expanding cylinder embedded in a porous medium. The novelty arises because of the conjunction of dissipative heat, and the additional heat source that enriches the heat transport phenomenon significantly. The application of the study is vital due to the flow of blood through the artery, a physiological study. Therefore, the study of Casson fluid plays an important role. The nonlinear partial differential equations that appeared in the formulation are now renovated to the coupled nonlinear ordinary differential equations. However, a numerical technique associated with shooting-based followed by Runge–Kutta fourth-order is employed for the solution of these transformed equations. The uniqueness of diverse pertinent parameters on the flow phenomena is scrutinized through graphs and numerically simulated results presented in tables. The important observations are as follows; the magnetic parameter and permeability augment the shear rate coefficients, whereas the Casson parameter rendered the opposite impact. Furthermore, the non-Newtonian Casson parameter retards the fluid temperature, and the curvature parameter significantly enhances it.     

MHD radiative Casson—Nanofluid stream above a nonlinear extending surface including chemical reaction through Darcy-Forchiemer medium

The current study aims to study the magnetohydrodynamics (MHD) Casson kind nanofluid stream through a permeable medium above a nonlinear extending surface considered along with Darcy-Forchimer relation and chemical reaction. Thermophoresis and Brownian diffusion effects are considered. The MHD effect is used to highlight the physical and thermal properties of the nanofluid. The Keller Box scheme is used to solve the guiding equations numerically. Graphs are plotted for various nondimensional parameters. To justify the method, the used local parameters are calculated and compared with the existing literature. The results specify that a decreasing tendency is observed in the velocity profile for Forchiemer, magnetic, and stretching rate parameters, whereas the opposite tendency is noted for the Casson parameter. On observing temperature profiles, declination is noticed for Casson, thermal slip parameters and raising nature is detected for increasing values of Brownian diffusion, and thermophoresis, radiation parameters. From the results, it is observed that the momentum boundary layer diminishes for a higher inertial influence and the opposing force offered by the porous media to the fluid flow.     

Spectral local linearisation method for MHD Casson fluid on stratified bioconvective porous medium flow due to gyrotactic microorganisms

In this paper, the effect of hall parameter on the flow of Casson nanofluid containing gyrotactic microorganisms over a stretching boundary in a porous medium is studied. The stratification, porosity, and Casson fluid parameters are also examined. Using suitable similarity transformations, the basic equations describing the flow are converted to nonlinear differential equations, which are then solved computationally using the spectral local linearisation method. The effects of key parameters such as the Hall parameter, the thermophoresis parameter, the porosity parameter, and Casson fluid parameters are analyzed. The results obtained suggest that the Hall parameter has the effect of decreasing the secondary flow, the heat and mass transfer rate, and density of the motile microorganisms. A decrease in the the Hall parameter is found to cause an increase in the transfer rate, the mass transfer rate, and the density of the motile microorganisms. An increase in the porosity parameter leads to a decline in the skin friction, heat transfer rate, mass transfer rate, and density of the motile microorganisms. The applications of this study arise in industrial areas, including Hall current accelerators, planetary dynamics, Hall current sensors, and magnetohydrodynamic power generators.     

Influence of radiation and viscous dissipation on MHD heat transfer Casson nanofluid flow along a nonlinear stretching surface with chemical reaction

The present article investigates the influence of Joule heating and chemical reaction on magneto Casson nanofluid phenomena in the occurrence of thermal radiation through a porous inclined stretching sheet. Consideration is extended to heat absorption/generation and viscous dissipation. The governing partial differential equations were transformed into nonlinear ordinary differential equations and numerically solved using the Implicit Finite Difference technique. The article analyses the effect of various physical flow parameters on velocity, heat, and mass transfer distributions. For the various involved parameters, the graphical and numerical outcomes are established. The analysis reveals that the enhancement of the radiation parameter increases the temperature and the chemical reaction parameter decreases the concentration profile. The empirical data presented were compared with previously published findings.     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Local thermal nonequilibrium effect on nanofluid filled porous cavity subject to mixed convection heat transfer

In this study, a numerical study is performed to determine the significance of local thermal nonequilibrium on mixed convection heat transfer of a copper water-based nanofluid in an inclined porous cavity. By employing the nonequilibrium hypothesis, the governing equations for nanofluid flow in a porous medium are solved by the Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. From the obtained results, the nanofluid flow and thermal characteristics are analyzed through streamlines and isothermal plots whereas the heat-transfer rate of the system is scrutinized via the average Nusselt number.     

Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model

This article deals with non‐Newtonian Casson nanofluid flow and heat transfer over stretching cylinder in a porous medium. The mode of heat transfer is presented considering temperature‐dependent thermal conductivity by integrating the Cattaneo–Christov heat flux and mass flux models. Boundary layer theory is applied to develop the governing partial differential equations from the physical problem. Employing proper similarity transformation, the governing boundary layer equations are transformed into dimensionless system of nonlinear ordinary differential equations. Then, the resulting problem is numerically solved by means of spectral relaxation method. The convergence analysis of the proposed numerical scheme is presented via a table, which confirms almost the 10th order of approximation is enough for the convergence of the skin friction coefficient, local heat transfer, and mass transfer rates. The effects of various embedded parameters on velocity, temperature, and concentration profiles as well as skin friction coefficient, surface heat and mass transfer rates are examined through graphs and tables. The findings reveal that the growth of permeability and velocity slip parameters appears to decelerate the velocity distributions of fluid. Thermal boundary layer thickness tends to develop with greater values of permeability and Brownian motion parameters. Also, the local heat transfer rate is less with Fourier's law of heat conduction than Cattaneo–Christov heat flux model. Furthermore, the validity and accuracy of the present result is checked with the available literature, and very sound agreement has been obtained.     

Impacts of variable thermal conductivity and mixed convective stagnation‐point flow in a couple stress nanofluid with viscous heating and heat source

The current study examines mixed (combined) convection stagnation‐point couple stress nanofluid over a stretched cylinder of variable thermal conductivity in the presence of viscous dissipation and internal heat source. The basic governing partial differential equations have been converted to coupled nonlinear differential equations by using adequate similarity transformations. By applying semi‐analytic technique (BVPh2.0), the equivalent ordinary differential equations are successfully solved and validated with a bvp4c solver. Graphs are presented to study the impact of various parameters on axial velocity, temperature, and volumetric nanofluid concentration profiles. The coefficient of skin friction (quantifying resistance) and the rate of heat and mass transfer on the surface due to flow variables are computed and explained. The axial velocity and momentum thickness are decreased with increasing couple stress parameter, whereas the reverse trend is noted with mixed convection and buoyancy ratio parameters. The temperature distribution increases for increasing Brownian motion and thermal conductivity parameter, whereas it decreases for increasing stagnation parameter.     

Analytical approach on magnetohydrodynamic Casson fluid flow past a stretching sheet via Adomian decomposition method

Flow phenomena of three-dimensional conducting Casson fluid through a stretching sheet are proposed in the present investigation with the impact of the magnetic parameter in a permeable medium. The adaptation of particular transformations is useful to modify the governing equations into their nondimensional as well as the ordinary form. However, these transformed equations are nonlinear and approximate analytical methods for the solution of the complex form of governing equations. In particular, the Adomian decomposition method is proposed for the solution. The behavior of several variables, such as the magnetic and porous matrix, on the flow profile as well as the rate of shear stress, are discussed via graphs and tables. The conformity of the current result with the earlier study shows a road map for further investigation. The major concluding remarks are; the retardation in the velocity distribution is rendered due to an increase in the Casson parameter moreover, the Casson parameter favors in reducing the rate of shear stress coefficient in magnitude.     

A numerical investigation of conjugated-natural convection heat transfer enhancement of a nanofluid in an annular tube driven by inner heat generating solid cylinder

Laminar conjugate heat transfer by natural convection and conduction in a vertical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal cylindrical boundary has been studied by a numerical method. It is assumed that the two sealed ends of the tube to be adiabatic. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. Results are presented for the flow and temperature distributions and Nusselt numbers on different cross sectional planes and longitudinal sections for Rayleigh number ranging from 10⁵ to 10⁸, solid volume fraction of 0‹φ‹0.05 with copper-water nanofluid as the working medium. Considering that the driven flow in the annular tube is strongly influenced by orientation of tube, study has been carried out for different inclination angles.     

Thermal analysis of buoyancy-motivated Casson fluid flow with time-independent chemical reaction under Lorentz forces

The present research study examines the magneto-hydrodynamic natural convection visco-elastic boundary layer of Casson fluid past a nonlinear stretching sheet with Joule and viscous dissipation effects under the influence of chemical reaction. To differentiate the visco-elastic nature of Casson fluid with Newtonian fluids, an established Casson model is considered. The present physical problem is modeled by utilizing the considered geometry. The resulting system of coupled nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations by applying suitable similarity transformations. Numerical solutions of these reduced nondimensional governing flow field equations are obtained by applying the Runge-Kutta integration scheme with the shooting method (RK-4). The physical behavior of different control parameters is described through graphs and tables. The present study describes that the velocity and temperature profiles decreased for increasing values of Casson fluid parameter. Velocity field diminished for the increasing nonlinear parameter whereas velocity profile magnified for increasing free convection parameter. Thermal field enhanced with increasing magnetic parameter in the flow regime. The concentration profile decreased for the rising values of the chemical reaction parameter. The magnitude of the skin-friction coefficient enhanced with increasing magnetic parameter. Increasing Eckert number increases the heat transfer rate and increasing chemical reaction parameter magnifies the mass transfer rate. Finally, the similarity results presented in this article are excellently matched with previously available solutions in the literature.     

Chemically reacting mixed convective Casson fluid flow in the presence of MHD and porous medium through group theoretical analysis

This paper explores the consequences of chemically reacting magnetohydrodynamic mixed convective fluid substances driven by the porous medium, slippery, incompressible, and laminar vertical channel flow. Casson fluid model in a vertical channel is strengthened with mixed convection flow. The effects of the heat source-sink parameter, the suction-injection parameter, slips on the slide wall, and thermal radiation are also considered. A Lie group method is taken into consideration and nonlinear partial differential equations are converted into nonlinear ordinary differential equations (ODEs). The NDSolve command solves these ODEs and shows the action of the related parameters in the velocity, temperature, and concentration figures. The Casson fluid parameter increases the velocity profile but reduces the concentration profile. The parameter of suction-injection enhances the velocity, temperature, and concentration profiles. The variations in skin-friction coefficient in the heat and mass transfer rate are addressed in the diagrams. Moreover, streamlines are plotted for suction-injection parameter.     

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.     

The lattice Boltzmann modeling on the nanofluid natural convective transport in a cavity filled with a porous foam

In this work, the natural convective transport was numerically investigated for nanofluids in a metal-foam cavity. A lattice Boltzmann (LB) model for the nanofluid natural convection in a porous medium was established by using the volume-averaging method. The velocity and temperature fields were obtained, and flow and thermal characteristics of the nanofluid convection in a porous medium were presented. The effects of the Rayleigh Number, the Darcy Number, the porosity, the solid thermal conductivity of porous medium, the nanoparticle thermal conductivity and the nanoparticle concentration on natural convection were examined. The average velocity was put forward to evaluate the convection effect and the natural convection onset was also discussed. It is shown that the Nusselt number of the natural convection increases with an increase in the Darcy number, the Rayleigh number, the porosity and the effective thermal conductivity. The change from the heat conduction regime to the convection regime is clearly shown from the numerical result, which verifies the onset point of the nanofluid natural convection in a porous medium. The highly conductive porous foam and the nanofluid can promote the thermal performance of the natural convection, which own great potential in practical thermal applications.     

Comparative analysis of a Sisko nanofluid over a stretching cylinder through a porous medium

The present article examines the Sisko nanofluid flow and heat transfer through a porous medium due to a stretching cylinder using Buongiorno's model for nanofluids. Suitable similarity transformations are used to transform the governing boundary layer equations of fluid flow into nonlinear ordinary differential equations. The finite difference method is used to solve coupled nonlinear differential equations with MATLAB software. The impact of different parameters viz., the Sisko material parameter, porosity parameter, curvature parameter, thermophoresis parameter, and Brownian diffusion parameter on the velocity and temperature distribution are presented graphically. Moreover, the effect of the involved parameters on the heat transfer rate is also studied and presented through table values. It is noticed from the numerical values that the porosity parameter reduces the velocity while enhancing the temperature. The curvature parameter enhances the velocity throughout the fluid regime and reduces the temperature near the surface while enhancing the temperature far away from the surface. The study reveals that the thermophoresis and Brownian diffusion parameters that characterize the nanofluid flow reduce the wall heat transfer rate, while the curvature parameter enhances it. This investigation of wall heating/cooling has essential applications in solar porous water absorber systems, chemical engineering, metallurgy, material processing, and so forth.     

Gyrotactic microorganisms bioconvection in combined convective magnetohydrodynamic Casson nanofluid flow over a vertically surfaced saturated porous media with variable viscosity

The current article focuses on mass and thermal transfer analysis of a two-dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature-dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters.     

Forced convection heat transfer of a Robertson-Stiff fluid between two coaxial rotating cylinders

Laminar flow and forced convection heat transfer of the time independent non-Newtonian fluid obeying Robertson-Stiff stress-strain relation have been investigated numerically in the annular space between two coaxial rotating cylinders. The problem is considered when the inner cylinder rotates about the common axis with constant angular velocity and the outer cylinder at the rest, and two cases of the third kind of the thermal boundary conditions. The tangential and axial momentum equations have been solved iteratively by using a finite difference method. Then the energy equation has been solved for the two cases. For the steady fully developed flow, the velocity distributions, temperature profiles, the average volumetric flow rate, torque and the average Nusselt numbers have been obtained for different values of the radius ratio and model parameters.     

Double dispersed bioconvective Casson nanofluid fluid flow over a nonlinear convective stretching sheet in suspension of gyrotactic microorganism

Microorganisms play a vital role in understanding the ecological system. The motions of micororganisms are self‐propelled while the impact of thermophoresis and Brownian motion property of nanoparticle shows more challenges in biotechnological and medical applications. The present problem is based on the understanding of double‐dispensed bioconvection for a Casson nanofluid flow over a stretching sheet. Suction phenomenon is introduced at the surface of the stretching sheet along with the convective boundary condition. The convection and movement of the microorganisms are assisted by an applied magnetic field, nonlinear thermal radiation, and first‐order chemical reaction. The governing equations are highly coupled and thus we used the spectral quasilinearization method to solve the governing equations. The study of the residual errors on the systemic parameters had given a confidence with the present results. The final outcomes are displayed through graphs and tables. The thermal dispersion coefficient shows a positive response in the temperature while a similar response is observed for the concentration with solutal dispersion coefficient. The response is reversible for the heat transfer rate at the surface with thermal dispersion coefficient. The density of the motile microorganism at the surface decreases with increase in the Casson number, thermal dispersion coefficient, and solute dispersion coefficient, while an opposite phenomenon was observed with increase in the density ratio of the motile microorganism.     

Heat transfer in a conical cylinder with porous medium

In this paper, numerical study of heat transfer in a conical annular cylinder fixed with saturated porous medium is presented. The heat transfer is assumed to take place by natural convection and radiation. The inner surface of conical cylinder is maintained at uniform wall temperature. The governing partial differential equations are non-dimensionalised using suitable non-dimensional parameters and then solved by using finite element method. The porous medium is divided using triangular elements with uneven element size. A computer software is used to solve the coupled momentum and energy equations in an iterative manner. The results are discussed for various values of geometric and physical parameters of porous medium with emphasis on cone angle of the cylinder. It is seen that the cone angle plays a vital role in heat transfer from the hot surface to porous medium.     

Study of mixed convection in an annular vertical cylinder filled with saturated porous medium,using thermal non-equilibrium model

The present study deals with numerical investigation of effects of different parameters on enhancement or retardation of the heat transfer rate in an annular vertical cylinder filled with saturated porous medium. The heat transfer is assumed to take place by mixed convection mode. The thermal non-equilibrium approach is considered. The inner surface of the annular cylinder is maintained at constant wall temperature whereas the outer surface remains at ambient temperature. The governing partial differential equations are solved using finite element method. The results are discussed for the effects of Peclet number, interphase heat transfer co-efficient and thermal conductivity ratio.