This paper analyzes the combined effects of buoyancy force, convective heating, Brownian motion, thermophoresis and magnetic field on stagnation point flow and heat transfer due to nanofluid flow ...towards a stretching sheet. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and Sherwood numbers. The results indicate that dual solutions exist for shrinking case. The effects of various controlling parameters on these quantities are investigated. It is found that both the skin friction coefficient and the local Sherwood number decrease while the local Nusselt number increases with increasing intensity of buoyancy force.
The problem of laminar fluid flow which results from the stretching of a flat surface in a nanofluid has been investigated numerically. This is the first paper on stretching sheet in nanofluids. The ...model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the Prandtl number
Pr, Lewis number
Le, Brownian motion number
Nb and thermophoresis number
Nt. The variation of the reduced Nusselt and reduced Sherwood numbers with
Nb and
Nt for various values of
Pr and
Le is presented in tabular and graphical forms. It was found that the reduced Nusselt number is a decreasing function of each dimensionless number, while the reduced Sherwood number is an increasing function of higher
Pr and a decreasing function of lower
Pr number for each
Le,
Nb and
Nt numbers.
•Here three-dimensional flow of Oldroyd-B is addressed over a stretched surface.•Stagnation point is considered.•Electrically conducting fluid is considered.•Ohmic heating and radiative heat flux are ...used in the mathematical modeling of energy equation.
This study addresses the three-dimensional (3D) stagnation point flow of non-Newtonian material (Oldroyd-B) with magnetohydrodynamics. Furthermore, Ohmic heating and radiative flux are used in the modeling of energy expression. The surface is convectively heated. Equal strengths of diffusions for homogeneous and heterogeneous reactions are counted. Results are computed and presented graphically. Heat transfer rate is numerically discussed through table.
Here the nonlinear differential system first converted into ordinary differential equation through implementation of appropriate similarity variables. The obtained ordinary system is tackled through homotopy technique for convergent solutions. The outcomes are presented through different graphs and discussed in section six.
The remarkable results of the present communication which is obtained from the semi analytical method i.e., “homotopy method” is summarized as
(i) Opposite impact is noticed for velocity components i.e., (f′(ξ), g(ξ)) for rising fluid parameter and rotation parameter.
(ii) The temperature is direct relation with Biot number and radiative variable.
(iii) Heat transfer rate is more versus Biot number and radiation variable.
(iv) The concentration field shows opposite impact versus homogeneous and heterogeneous parameters.
•Entropy optimized Darcy-Forchheimer flow of nanofluid with magnetohydrodynamic is addressed.•Two types of nanoparticles i.e., Molybdenum disulfide (MOS2) and Silicon dioxide (SiO2) are ...considered.•Electrically conducting fluid is considered and flow is generated via stretched surface of sheet.•The total entropy rate which is depends on four types of irreversibilities i.e., heat transfer, porosity, fluid friction and dissipation) is calculated via second law of thermodynamics.•The energy expression is mathematically modeled and discussed subject to heat generation/absorption, dissipation, thermal radiation and Joule heating.
Background In this research communication, entropy optimized Darcy-Forchheimer flow with magnetohydrodynamic over a stretched surface is considered. Here Molybdenum disulfide (MOS2) and Silicon dioxide (SiO2) are taken as a nanoparticles and Propylene glycol as a continuous phase liquid. Electrically conducting fluid is considered and flow is generated via stretched surface of sheet. The total entropy rate which is depends on four types of irreversibilities i.e., heat transfer, porosity, fluid friction and dissipation) is calculated via second law of thermodynamics. The energy expression is mathematically modeled and discussed subject to heat generation/absorption, dissipation, thermal radiation and Joule heating. Furthermore, temperature dependent viscosity is accounted.
Method The nonlinear PDE’s (partial differential equations) are first changed to ODE’s (ordinary differential equations) through implementation of appropriate similarity variables (transformations). The numerical results of ordinary ones are computed via Built-In-Shooting method. The results for the flow field, temperature, skin friction, Nusselt number and entropy generation are discussed against various sundry flow parameters graphically.
Results Salient characteristics of sundry flow parameters on the entropy generation rate, velocity, Bejan number, gradients of velocity, gradient of temperature and temperature are examined and display graphically. The results are computed for both nanoparticles. From obtained results it is observed that temperature field increases versus higher thermal Biot number for both nanoparticles. It is also observed that the thermal field is more in presence of Molybdenum disulfide as compared to Silicon dioxide, because the thermal conductivity of Molybdenum disulfide is higher than Silicon dioxide. Entropy generation and Bejan number show contrast impact versus higher estimations of Brinkman number versus both nanoparticles.
The combined effects of Navier slip and magnetic field on boundary layer flow with heat and mass transfer of a water-based nanofluid containing gyrotactic microorganisms over a vertical plate are ...investigated. Using Oberbeck–Boussinesq approximation and similarity transformation, the nonlinear model equations are obtained and tackled numerically to obtain the dimensionless velocity, temperature, nanoparticle concentration and density of motile microorganisms together with the reduced Nusselt, Sherwood and motile microorganism numbers. The present numerical results are compared with available data and are found in an excellent agreement. Pertinent results are presented graphically and discussed quantitatively with respect to variation in the controlling parameters. It is observed that the magnetic field suppresses the dimensionless velocity and increases the dimensionless temperature inside the boundary layers. The bioconvection parameters tend to reduce the concentration of the rescaled density of motile microorganisms. It is also found that the reduced Nusselt, Sherwood and density numbers of microorganisms depend strongly upon the magnetic, buoyancy, nanofluid and bioconvection parameters.
MHD laminar boundary layer flow with heat and mass transfer of an electrically conducting water-based nanofluid containing gyrotactic microorganisms along a convectively heated stretching sheet is ...investigated numerically. The governing equations are reduced to non-linear ordinary differential equations using Oberbeck–Boussinesq approximation and similarity transformations. The effects of the governing parameters on the dimensionless quantities like velocity, temperature, nanoparticle concentration, density of motile microorganisms, local Nusselt, and local Sherwood numbers for both nanoparticles and motile microorganism density are explored. It is found that the dimensionless velocity decreases with increasing buoyancy ratio and bioconvection Rayleigh number and the dimensionless temperature at the surface increases with an increase in the convective parameter, whereas it decreases with increasing buoyancy ratios.
•Investigate nanofluids containing motile gyrotactic microorganisms.•Buongiorno model is employed with convective boundary condition.•The Nusselt numbers decrease with increasing magnetic field.•The Sherwood numbers decrease with increasing magnetic field.•The density number decreases with increasing magnetic field.
•Here entropy generation in viscous fluid flow over a variable thicked surface is addressed.•Electrical conducting fluid is considered.•Heat generation/absorption, dissipation and Joule heating ...effects are considered.•Brownian and thermophoresis diffusion effects are further accounted.
Here we investigate the irreversibility aspects in magnetohydrodynamics flow of viscous nanofluid by a variable thicked surface. Viscous dissipation, Joule heating and heat generation/absorption in energy expression is considered. Behavior of Brownian diffusion and thermophoresis are also discussed. The nanoliquid is considered electrical conducting under the behavior of magnetic field exerted transverse to the sheet. Using similarity variables the nonlinear PDEs are altered to ordinary one. The obtained system are computed through Newton built in shooting method. Significant behavior of various involving parameters on entropy generation rate, velocity, concentration, Bejan number and temperature are examined. Gradient of velocity and heat transfer rate are numerically computed through tabulated form. Velocity field is augmented versus power index (n). Temperature and velocity profiles have opposite characteristics for larger approximation of Hartmann number. Concentration profile has similar impact against Brownian diffusion variable and Lewis number. Entropy optimization is boost up via rising values of Brinkman and Hartmann numbers. Bejan number is declined for increasing value of Hartmann number.
The flow and heat transfer in a trapezoidal cavity were investigated numerically. Water-based ferrofluid with Fe3O4 nanoparticles and porous medium with low Darcy number were chosen for the ...investigation. Both side walls were maintained at a constant cold temperature, the top wall was adiabatic, and the heater is placed at the bottom wall. The dimensionless governing equations are solved numerically using finite element method. A uniform magnetic field of strength B0 was imposed. It is assumed that the magnetic Reynolds number is much smaller than the induced magnetic field so that it can be neglected when compared to the applied magnetic field. No slip boundary conditions were applied at the walls. The streamlines and isotherms were generated to explain the behaviour of dimensionless velocity and temperature inside the cavity. It is demonstrated that the magnetic field, thermal buoyancy, porous medium permeability and the length of the heating element play a crucial role in the enhancement of dimensionless average heat transfer rate.
•Here second order velocity slip flow by a rotating surface disk is considered.•Nonlinear mixed convection is accounted.•Slip mechanism of Buongiorno’s nanofluid model i.e., Brownian motion and ...thermophoretic diffusion is incorporated in the mathematical modeling.•Heat transport aspects are examined via Joule heating, thermal radiation and dissipation.•Chemical reaction subject to activation energy is also considered.
Hydromagnetic second order velocity slip flow of viscous material with nonlinear mixed convection towards a stretched rotating disk is numerically examined here. Important slip mechanism of Buongiorno’s nanofluid model i.e., Brownian motion and thermophoretic diffusion is incorporated in the mathematical modeling. Heat transport aspects are examined via Joule heating, thermal radiation and dissipation. Convective conditions at the stretchable surface of disk is implemented for the heat transport analysis. Chemical reaction subject to activation energy is also considered. Through appropriate transformations and shooting method the outcomes are computed and demonstrated graphically. The flow field, temperature, surface drag force, concentration and Nusselt number are deliberated subject to pertinent parameters. Total entropy rate is obtained. The outcomes show that magnetic field significantly affects the flow field as well as entropy rate.
The steady boundary layer free convection flow past a horizontal flat plate embedded in a porous medium filled by a water-based nanofluid containing gyrotactic microorganisms is investigated. The ...Oberbeck-Boussinesq approximation is assumed in the analysis. The effects of bioconvection parameters on the dimensionless velocity, temperature, nanoparticle concentration and density of motile microorganisms as well as on the local Nusselt, Sherwood and motile microorganism numbers are investigated and presented graphically. In the absence of bioconvection, the results are compared with the existing data in the open literature and found to be in good agreement. The bioconvection parameters strongly influence the heat, mass, and motile microorganism transport rates.
► Free convection on a horizontal plate. ► Porous medium saturated with nanofluid containing gyrotactic microorganisms. ► Numerical solutions for velocity, temperature, nanoparticle concentration and motile microorganisms density. ► Graphs for local Nusselt, Sherwood and motile microorganism numbers. ► Effects of bioconvection and buoyancy parameters.
