Search

As part of the growing evolution in nanotechnology and thermal sciences, nanoparticles are considered as an alternative solution for the energy depletion due to their ultra-high thermal effectives. Nanofluids reflect inclusive and broad-spectrum significances in engineering, industrial and bio-engineering like power plants, energy source, air conditioning systems, surface coatings, evaporators, power consumptions, nano-medicine, cancer treatment, etc. The present study describes the bio-convective peristaltic flow of a third-grade nanofluid in a tapered asymmetric channel. Basic conservation laws of mass, momentum, energy, and concentration as well as the microorganism diffusion equation are utilized to model the problem. The simplified form of the modeled expressions is accounted with long wavelength assumptions. For solving the resulting coupled and nonlinear equations, a well-known numerical method implicit finite difference scheme has been utilized. The graphical results describe the velocity, temperature and concentration profiles, and the density of motile microorganisms at the nanoscale. Furthermore, microorganism concentration lines are analyzed.

The peristaltic phenomenon has intended the researcher’s attention due to its extensive applications in bio-mechanics, industries and biological sciences. The applications of peristaltic transport problems are observed in the transportation of cilia, food mixing in digestive tract, small blood vessels vasomtion, urine transportation etc. Following to such motivating applications in minds, this theoretical analysis presents the peristaltic flow of magnetized Jeffery fluid through accounted by curved channel in presence of heat transfer. The assumed flow is confined by different wave frames. The heat transfer inspection has been performed by utilizing the non-linear thermal radiation and joule heating features. The curvilinear coordinate system is used to model the two dimensional, laminar and incompressible Jeffrey fluid with peristaltic phenomenon. The partial differential equations are transformed into ordinary differential equations in view of appropriate quantities. The implementation of wave length with long magnitude and the assumptions of smaller Reynolds assumptions, the governing system of ordinary system is solved numerically by using shooting technique. The dynamic of involved quantities and physical variables is observed carefully. A declining observation in the temperature in all forms of waves has been noticed for increasing the viscoelastic parameter. The heat transfer coefficient for all waves enhanced for the radius of curvature. Moreover, the velocity of the fluid declines in the lower half of the channel and rises near upper wall of the curved channel due to magnetic parameter.

This numerical study elaborates on the impacts of non-linear thermal radiation, Ohmic heating quadratic chemical reaction, an applied magnetic field on thermal characteristics of an axisymmetric fl...

In the current paper, numerical study is carried out to investigate the peristaltic propulsion of Eyring–Powell fluid in a vertical symmetric channel with electro-kinetic pumping and transvers Lorentz force. The mass, momentum and energy equations for non-Newtonian fluid are formulated and simplified using suitable transformations and dimensionless variables. The governing equations in dimensionless form are solved numerically by implicit finite difference scheme for stream function and temperature profile in computational software Mathematica 9. The impact of several parameters of interest is analyzed and discussed for both values of Helmholtz–Smoluchowski velocity UHS and Joule heating parameter through graphs. An entropy generation analysis is also considered and observed for various values of involved parameters. The nonlinear dimensionless equations are also solved by another numerical technique which is built in routine in MATLAB which is commonly known as bvp4c. The results for velocity and temperature are compared by both techniques. The Joule heating parameter also increases the size and number of isothermal bolus. The entropy of the system can be controlled for assisting pumping, i.e., UHS 0.

Flow and heat transportation in hybrid nanofluid impinging obliquely on a vertical cylinder are investigated numerically in this communication. Silver A g and aluminum oxide A l 2 O 3 nanoparticl...

In this study, we investigate the physical mechanism of the electro-osmosis fluid flow within a non-uniform channel. Fluid model is characterized by the constitutive relation of the Oldroyd 4-constant fluid. We retrieved the Poisson equations by utilizing the mass and momentum conservation models in order to obtain the mathematical formulation of the given problem. The methodology used in obtaining the solution is classified into three different steps. Firstly, we linearized the given differential equations to ascertain the potential Debye–Huckel function. Secondly, we implemented the widely-used assumptions like low Reynolds number and long wavelength to reduce the momentum (partial differential) equations into a system of ordinary differential equations. Thirdly, we solved the simplified differential equations numerically by using the shooting method. Subsequently, we have calculated the graphical results to evaluate the influence of various emerging parameters such as the electroosmotic parameter, viscoelastic fluid parameters and non-uniform parameter on the fluid flow within a non-uniform channel. We have also computed several features of peristaltic pumping for the case of Helmholtz-Smoluchowski velocity. Our results reveal that the behavior of velocity magnitude shows an increasing trend by enhancing the values of the electroosmotic parameter, whereas it also manifests a decreasing trend if the value of the non-uniform parameter is raised.

In this paper simultaneous effects of Coriolis forces, Brownian motion and thermophoresis on the peristaltic motion of Newtonian fluid are incorporated. The governing nonlinear flow equations with appropriate conditions are converted into non-dimensional form, afterward, they were solved numerically by the Keller box procedure. Also, another numerical method is used to solve these transformed equations and by tabular data, we made a comparison of the numerical values of velocities, temperature and concentration profiles. A parametric investigation was conducted and the influence of various parameters on primary and secondary velocities is conducted for both slip and no-slip flow cases. The obtained results are compared with the existing literature as a particular case and found with an excellent agreement. Furthermore graphical results for temperature and nanoparticle concentration profiles are reported for both rotating and non-rotating frames. It is worth mentioning that the effects of Nt and Nb are the dominant in rotating frame as compared to the non-rotating frame of reference and the magnitude of temperature distribution is small for slip flow.

Hybrid nanofluids are used to enhance therapeutic effects and reduce the side effects in tumour therapy. These nanoparticles are transported nearest to the cancer’s tissues under the action of the peristaltic waves generated on the walls of the blood vessel. The motion of hybrid nanoparticles in non-uniform vertical channel having flexible boundaries is numerically elaborated in present study. Poisson equations are used on the basis of electro-osmotic theory to encounter the phenomena of applied electric field on the walls of the channel. Lubrication approach and Debye–Huckel linearization approximations are utilized to obtain the system of coupled ordinary differential equations from the basic conservation laws which are solved by using implicit finite difference scheme which is commonly known as Keller–Box method and MATLAB built in subroutine Bvp5c. The impact of electro-osmotic parameter on all features of flow of nanoparticles observed through several graphs and various tables. The current study is applicable and helpful in the design of micropumps and nanomedicine technologies.

The hybrid nanofluids are more effective and stable to improve the thermal activities of many base liquids. With eminent thermal consequences, the hybrid nanofluids are preferred as compared to simple nanofluids which present the applications in industrial and engineering sectors. This mathematical model described in the thermal applications of hybrid nanofluids due to a non-orthogonal stagnation point addressed over a stretching cylinder. The hybrid nanofluid constrains the multi-walled carbon nanotubes (MWCNT) and single-walled carbon nanotubes (SWCNT). The Ethylene glycol is considered as base fluid. The heat generation features and slip constraints are also introduced to modify the thermal model. The assumed flow is observed due to stretched cylinder with applications of oblique stagnation point flow. The phenomenon of oblique stagnation point flow pattern is quite interesting. The similarity transformations are used to reduce the governing system of partial differential equations into system of ordinary differential equations. The results are exhibited in the present analysis by using efficient and second order accurate numerical scheme Keller box method. The graphical results for different features of flow and heat transfer are presented and discussed. It is observed that the tangential velocity declines with the velocity ratio parameter which is more progressive when the slip features are dominant. An increase in the solid volume fraction results a lower change in temperature profile. With increase in the curvature parameter, the heat transfer rate improved for non-convective stretching cylinder while the opposite observations are claimed for convective stretched cylinder.

The thermal characteristics of modified hybrid nanoparticles have been studied between two parallel walls with applications of entropy generation and nonlinear thermal radiation. Three types of nanoparticles namely copper oxide (CuO), copper nanoparticles (Cu) and aluminum oxide (Al2O3) are utilized to thermal determination of heat transfer. The contribution of viscous dissipation and Joule heating is also inspected. Moreover, the shape effects for the three types of nanoparticles are addressed as a novelty. The mathematical model is developed in view of associated laws and thermal properties of modified hybrid nanofluid. The problem is first modeled in terms of partial differential equations for which the similarity variables are followed to convert the system into dimensionless form. The Keller box numerical scheme is used to obtain the solution. The thermo-physical properties of nanoparticles and fluctuation in the heat transfer rate are reported for the flow parameters. The results claimed that the temperature profile enhanced solid volume faction of copper oxide nanoparticles. A lower change in the entropy generation is observed for the solid volume fraction of aluminum oxide and copper nanoparticles.

With extraordinary thermal activities, the nanofluids play the important role in industrial and engineering sector. The phenomenon of optimized assessment is also quite important to reduce the energy loss and subsequently enhance the thermal pattern of heat transfer which is the pioneer phenomenon in almost all industries. This continuation presents the phenomenon of entropy generation for the flow of water-based hybrid nanofluid in the presence of copper $$\left( {Cu} \right)$$ and alumina $$\left( {Al_{2} O_{3} } \right)$$ nanoparticles through a porous channel. The effects of magnetic field, heat source, Joule heating, viscous dissipation are also taken into account. The radiative mode of heat transfer is also incorporated to improve the thermal rate of hybrid nanofluid. The lower wall of channel stretched uniformly. The fundamental conservations laws of mass, momentum and energy are used to formulate the problem in Cartesian coordinates. The equations obtained from conservation laws are simplified using the similarity transformations axial velocity, and temperature profile is numerically approximated via implicit finite difference scheme, namely Keller Box method. The effect of applied electric field and thermal radiation is shown on different flow and temperature characteristics through various graphs. The heat transfer coefficient is presented and compared for hybrid nanofluid and nanofluid.

This numerical study elaborate the Von Karman swirling flow of second grade fluid having temperature dependent viscosity. The governing non-linear partial differential equations converted into non-dimensional ordinary differential equations using suitable transformations. The system of resulting ordinary differential equations are solved using the well-known implicit finite difference scheme. Then the results are presented graphically and the impact of various involved parameters on velocity, temperature, and concentration profiles. Redial and transversal shear stress on the surface of the disk, local Nusselt and Sherwood numbers are presented through tables. It is found that Variable viscosity parameter $${\theta }_{\delta }$$ , Thermorpheratic parameter, Brownian motion and the suction parameter oppose the motion while the Non-Newtonian fluid parameter and the Prandtl number assist the fluid motion. Variable viscosity parameter enhance both temperature and concentration fields but reduces the magnitude of radial and transversal shear stresses. The results are compared with the existing results and found to be an excellent agreement.

In this paper peristaltic motion of an Oldroyd-4 constant nanofluid under the influence of Buoyancy forces is taken into account. The Buongiorno model is utilized to see the effects of Brownian motion and thermophoresis on the different features of the flow, heat transfer and concentration. In order to facilitate the solution of modeled equations first the governing equations are transformed to system of ordinary differential equations under the assumption of long wavelength and low Reynolds number. The resulting equations are solved using shooting method along with fourth order R. K. method. It is observed that the amplitude of heat flux rises and effective moment of nanoparticles from wall to the center line of the channel which enhance the thermal conductivity at the wall. This is due to the increase in the kinetic energy and Brownian motion. The effects of different parameters are illustrated through graphs and tabulated data is given to compare the effects of shear stress on walls of the channel with Newtonian fluids.

The flow of nanoparticles presents many dynamic applications in thermal sciences, solar systems, cooling and heating phenomenon, energy resources and much other multidisciplinary significance. Following to such valuable applications and motivations in mind, this research pronounced the thermal applications of radiative Casson nanoparticles in presence of radiative phenomenon and activation energy. The oblique stagnation point flow has been considered due to the stretching cylinder. To analyze the flow problem, the problem is formulated in the cylindrical coordinates. The numerical solution is computed via bvp4c built solver by using the MATLAB software. The impact of different involved parameters on skin fraction, heat transfer rate and mass transfer rate is reported and discussed in tables.

Steady flow of non-Newtonian nanofluid impinging on a vertical lubricated surface is numerically investigated. The rheological behaviour of the base fluid is characterized by the constitutive equation of third-grade fluid and the power-law fluid model is used for lubricant. Higher-order chemical reaction and nonlinear radiative heat flux are also taken into account. The governing nonlinear partial differential equations are simplified using the Prandtl boundary layer theory and similarity transformations. An efficient and accurate implicit finite difference method is applied to approximate the resulting nonlinear coupled differential equations with complicated boundary conditions for several values of parameters of interest. The velocity, temperature, nanoparticles concentration profiles Nusselt number, and streamlines are illustrated through graphs for full slip and no–slip case as well as assisting and opposing flow cases. The temperature and concentration profiles are also described for linear and non-linear thermal radiation and for different order chemical reactions. The numerical results are compared with the existing literature and found good agreement. It is found that heat and mass transfer rates reduces over the lubricated surface compared with the rough surface.

Mixed convective peristaltic flow of an Oldroyd 4-constant fluid in a two dimensional channel with flexible walls was studied in this article. The arising complicated nonlinear equations are reduced into solvable form using small Reynolds number and long wavelength assumption. The resulting equations are solved numerically by shooting method and implicit finite difference scheme. The results are compared for both velocity and temperature profiles and also compared with available literature. The impacts of involved parameter on non-dimensional velocity, temperature, pressure gradient, pressure rise per wave length and trapping are presented graphically. By the influence of buoyancy forces the symmetry of the velocity profile is disturbed about the central line of the channel and also the size of the trapped bolus increases in the left half of the channel. Also the decrease in the pressure drop per wavelength is observed for the increasing values of thermal Grashof number.

The present study particularizes the effects of nonlinear thermal radiation and the novel accepts of activation energy in the axisymmetric rotational stagnation point flow of hybrid fluid. Thermophysical properties of water and CWCNT/MWCNT are used for base fluid and nanoparticles respectively. The modeled partial differential equations are reduces to system of ordinary differential equations. The resulting equations are integrated numerically and the impact of involved parameters on velocity, temperature and nanoparticle concentration presented graphically. The tabular values for local Nusselt numbers in case of linear and nonlinear thermal radiation and the Sherwood number with and without activation energy are documented. It is observed that concentration of nanoparticles reduces with activation energy and increasing the solid volume fraction of SWCNT as well as MWCNT nanoparticles. Moreover the axial velocity increases while secondary velocity decreases by increasing the rotation parameter.

In this paper, a generalized Newtonian nanofluid in a bio-microfluidics channel due to combined effects of peristalsis and external applied electric field in the presence of thermal radiation and Joule heating is considered. The Poisson and Nernst-Planck equations are taken into account. The obtained non-linear coupled ordinary differential equations are simulated numerically. The impacts of several parameters under the applied electric field on velocity, temperature, concentration, trapping isothermal lines, Nusselt, and Sherwood numbers are presented graphically. It is observed that the number of isothermal lines increases with the electro-osmotic parameter thermophoresis parameter and Brownian motion parameter while perter out with thermal radiation. The results are helpful to design the micro pumps/chips used in medical engineering and improved the thermal efficiency and the durability of microchip cooling devices.

Oblique stagnation point flow of incompressible Maxwell nanofluid past a stretching cylinder with active and passive controlled nanoparticles concentration condition is discussed numerically. The suitable coordinate decomposition reduce the governing boundary layer equations into the system of nonlinear ordinary differential equations which are approximated by Keller box procedure for several values of pertinent parameters. The Numerical results are compared and validated with existing ones as particular cases and found to be an excellent agreement. Velocity profile and lines of flow are sketched to discuss the Obliqueness of the flow. The temperature and concentration profiles drawn to illustrate the influence of involved parameters also variations in local Nusselt and Sherwood numbers are presented through tabular data. It is observed that the behavior of tangential velocity for the viscoelastic fluid and concentration of nanoparticles against thermophoresis diffusion over the cylinder are quite opposite when compared with the results over flat sheet. The temperature distribution and concentration of nanoparticles decreases with elasticity of the fluid.

This study elaborates on the flow of viscoelastic nanofluid consisting of gyrotactic microorganism over a rotating stretching disk along with convective boundary and zero mass flux conditions. Using the similarity transformations the nonlinear coupled partial differential equations regulating the present problem are converted into a set of ordinary differential equations which are approximated numerically by the Keller Box method. The numerically obtained results are verified with the available existing literature for particular values of the involved parameters which are limiting cases of the present analysis. Variation of heat and mass transfer and density numbers are presented graphically and the influence of various parameters on both radial and azimuthal velocities, temperature, concentration, and density of motile-microorganisms for convective and non-convective surfaces is shown through various plots and discussed.