Flow of Casson fluid with nanoparticles

The boundary layer flow of a Casson fluid due to a stretching cylinder is discussed in the presence of nanoparticles and thermal radiation. All physical properties of the Casson fluid except the thermal conductivity are taken constant. Appropriate transformations yield the nonlinear ordinary differential systems. Convergent series solutions are developed and analyzed. The numerical results for the local Nusselt and Sherwood numbers are demonstrated. It is found that an increase in the strength of the Brownian motion decays the temperature noticeably. However, the rate of heat transfer and the concentration of the nanoparticles at the surface increase for larger Brownian motion parameters.     

Dual solutions of time-dependent magnetohydrodynamic stagnation point boundary layer micropolar nanofluid flow over shrinking/stretching surface

Time-dependent, two-dimensional(2 D) magnetohydrodynamic(MHD)micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered. Mass and heat transfer characteristics are incorporated in the problem. A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations. The obtained equations are numerically solved by a shooting scheme in the MAPLE software. Dual solutions are observed at different values of the specified physical parameters. The stability of first and second solutions is examined through the stability analysis process. This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible. Furthermore, the natures of various physical factors on the drag force, skin-friction factor, and rate of mass and heat transfer are determined and interpreted. The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters, whereas it increases by increasing the unsteadiness parameter.The temperature of the micropolar nanofluid rises with increase in the Brownian motion,radiation, thermophoresis, unsteady and magnetic parameters, but it decreases against an increment in the thermal slip constraint and Prandtl number. The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.     

Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation

In this paper an analysis has been made to study heat and mass transfer in two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in the presence of buoyancy force and thermal radiation. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations containing Prandtl number, Schmidt number and Sherwood number which are solved numerically with appropriate boundary conditions for various values of the dimensionless parameters. Comparison of the present numerical results are found to be in excellent with the earlier published results under limiting cases. The effects of various physical parameters on the boundary layer velocity, temperature and concentration profiles are discussed in detail for both the cases of assisting and opposing flows. The computed values of the skin friction coefficient, local Nusselt number and Sherwood number are discussed for various values of physical parameters. The tabulated results show that the effect of radiation is to increase skin friction coefficient, local Nusselt number and Sherwood number.     

Influence of induced magnetic field on the peristaltic flow of nanofluid

This article investigates the effects of an induced magnetic field on the mixed convection peristaltic motion of nanofluid in a vertical channel. Transport equations involve the combined effects of Brownian motion and thermophoretic diffusion of nanoparticles. Analysis has been addressed subject to long wavelength and low Reynolds number assumptions. Explicit expressions of stream function, magnetic force function, temperature and nanoparticles concentration are developed. Analytic expressions are validated with the obtained numerical solutions. Peristaltic pumping rate is found to increase upon increasing the strengths of electric and magnetic fields and the buoyancy force due to temperature gradient. Moreover temperature rises and nanoparticles concentration decreases with an intensification in the Brownian motion effect.     

Heat transfer characteristics of an annular turbulent impinging jet with a confined wall measured by thermosensitive liquid crystal

The present paper describes the heat transfer characteristics of an annular turbulent impinging jet with a confined wall. The local temperature distribution on the impingement surface was measured using a thermosensitive liquid crystal sheet and an image processor. The net heat flux was evaluated by considering the heat conduction in the heated substrate and the thermal radiation between an upper confining insulated wall and an impingement surface. Distributions of the temperature and Nusselt number on the impingement surface were captured in two-dimensional maps. Effects of the diameter ratio of the annular nozzle, the space between nozzle and impingement surface and the Reynolds number on radial distributions of the local Nusselt number were examined. Experimental formulas of the local Nusselt number were obtained in power-law expressions of r/r_p for the major and minor flow regions.     

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

The effect of nonlinear mixed convection in stretched flows of rate-type non-Newtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.     

Heat transfer by conduction,natural convection and radiation across a rectangular cellular structure

This paper describes results on the effects of wall conduction and radiation heat exchange among surfaces on laminar natural convection heat transfer in a two-dimensional rectangular cavity modelling a cellular structure. Parametric heat transfer calculations have been performed, and numerical results are presented in graphical and tabular form. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The findings suggest that the local or the average Nusselt number is one of many parameters that control conjugate heat transfer problems. The results indicate that natural convection heat transfer in the cavity is reduced by heat conduction in the walls and radiation exchange among surfaces. The results obtaibed for the total heat transfer rate through the system using the two-dimensional model are compared with those based on a one-dimensional model.     

Influence of Hall current and Joule heating on entropy generation during electrokinetically induced thermoradiative transport of nanofluids in a porous microchannel

A comprehensive theoretical study of entropy generation during electrokinetically driven transport of a nanofluid is of prime concern in the paper. The flow is considered to take place on a wavy channel under the action of an external transverse magnetic field and an external pressure gradient. Navier slips at the walls of the channel and thermal radiation have been taken into account in the study. The theoretical study has been carried out by developing a mathematical model by taking into account the effects of Joule heating, viscous dissipation, and the transverse magnetic field on heat transfer during the electrokinetic transport of the fluid. The derived analytical expressions have been computed numerically by considering the nanofluid as a mixture of blood and ferromagnetic nanoparticles. Variations in velocity, streaming potential, temperature distribution, Nusselt number, and Bejan number associated with the electrokinetic flow in capillaries have been investigated by the parametric variation method. The results have been presented graphically. The present investigation reveals that streaming potential decreases due to the Hall effect, while for the cooling capacity of the microsystem,we find an opposite behavior due to the Hall effect. The study further reveals that the fluidic temperature is reduced due to increase in the Hall current, and thereby thermal irreversibility of the system is reduced significantly. The results presented here can be considered as the approximate estimates of blood flow dynamics in capillaries during chemotherapy in cancer treatment.     

Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation

This paper examined the hydromagnetic mixed convection stagnation point flow towards a vertical plate embedded in a highly porous medium with radiation and internal heat generation. The governing boundary layer equations are formulated and transformed into a set of ordinary differential equations using a local similarity approach and then solved numerically by shooting iteration technique together with Runge-Kutta sixth-order integration scheme. A representative set of numerical results are displayed graphically and discussed quantitatively to show some interesting aspects of the pertinent parameters on the dimensionless axial velocity, temperature and the concentration profiles, local skin friction, local Nusselt number and local Sherwood number, the rate of heat and mass transfer. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases.     

Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition

Heat transfer characteristics of a two-dimensional steady hydromagnetic natural convection flow of nanofluids over a non-linear stretching sheet taking into account the effects of radiation and convective boundary condition has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The local similarity solutions are obtained by using very robust computer algebra software Maple 13. The results corresponding to the dimensionless temperature profiles and the reduced Nusselt number, Sherwood number and skin friction coefficient are displayed graphically for various pertinent parameters. The results show that temperature within the boundary layer is enhanced with the increase of the Biot number, buoyancy due to nanoparticle concentration, strength of the applied magnetic field, Brownian motion parameter, and thermophoresis parameter. An opposite trend is observed for the increase of the buoyancy due to temperature, stretching index, and the radiation parameter. The results also show that the local rate of heat transfer strongly depends on the nonlinear stretching index, radiation parameter, Biot number, Brownian motion parameter, and thermophoresis parameter.     

Forced Convection Heat Transfer of Nanofluids in a Porous Channel

This article is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of force convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully developed flow and steady Darcy?CBrinkman?CForchheimer equation is employed in porous channel. The thermal equilibrium model is assumed between nanofluid and solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result the volume fraction distribution equation is also coupled with governing equations. The effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are completely studied. The results show that the local Nusselt number is decreased when the Lewis number is increased. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased and as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number, and modified diffusivity ratio on the volume fraction distribution are also studied and discussed.     

Thermal radiation effect on mixed convection heat and mass transfer of a non-Newtonian fluid over a vertical surface embedded in a porous medium in the presence of thermal diffusion and diffusion-thermo effects

Thermal radiation, thermal diffusion, and diffusion-thermo effects on heat and mass transfer by mixed convection of non-Newtonian power-law fluids over a vertical permeable surface embedded in a saturated porous medium are investigated. The governing equations describing the problem are non-dimensionalized and transformed into a non-similar form. The transformed equations are solved by using the local non-similarity method combined with the shooting technique. The effects of the physical parameters of the problem on the fluid temperature and concentration are illustrated graphically and analyzed. Also, the effects of the pertinent parameters on the local Nusselt number and the local Sherwood number are presented.     

Effects of thermophoresis and radiation on laminar flow along a semi-infinite vertical plate

The present contribution deals with the thermophoresis particle deposition and thermal radiation effects on the flow, heat and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by means of the fourth-order Runge–Kutta method with a shooting technique. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are tabulated and discussed.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption

The problem of magneto-hydrodynamic mixed convective flow and heat transfer of an electrically conducting, power-law fluid past a stretching surface in the presence of heat generation/absorption and thermal radiation has been analyzed. After transforming the governing equations with suitable dimensionless variables, numerical solutions are generated by an implicit finite-difference technique for the non-similar, coupled flow. The solution is found to be dependent on the governing parameters including the power-law fluid index, the magnetic field parameter, the modified Richardson number, the radiation parameter, the heat generation parameter, and the generalized Prandtl number. To reveal the tendency of the solutions, typical results for the velocity and temperature profiles, the skin-friction coefficient, and the local Nusselt number are presented for different values of these controlling parameters.     

Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory

A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications...     

Transient free convection flow between long vertical parallel plates with ramped wall temperature at one boundary in the presence of thermal radiation and constant mass diffusion

The unsteady laminar free convection flow between two long vertical parallel plates with ramped wall temperature at one boundary has been investigated in the presence of thermal radiation and chemical species concentration. The exact solutions of the momentum, energy and concentration equations have been obtained using the Laplace transform technique. The velocity and temperature profiles, skin-friction and Nusselt number variations are shown graphically and the numerical values of the volume flow rate, the total heat rate and species rate added to the fluid are presented in a table. The influence of different system parameters such as the radiation parameter (R), buoyancy ratio parameter (N), Schmidt number (Sc) and time (t) has been analyzed carefully. A critical analysis of the coupled heat and mass transfer phenomena is provided. The free convective flow due to ramped wall temperature has also been compared with the baseline case of flow due to constant wall temperature.     

An analytical treatment for combined heat transfer by radiation,convection and conduction within a heat insulating wall structure

An analytical procedure has been proposed to attack a highly conjugate thermal problem associated with radiation, convection and conduction within a heat insulating wall structure. Firstly, an analytical solution is derived for fully-developed mixed convective flow through parallel plates. Secondly, the resulting expressions for convection are coupled with radiation and conduction equations to form a set of heat balance equations for each heat transfer surface. Illustrative calculations are conducted to estimate heat transfer rates through a heat insulating roof structure with an aluminum partition with high reflectivity, subject to solar radiation in summer. The effect of an aluminum partition on the heat insulation is elucidated.     

Experimental investigation of TiO2/water nanofluid laminar forced convective heat transfer through helical coiled tube

Coiled tubes and nanofludics are two significant techniques to enhance the heat transfer ability of thermal equipments. The forced convective heat transfer and the pressure drop of nanofluid inside straight tube and helical coiled one with a constant wall heat flux were studied experimentally. Distilled water was used as a host fluid and Nanofluids of aqueous TiO₂ nanoparticles (50 nm) suspensions were prepared in various volume concentrations of 0.25–2 %. The heat transfer coefficient of nanofluids is obtained for different nanoparticle concentrations as well as various Reynolds numbers. The experiments covered a range of Reynolds number of 500–4,500. The results show the considerable enhancement of heat transfer rate, which is due to the nanoparticles present in the fluid. Heat transfer coefficient increases by increasing the volume concentration of nanoparticles as well as Reynolds number. Moreover, due to the curvature of the tube when fluid flows inside helical coiled tube instead of straight one, both convective heat transfer coefficient and the pressure drop of fluid grow considerably. Also, the thermal performance factors for tested nanofluids are greater than unity and the maximum thermal performance factor of 3.72 is found with the use of 2.0 % volume concentration of nanofluid at Reynolds number of 1,750.     

Two phase mixed convection Al2O3–water nanofluid flow in an annulus

Heat transfer enhancement of a mixed convection laminar Al₂O₃–water nanofluid flow in an annulus with constant heat flux boundary condition has been studied employing two phase mixture model and effective expressions of nanofluid properties. The fluid flow properties are assumed constant except for the density in the body force, which varies linearly with the temperature (Boussinesq’s hypothesis), thus the fluid flow characteristics are affected by the buoyancy force. The Brownian motions of nanoparticles have been considered to determine the effective thermal conductivity and the effective dynamic viscosity of Al₂O₃–water nanofluid, which depend on temperature. Three-dimensional Navier–Stokes, energy and volume fraction equations have been discretized using the finite volume method while the SIMPELC algorithm has been introduced to couple the velocity–pressure. Numerical simulations have been presented for the nanoparticles volume fraction (?) between 0 and 0.05 and different values of the Grashof and Reynolds numbers. The calculated results show that at a given Re and Gr, increasing nanoparticles volume fraction increases the Nusselt number at the inner and outer walls while it does not have any significant effect on the friction factor. Both the Nusselt number and the friction coefficient at the inner wall are more than their corresponding values at the outer wall.