Hybrid Nanofluid Flow with Homogeneous-Heterogeneous Reactions

This study examines the stagnation point flow over a stretching/shrinking sheet in a hybrid nanofluid with homogeneous-heterogeneous reactions. The hybrid nanofluid consists of copper (Cu) and alumina (Al₂O₃) nanoparticles which are added into water to form Cu-Al₂O₃/water hybrid nanofluid. The similarity equations are obtained using a similarity transformation. Then, the function bvp4c in MATLAB is utilised to obtain the numerical results. The dual solutions are found for limited values of the stretching/shrinking parameter. Also, the turning point arises in the shrinking region (λ < 0). Besides, the presence of hybrid nanoparticles enhances the heat transfer rate, skin friction coefficient, and the concentration gradient. In addition, the concentration gradient is intensified with the heterogeneous reaction but the effect is opposite for the homogeneous reaction. Furthermore, the velocity and the concentration increase, whereas the temperature decreases for higher compositions of hybrid nanoparticles. Moreover, the concentration decreases for larger values of homogeneous and heterogeneous reactions. It is consistent with the fact that higher reaction rate cause a reduction in the rate of diffusion. However, the velocity and the temperature are not affected by these parameters. From these observations, it can be concluded that the effect of the homogeneous and heterogeneous reactions is dominant on the concentration profiles. Two solutions are obtained for a single value of parameter. The temporal stability analysis shows that only one of these solutions is stable and thus physically reliable over time.     

What dominates heat transfer performance of hybrid nanofluid in single pass shell and tube heat exchanger?

Influence of nanoparticle volume concentration and proportion on heat transfer performance (HTP) of Al₂O₃ – Cu/water hybrid nanofluid in a single pass shell and tube heat exchanger is analyzed. Multiphase mixture model is adopted to model the flow. Three-dimensional governing equations and associated boundary conditions are solved using finite volume method. The numerical results are validated with the experimental results. Results indicate that optimized nanoparticle volume concentration and proportion dominate HTP of hybrid nanofluid. Heat transfer coefficient and Nusselt number are monotonic increase functions of nanoparticle volume concentration and proportion. The percentage increase in heat transfer coefficient of hybrid nanofluid is 139% than water and 25% than Cu/water nanofluid. At higher Reynolds number, the increment in Number of Transfer Units (NTU) between water and hybrid nanofluid is close to 75%. Maximum enhancement in Nusselt number for hybrid nanofluid exceeds 90% when compared to nanofluid (Al₂O₃/Water nanofluid). Consequently, highest heat transfer performance is attained for hybrid nanofluid systems. Effectiveness of heat exchanger increases almost to 124% when hybrid nanofluid is employed. We show that it is higher than water as well (conventional coolant). Results are expected to be helpful in further industrial-scale deployment of nanofluids, which is an area that is currently relevant for ongoing academia-industry partnership efforts worldwide.     

Numerical simulation of thermogravitational energy transport of a hybrid nanoliquid within a porous triangular chamber using the two-phase mixture approach

This study is a computational investigation of transient thermogravitational energy transport in H₂O/Al₂O₃ nanoliquid and water-based copper/aluminum oxide hybrid nanofluid (water/Al₂O₃-Cu) inside a horizontal isosceles triangular enclosure with porous medium. The governing equations for two-phase mixture flow have been derived by the use of Darcy-Brinkman model for porous media without the Forchheimer term (inertia loss). The control equations have been discretized using the finite volume technique. The effects of porosity factor, Rayleigh number, and Darcy number on the liquid motion and transient energy transport have been studied. The results have shown that convective thermal transmission in the nanofluid inside the triangular cavity generally consists of three phases: initial, transient, and quasi-steady, all of which are described in detail. It has been found that a rise of the porosity factor, Rayleigh number, or Darcy number always leads to an increment of the average Nusselt number and energy transport intensity. It has been also observed that with a rise of the Darcy number and strengthening of flow motion (convection), the instability in both flow and temperature fields increases and the distribution of isotherms and streamlines becomes completely asymmetric.     

Experimental hydrothermal characteristics of minichannel heat sink using various types of hybrid nanofluids

The hydrothermal characteristics of minichannel heat sink are analyzed experimentally by using deionized (DI) water based different nanoparticles mixture dispersed hybrid nanofluids. Al₂O₃, MgO, SiC, AlN, MWCNT and Cu nanoparticles are considered for this study. Different nanoparticles combinations (oxide-oxide, oxide-carbide, oxide-nitride, oxide-carbon nanotube and oxide-metal) in 50/50 vol ratio with base fluid (DI water) have been taken as coolants for volume concentration of 0.01%. Effects of volume flow rate (0.1–0.5LPM), fluid inlet temperature (20–40 °C) and Reynolds number (50–500) are studied for heat flux of 50 W/cm². Convective heat transfer coefficient and pressure drop are increased by about 42.24% and 22% for Al₂O₃ + MWCNT hybrid nanofluid. The maximum reduction of 21.36% in thermal resistance is obtained for Al₂O₃ + MWCNT hybrid nanofluid in comparison to DI water. Heat transfer effectiveness and figure of merit are above one for all the hybrid nanofluids which conclude that hybrid nanofluid is better option for electronics cooling over DI water. Al₂O₃ + MWCNT hybrid nanofluid is better in terms of heat transfer effectiveness; whereas, Al₂O₃ + AlN hybrid nanofluid (oxide-nitrite mixture) has maximum heat transfer coefficient to pressure drop ratio and coefficient of performance.     

Exact-solution of entropy generation for MHD nanofluid flow induced by a stretching/shrinking sheet with transpiration: Dual solution

In this article, attempts are made to present an exact solution for the fluid flow and heat transfer and also entropy generation analysis of the steady laminar magneto-hydrodynamics (MHD) nanofluid flow induced by a stretching/shrinking sheet with transpiration. This paper is the first contribution to the study of entropy generation for the nanofluid flow via exact solution approach. The governing partial differential equations are transformed into nonlinear coupled ordinary differential equations via appropriate similarity transformations. The current exact solution illustrates very good correlation with those of the previously published studies in the especial cases. The entropy generation equation is derived as a function of the velocity and the temperature gradients. The influences of the different flow physical parameters including the nanoparticle volume fraction parameter, the magnetic parameter, the mass suction/injection parameter, the stretching/shrinking parameter, and the nanoparticle types on the fluid velocity component, the temperature distribution, the skin friction coefficient, the Nusselt number and also the averaged entropy generation number are discussed in details. This study specifies that nanoparticles in the base fluid offer a potential in increasing the convective heat transfer performance of the various liquids. The results show that the copper and the aluminum oxide nanoparticles have the largest and the lowest averaged entropy generation number, respectively, among all the nanoparticles considered.     

Estimation of magnetohydrodynamic radiative nanofluid flow over a porous non‐linear stretching surface: application in biomedical research

The present study investigates the effects of thermal radiation and chemical reaction on magnetohydrodynamic flow, heat, and mass transfer characteristics of nanofluids such as Cu–water and Ag–water over a non‐linear porous stretching surface in the presence of viscous dissipation and heat generation. Using similarity transformation, the governing boundary layer equations of the problem are transformed into non‐linear ordinary differential equations and solved numerically by the shooting method along with the Runge–Kutta–Fehlberg fourth–fifth‐order integration scheme. The influences of various parameters on velocity, temperature, and concentration profiles of the flow field are analysed and the results are plotted graphically. A backpropagation neural network is applied to predict the skin friction coefficient, Nusselt number, and Sherwood number and these results are presented through graphs. The present numerical results are compared with the existing results and are found to be in good agreement. The results of artificial neural network and the obtained numerical values agree well with an error <5%.Inspec keywords: silver, copper, transforms, nanofluidics, friction, backpropagation, heat radiation, water, external flows, partial differential equations, nonlinear differential equations, boundary layers, Runge‐Kutta methods, mass transfer, flow through porous media, magnetohydrodynamicsOther keywords: magnetohydrodynamic radiative nanofluid flow, nonlinear stretching surface, biomedical research, thermal radiation, chemical reaction, magnetohydrodynamic flow, nonlinear porous stretching surface, viscous dissipation, similarity transformation, governing boundary layer equations, nonlinear ordinary differential equations, shooting method, Runge–Kutta–Fehlberg fourth–fifth‐order integration scheme, flow field, backpropagation neural network, Cu–water nanofluid, Ag–water nanofluid, skin friction coefficient, Nusselt number, Sherwood number, artificial neural network, Ag‐H₂ O, Cu‐H₂ O     

MHD boundary-layer flow due to a moving extensible surface

The flow due to a moving extensible sheet that obeys a more general stretching law is considered. The sheet occupies the negative x-axis and is moving continually in the positive x-direction, in an incompressible viscous and electrically conducting fluid. The sheet somehow disappears in a sink that is located at (x, y) = (0, 0). The governing system of partial differential equations is first transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using a finite-difference scheme, namely the Keller-box method. The features of the flow and heat-transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the flow near x = 0, where the velocity profiles show a reversed flow.     

Improving hydrothermal performance of hybrid nanofluid in double tube heat exchanger using tapered wire coil turbulator

Tapered wire coil insert is proposed as a novel enhancer in the double tube heat exchanger and experimental studies on Al₂O₃ + MgO hybrid nanofluid flowing under the turbulent condition are performed to investigate the hydrothermal characteristics. Effects of using tapered wire coil turbulator and hybrid nanofluid on the hydrothermal behaviors are examined for different coil configurations (Converging (C) type, Diverging (D) type and Conversing-Diverging (C-D) type) and hybrid nanofluid inlet temperatures and volume flow rates. Results show that D-type wire coil insert promotes better hydrothermal performance as compared to C-type and C-D type. Nusselt number and friction factor of hybrid nanofluid using D-type, C-D type and C-type wire coil inserts enhance up to 84%, 71% and 47%, and 68%, 57% and 46%, respectively than that of water in tube without insert. The entropy generation of hybrid nanofluid is lower than that of base fluid in all cases. The thermal performance factor for hybrid nanofluid is found more than one with all inserts. The thermal performance factor is observed a maximum of 1.69 for D-type coil. The study reveals that the hybrid nanofluid and tapered wire coil combination is promising option for improving the hydrothermal characteristics of double pipe heat exchanger.     

Unsteady mixed-convection boundary layer flow along a symmetric wedge with variable surface temperature

Laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past a sharp wedge has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity boundary layer equations, which are solved analytically for small time. Perturbation solutions are also obtained for small and large dimensionless time, τ. Solutions of the governing equations for all time are obtained employing the implicit finite difference method. Here we have focused our attention on the evolution of skin-friction coefficient (C_f) and local Nusselt number (Nu) (heat transfer rate), fluid velocity and fluid temperature with the effects of different governing parameters such as different time, τ, the exponent, m (=0.2, 0.4, 0.6, 0.8, 1.0), mixed convection parameter, λ (= 0.0, 0.5, 1.0) for fluids having Prandtl number, Pr = 0.1, 0.7, and 7.0.     

Entropy Generation for Flow and Heat Transfer of Sisko-Fluid Over an Exponentially Stretching Surface

In the present study, the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered. The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations. Runge-Kutta-Fehlberg method is used to solve the governing problem. The effects of magnetic field parameter M, local slip parameter λ, generalized Biot number γ, Sisko fluid material parameter A, Eckert number Ec, Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity, temperature, local entropy generation number N_G and Bejan number Be are inspected. Moreover, the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited. The current results are helpful in checking the entropy generation for Sisko-fluid. It is found that, an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity. For shear thinning fluids (n < 1), the temperature dominates and the velocity rises. Local entropy generation number is more for larger generalized Biot number, magnetic field parameter and Brinkman number. The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases. The local Nusselt number decreases as magnetic field parameter, local slip parameter and Eckert number are increase, while it increases as material parameter, generalized Biot number and Prandtl number are increase.     

Viscous flow due to an exponentially shrinking permeable sheet in nanofluid in presence of slip

Classical problem of steady boundary layer flow of nanofluid over an exponentially permeable shrinking sheet in presence of slip is investigated. The model used for nanofluid includes Brownian motion and thermophoresis effects. The governing equations for momentum, energy, and nanofluid solid volume fraction are transformed to ordinary differential equations with the help of similarity transformations and then solved numerically using fourth order Runge–Kutta method with shooting technique. It is found that the governing parameters, viz. the suction/blowing parameter, velocity slip, thermal and mass slip parameters, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number significantly affect the flow field, heat, and mass transfer. The results obtained indicate that the dual solutions exist for certain values of the mass suction parameter. Velocity increases whereas the temperature and nanoparticle volume fraction decrease due to suction through the porous sheet. It is noted that with the increase in velocity slip fluid velocity increases whereas temperature and concentration decrease. Due to increase in thermal slip and mass slip both temperature and concentration decrease.     

Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger

In present study, heat transfer and turbulent flow of water/alumina nanofluid in a parallel as well as counter flow double pipe heat exchanger have been investigated. The governing equations have been solved using an in-house FORTRAN code, based on finite volume method. Single-phase and standard k-ε models have been used for nanofluid and turbulent modeling, respectively. The internal fluid has been considered as hot fluid (nanofluid) and the external fluid, cold fluid (base fluid). The effects of nanoparticles volume fraction, flow direction and Reynolds number on base fluid, nanofluid and wall temperatures, thermal efficiency, Nusselt number and convection heat transfer coefficient have been studied. The results indicated that increasing the nanoparticles volume fraction or Reynolds number causes enhancement of Nusselt number and convection heat transfer coefficient. Maximum rate of average Nusselt number and thermal efficiency enhancement are 32.7% and 30%, respectively. Also, by nanoparticles volume fraction increment, the outlet temperature of fluid and wall temperature increase. Study the minimum temperature in the solid wall of heat exchangers, it can be observed that the minimum temperature in counter flow has significantly reduced, compared to parallel flow. However, by increasing Reynolds number, the slope of thermal efficiency enhancement of heat exchanger gradually tends to a constant amount. This behavior is more obvious in parallel flow heat exchangers. Therefore, using of counter flow heat exchangers is recommended in higher Reynolds numbers.     

Group method analysis of mixed convection boundary-layer flow of a micropolar fluid near a stagnation point on a horizontal cylinder

Summary The transformation group theoretic approach is applied to the system of equations governing the unsteady mixed convection boundary-layer flow of a micropolar fluid near a stagnation point on a horizontal cylinder. The application of a two-parameter group reduces the number of independent variables by two, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The possible forms of surface-temperature T_w, potential velocity U and sin with position and time are derived in steady and unsteady cases. New formulae of dimensionless temperature are presented using the group method analysis. Hiemenz and Falkner-Skan equations are obtained as special cases. The new similarity representations and similarity transformations in steady/unsteady states are obtained. The family of ordinary differential equations has been solved numerically using a fourth-order Runge-Kutta algorithm with the shooting technique. The effect of varying parameters governing the problem is studied.     

Blasius and Sakiadis problems in nanofluids

The classical problems of forced convection boundary layer flow and heat transfer past a semi-infinite static flat plate (Blasius problem) and past a moving semi-infinite flat plate (Sakiadis problem) using nanofluids are theoretically studied. The similarity equations are solved numerically for three types of metallic or nonmetallic nanoparticles such as copper (Cu), alumina (Al₂O₃), and titania (TiO₂) in the base fluid of water with the Prandtl number Pr = 6.2 to investigate the effect of the solid volume fraction parameter ?? of the nanofluids. Also, the case of conventional or regular fluid (?? = 0) with Pr = 0.7 is considered for comparison with known results from the open literature. The comparison shows excellent agreement. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles are presented and discussed in detail. It is found that the solid volume fraction affects the fluid flow and heat transfer characteristics.     

Variable viscosity effect on hydromagnetic flow and heat transfer about a fluid underlying the axisymmetric spreading surface

Summary. The effect of variable viscosity on the flow and heat transfer about a fluid underlying the axisymmetric spreading surface in the presence of an axial magnetic field has been investigated. The viscosity of the fluid is assumed to vary as an inverse linear function of temperature and the magnetic field strength is inversely proportional to the radial coordinate. The partial differential equations, governing the present problem, have been transformed, by suitable similarity variables, into a system of ordinary differential equations. This system is solved numerically by the shooting technique. Numerical results are introduced in graphical form for different values of viscosity parameter, _r, and magnetic field parameter. In the presence of variable viscosity, an increase in Prandtl number leads to a rise in the velocity field. Generally, it leads to a fall in the temperature field. Both magnetic field and variable viscosity raise the heat transfer and suppress the fluid flow.     

Analytical solutions of hydromagnetic boundary-layer flow of a non-Newtonian power-law fluid past a continuously moving surface

Summary The boundary-layer flow of a power-law non–Newtonian fluid over a continuously moving surface in the presence of a magnetic field B(x) applied perpendicular to the surface has been investigated. An analytical solution is obtained and compared with the numerical solution of the resulting non linear ordinary differential equation. The effects of the Stewart number (N) and the power law-index (n) on the velocity profiles and the skin-friction are studied.     

Injection of a non-Newtonian fluid through one side of a long vertical channel

Summary The problem considered here is the injection of a non-Newtonian fluid with elastic properties through one side of a long vertical channel. Using the transformations proposed by Wang and Skalak [14] for the velocity components, the basic equations governing the flow and heat transfer are reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions. The effect of the non-Newtonian parameter,S, on the velocity field and heat transfer on the walls is examined carefully.     

Numerical study on heat transfer and entropy generation of developing laminar nanofluid flow in helical tube using two-phase mixture model

Nanofluids and helical tubes are among the best methods for heat transfer enhancement. In the present study, laminar, developing nanofluid flow in helical tube at constant wall temperature is investigated. The numerical simulation of Al₂O₃-water nanofluid with temperature dependent properties is performed using the two-phase mixture model by control volume method in order to study convective heat transfer and entropy generation. The numerical results is compared with three test cases including nanofluid forced convection in straight tube, velocity profile in curved tube and Nusselt number in helical tubes that good agreement for all cases is observed. Heat transfer coefficient in developing region inside a straight tube using mixture model shows a better prediction compared to the homogenous model. The effect of Reynolds number and nanoparticle volume fraction on flow and temperature fields, local and overall heat transfer coefficient, local entropy generation due to viscous dissipation and heat transfer, and the Bejan number is discussed in detail and compared with the base fluid. The results show that the nanofluid and the base fluid have almost the same axial velocity profile, but their temperature profile has significant difference in developing and fully developed region. Entropy generation ratio by nanofluid to the base fluid in each axial location along the coil length showed that the entropy generation is reduced by using nanofluid in at most length of the helical tube. Also, better heat transfer enhancement and entropy generation reduction can be achieved at low Reynolds number.     

Moving wedge and flat plate in a micropolar fluid

Similarity solutions for a moving wedge and flat plate in a micropolar fluid may be obtained when the fluid and boundary velocities are proportional to the same power-law of the downstream coordinate. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solve numerically using a finite-difference scheme known as the Keller-box method. Numerical results are given for the dimensionless velocity and microrotation profiles, as well as the skin friction coefficient for several values of the Falkner–Skan power-law parameter (m), the ratio of the boundary velocity to the free stream velocity parameter (λ) and the material parameter (K). Important features of these flow characteristics are plotted and discussed. It is found that multiple solutions exist when the boundary is moving in the opposite direction to the free stream, and the micropolar fluids display a drag reduction compared to Newtonian fluids.     

On some helical flows of Oldroyd-B fluids

Summary In this study the velocity fields and the associated tangential stresses corresponding to some helical flows of Oldroyd-B fluids between two infinite coaxial circular cylinders and within an infinite circular cylinder are determined in forms of series in terms of Bessel functions. At time t = 0 the fluid is at rest and the motion is produced by the combined action of rotating and sliding cylinders. The solutions that have been obtained satisfy the governing differential equations and all imposed initial and boundary conditions. For λ _r = 0, λ = 0 or λ _r = λ = 0 they reduce to the similar solutions for a Maxwell, second grade or Newtonian fluid, respectively. Finally, for comparison, the velocity profiles corresponding to the four models are plotted for different values of t.