Opposing Flow Cases Research Articles

Double-diffusive convection: Flow of nanofluid of variable heat capacity inside rectangular and inclined walls

Double-diffusive convection has been investigated in the flow of nanofluid of variable heat capacity, whereas the flow is maintained inside rectangular and inclined walls. The effective transport of heat in many engineering systems is ensured by considering the appropriate and suitable geometrical structure of such systems and the types of coolant used for those purposes. Therefore, these two key features have been the focus of this investigation. The well-known Buongiorno model is taken for the flow of nanofluid of variable heat capacity, whereas the fluid flow model is simulated for the upper half channel only. The governing partial differential equations are simplified and converted into a system of ordinary differential equations. The nature and behaviour of velocity, temperature and concentration (nanoparticles) profiles have been studied and analysed inside a converging–diverging channel in the presence of assisting and opposing flow cases with variation of heat capacity and thermal conductivity of nanomaterial in the base (host) fluid. Moreover, linear, nonlinear, uniform, increasing, decreasing and asymptotic nature of the field variables (velocity, temperature and concentration functions) has been found in the presence of existing parameters, whereas, the three quantities of physical interest i.e. pressure, skin friction and rates of heat and mass transfer have been determined at the upper wall of the channel against the different parameters, involved in the problem.

Assisting and opposing flow of a MHD hybrid nanofluid flow past a permeable moving surface with heat source/sink and thermal radiation

The aim of the current investigation is to study the assisting and opposing flow effects on hybrid nanofluid ( SiO 2 - MoS 2 /water) flow past a moving surface under the impact of heat source/sink, thermal radiation and velocity slip. Also, the moving surface is exposed to convective heating and surface is assumed to be permeable in an attempt to achieve the suction/injection of hybrid nanofluid boundary layer through the surface. As a novelty, we have presented a comparative analysis of all the results for assisting and opposing flow cases. Similarity transformations are utilized to transcribe the momentum and thermal equations in non-dimensional form. The “bvp4c” solver is used to solve the hybrid nanofluid flow problem numerically. Effects of the assisting and opposing flow with nanoparticles volume fraction, heat source/sink, Biot number, thermal radiation parameter, velocity slip parameter and suction/injection parameter on the temperature and velocity profiles are studied. The variations in skin friction and heat transfer coefficient are discussed through tables outlined and three-dimensional figures. Results reveals that hybrid nanofluid velocity is higher in case of assisting flow in comparison to opposing flow. The role of increasing values of Biot number and thermal radiation parameter is to surge the temperature of the hybrid nanofluid ( SiO 2 - MoS 2 /water) flow as well as rate of heat transfer at the surface. The nanoparticles volume fraction (of MoS 2 and SiO 2 ) also enhances the temperature at the wall. It is revealed that slip parameter has contrary effects on both heat transfer and skin friction coefficient for assisting and opposing flow.

Numerical investigation of mixed convection boundary layer flow for nanofluids under quasilinearization technique

The study of boundary layer flow under mixed convection has been investigated numerically for various nanofluids over a semi-infinite flat plate which has been placed vertically upward for both buoyancy-induced assisting and buoyancy-induced opposing flow cases. To facilitate numerical calculations, a suitable transformation has been made for the governing partial differential equations (PDEs). Then, similarity method has been applied locally to approximate the nonlinear PDEs into a coupled nonlinear ordinary differential equations (ODEs). Then, quasilinearization method has been taken for linearizing the nonlinear terms which are present in the governing equations. Thereafter, implicit trapezoidal rule has been taken for integration numerically along with principle of superposition. The effect of physical parameters which are involved in the study are analyzed on the flow and heat transfer characteristics. This study reveals the presence of dual solutions in case of opposing flow. Further, this study shows that with increasing phi and Pr, the range of existence of dual solutions becomes wider. Also, it has been noted that nanofluids enhance the process of heat transfer for buoyancy assisting flow and it delays the separation point in case of opposing flow.

Flow towards a Stagnation Region of a Curved Surface in a Hybrid Nanofluid with Buoyancy Effects

This paper examines the impact of hybrid nanoparticles on the stagnation point flow towards a curved surface. Silica (SiO2) and alumina (Al2O3) nanoparticles are added into water to form SiO2-Al2O3/water hybrid nanofluid. Both buoyancy-opposing and -assisting flows are considered. The governing partial differential equations are reduced to a set of ordinary differential equations, before being coded in MATLAB software to obtain the numerical solutions. Findings show that the solutions are not unique, where two solutions are obtained, for both buoyancy-assisting and -opposing flow cases. The local Nusselt number increases in the presence of the hybrid nanoparticles. The temporal stability analysis shows that only one of the solutions is stable over time.

Implications of the third-grade nanomaterials lubrication problem in terms of radiative heat flux: A Keller box analysis

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.

Numerical study and error estimation in power-law nanofluid flow over vertical frustum of a cone

The aim of this article is to analyze the mixed convective Ostwald–de Waele power-law nanofluid flow over vertical frustum of a cone in a non-Darcy porous medium using an efficient numerical technique. The involved power-law nanofluid model utilizes water as the base fluid, and Ti-alloy (Ti6Al4V) and multi-wall carbon nanotubes (MWCNTs) as the nanoparticles. The solution of resultant non-similarity equations subjected to boundary conditions is described using the local non-similarity technique along with an efficient spectral local linearization method. The error estimation is provided to show the efficiency of above-mentioned solution procedure. A detailed explanation about the impact of nanoparticle volume fraction on the dimensionless velocity and temperature profiles along with heat transfer rate and skin friction coefficient is also provided for both the opposing and aiding flow cases. On comparison of the present results in particular cases with the relevant published data, it is assured that this method gives highly accurate outcomes for this kind of very complex fluid flow problems. The domination of dilatant nanofluid over pseudo-plastic nanofluid in both the aiding and opposing flow cases is noticed for velocity profiles, and the velocity is decreased with an increment in the nanoparticle volume fraction. Also, the variation in profiles with a streamwise coordinate $$\xi$$ shows non-similar nature of the problem. The use of Ti-alloy and MWCNTs in this work makes it very profitable in various important sectors like aerospace and medical sector.

Effect of dispersion on thermally stable stratified power‐law fluids over the vertical frustum of a cone in a non‐Darcy porous medium: Flow separation

AbstractThe present problem shares out the influences of convective heating and thermal dispersion on thermally stable stratified power‐law fluid flow over the vertical frustum of a cone situated in a non‐Darcy porous medium. For the first time, it is considered in both aiding and opposing flow cases as it is readily applicable in realistic, practical situations. The local nonsimilarity approach, along with the spectral local linearization method, is used to analyze the fluid behavior and heat transfer within the boundary layer region. In addition, error analysis and comparison with the existing results are also included to validate the obtained results wherever feasible. It is significant to perceive the existence of flow separation in this study as more gain of the velocity of a power‐law fluid is seen for aiding flow case in comparison with the opposing flow case. Also, it is evident from these results that the separation of flow is less in the presence of thermal stratification, but it is more in the absence of thermal stratification. Finally, thermal stratification significantly affects the heat transfer rate of power‐law fluids besides delaying the boundary layer separation.

Magnetohydrodynamics (MHD) stagnation point flow past a shrinking/stretching surface with double stratification effect in a porous medium

The present work emphasizes the MHD mixed convective stagnation point flow over a shrinking/stretching surface saturated in a porous medium. The double stratification with heat source effects are also considered while the magnetic field is imposed normal to the sheet. The governing model (partial differential equations) is converted into a system of ordinary (similarity) differential equations using similarity transformations. The boundary value problem solver (bvp4c) in the MATLAB software is utilized for the numerical computations. Numerical results are graphically illustrated in the form of velocity, temperature and concentration profiles for several values of buoyancy, magnetic, thermal and solutal stratification parameters. The graphs of skin friction coefficient, local Nusselt and Sherwood numbers portray that the dual solutions are achievable within a certain range of the buoyancy and velocity ratio parameters. Both assisting and opposing flow cases can generate two solutions, whereas the forced convective flow only produces a unique solution. The execution of stability analysis affirms the reliability of the first solution. Both heat and mass transfer rates intensify with the increment of the velocity ratio parameter for all type of convective flows. The fluid temperature and concentration decrease with the increment of the thermal and solutal stratification parameters, respectively, whereas the magnetic and buoyancy parameters reduce both temperature and concentration profiles.

Wavelet analysis of stagnation point flow of non-Newtonian nanofluid

The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.

The Effectiveness of Variable Properties on Thermophoresis Particle Deposition at The Levels of 1st and 4th Orders of Chemical Reaction of Buoyancy-driven Flows of Second Grade Fluid

This article presents the analytic solution to a steady, incompressible, free convective flow of an electrically conducting second grade fluid past a vertical surface with variable properties namely: variable viscosity; variable thermal conductivity and variable concentration diffusivity in the presence of thermophoresis, chemical reaction and convective boundary condition. The impact of different orders of chemical reaction on thermophoresis and the transport process of flow, heat and mass transfer in the boundary layer for assisting and opposing flow cases are properly examined and discussed. The governing equations associated with the fluid model are transformed and parameterized to a system of coupled nonlinear ordinary differential equations using similarity transformations. The resulting coupled ordinary differential equations (ODEs) were solved by adopting the Optimal Homotopy Analysis Method (OHAM). The results indicate that velocity and temperature distributions are decreasing functions of second grade parameter for both cases of assisting and opposing flows. Also, concentration distribution is a decreasing function of thermophoretic parameter for low and high orders of chemical reaction.

Effects of thermophoresis and variable properties on mixed convection along a vertical wavy surface in a fluid saturated porous medium

This paper investigates the influence of thermophoresis on mixed convection heat and mass transfer flow over a vertical wavy surface in a porous medium with variable properties, namely variable viscosity and variable thermal conductivity. The effect of wavy surface is incorporated into non-dimensional equations by using suitable transformations and then transformed into non-linear ordinary differential equations by employing the similarity transformations and then solved numerically. The transport process of flow, heat and mass transfer in the boundary layer for aiding and opposing flow cases is discussed. The structure of flow, temperature and concentration fields in the Darcy porous media are more pronounced by complex interactions among variable viscosity, variable thermal conductivity, mixed convective parameter, thermophoresis and amplitude of the wavy surface. Increasing thermophoresis parameter enhances velocity profile, concentration distribution and Sherwood number while reduces Nusselt number. As increase in variable viscosity, temperature and concentration distributions are enhanced while velocity profile, Nusselt number and Sherwood numbers are reduced. This study finds applications in aerosol Technology, space technology and processes involving high temperatures.

Magnetohydrodynamic (MHD) mixed convection stagnation point flow of a nanofluid over a vertical plate with viscous dissipation

In this study, magnetohydrodynamic effects on the mixed convection flow of nanofluid particles, namely, Cu (copper) and Al2O3 (alumina) near a stagnation region over a vertical plate in the presence of viscous dissipation is investigated. The governing equations of the nanofluid flow model proposed by Tiwari and Das (Int. J. Heat Mass Transfer, 50, 2002 (2007). doi:10.1016/j.ijheatmasstransfer.2006.09.034) are converted into a dimensionless nonlinear system of ordinary differential equations by using the similarity transformation. The solution of the resulting equations is obtained numerically by using a very efficient implicit scheme known as the Keller box method. A comparison with previous studies is shown in tabular form and excellent agreement is found. The effects of pertinent parameters like magnetic parameter M, Eckert number Ec, and volume fraction parameter ϕ on velocity, temperature, skin friction coefficient, and local Nusselt number with fixed value of Prandtl number Pr = 6.2 are shown graphically and discussed. These results show that the skin friction coefficient increases for both nanoparticles in assisting and opposing flow cases because of increasing absolute values of M and Ec, on the other hand heat transfer rate is enhanced in the opposing flow case and reduced in the assisting flow case. The values of skin friction coefficient for both nanoparticles, namely, Cu and Al2O3 increase with the increase in volume fraction parameter ϕ in both assisting and opposing flow cases and Cu has a higher value than Al2O3. The same behavior is observed for local Nusselt number in opposing flow, but in assisting flow the value of local Nusselt number decreases with the increase of ϕ in the presence of magnetic and viscous dissipation effects and Cu has a smaller value than Al2O3.

Axisymmetric stagnation point flow and heat transfer towards a permeable moving flat plate with surface slip condition

The steady axisymmetric stagnation point flow and heat transfer of a viscous and incompressible fluid due to a permeable moving flat plate with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the partial differential Navier–Stokes and energy equations to ordinary (similarity) differential equations, which are then solved numerically. Analytical solutions for the energy similarity equation have been also obtained for some particular values of the governing parameters. The important finding in this paper is the combined effect of the partial slip with the moving and the suction parameters on the skin friction coefficients, heat transfer, and the velocity and temperature profiles. Dual solutions are found for suction and opposing flow cases.

Mixed convection flow of a viscoelastic fluid near the orthogonal stagnation-point on a vertical surface

An analysis of the steady mixed convection flow of a viscoelastic fluid stagnating orthogonally on a heated or cooled vertical flat plate has been studied. Using similarity variables, the governing equations are transformed into a system of two coupled non-linear ordinary differential equations. The resulting equations are then solved numerically using the spectral method. It is observed that the skin friction coefficient and the local heat transfer are decreasing when the Weissenberg number We is increasing in both assisting and opposing flow cases. On the other hand, the skin friction is decreasing and the local heat transfer is increasing when the Prandtl number Pr is increasing in the case of assisting flow. In the case of opposing flow, the skin friction and the local heat transfer are increasing as Pr is increasing.

MHD mixed convection boundary layer flow towards a stretching vertical surface with constant wall temperature

This work considers a steady two-dimensional magnetohydrodynamic (MHD) flow of a viscous, incompressible and electrically conducting fluid over a stretching vertical surface with constant wall temperature. The external flow and the stretching velocities are assumed to vary with x , where x is the distance from the slot where the surface is issued. The transformed boundary layer equations are solved numerically for some values of the related parameters, namely the magnetic parameter M, the velocity ratio parameter ε and the mixed convection or buoyancy parameter λ, while the Prandtl number Pr is fixed to unity, using a finite-difference scheme known as the Keller-box method. Both assisting and opposing flow cases are considered. It is found that the magnetic parameter M significantly affects the flow and the thermal fields, besides increasing the range of λ for which the solution exists. Dual solutions are found to exist for some range of the mixed convection parameter.

Mixed convection boundary layer flow along vertical thin needles: Assisting and opposing flows

The problem of steady laminar mixed convection boundary layer flow of an incompressible viscous fluid along vertical thin needles for both assisting and opposing flow cases is considered in this paper. The transformed boundary layer equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method. Numerical computations are carried out for various values of the dimensionless parameters of the problem, namely the mixed convection parameter λ and the parameter a representing the needle size, with Prandtl number, Pr=0.7. It has been found that the flow and heat transfer characteristics are significantly influenced by these parameters.

Mixed convection boundary layer flow along vertical moving thin needles with variable heat flux

The problem of steady laminar mixed convection boundary layer flow of an incompressible viscous fluid along vertical moving thin needles with variable heat flux for both assisting and opposing flow cases is theoretically considered in this paper. The governing boundary layer equations are first transformed into non-dimensional forms. The curvature effects are incorporated into the analysis whereas the pressure variation in the axial direction has been neglected. These equations are then transformed into similarity equations using the similarity variables, which are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for a blunt-nosed needle (m = 0). Numerical calculations are carried out for various values of the dimensionless parameters of the problem, which include the mixed convection parameter λ, the Prandtl number Pr and the parameter a representing the needle size. It is shown from the numerical results that the skin friction coefficient, the surface (wall) temperature and the velocity and temperature profiles are significantly influenced by these parameters. The results are presented in graphical form and are discussed in detail.

Steady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface

PurposeTo study the steady mixed convection boundary‐layer flow of a micropolar fluid near the region of the stagnation point on a double‐infinite vertical flat plate is studied. The results of this paper are important for the researchers in the area of micropolar fluids.Design/methodology/approachFor the case considered the problem reduces to a system of ordinary differential equations, which is solved numerically using the Keller‐box method. This method is very efficient for solving boundary‐layer problems and it can easily be applied to other general situations than that presented in this paper. Any PhD student can learn and apply it very easily.FindingsRepresentative results for the velocity, microrotation and temperature profiles, as well as for the reduced skin friction coefficient and the local Nusselt number have been obtained for the case of strong concentration, Prandtl number of 0.7, some values of the material parameter K and the mixed convection parameter λ(≥0). Both assisting and opposing flow cases are considered. Results for the reduced skin friction coefficient and reduced local Nusselt number as well as for the reduced velocity, temperature and microrotation profiles are given in tables and figures. The obtained results are compared with ones from the open literature and it is found that they are in excellent agreement. The important conclusion is, we have been able to show that for opposing flow solutions are possible are possible only for a limited range of values of the mixed convection parameter λ.Research limitations/implicationsThe results of this paper are valid only in the small region around the stagnation point on a vertical surface and they are not applicable outside this region.Practical implicationsThe theory of micropolar fluids and also the results of the present paper can be used to explain the characteristics in certain fluids such as exotic lubricants, colloidal suspensions or polymeric fluids, liquid crystals, and animal blood.Originality/valueThe paper is very well prepared, presented and readable. We believe that the results are original and important from both theoretical and application point of views.

Mixed convection boundary layer flow about an isothermal sphere in a micropolar fluid

The steady mixed convection boundary layer flow of a micropolar fluid about a sphere with a constant surface temperature is considered for both the assisting and opposing flow cases. The transformed conservation equations of the non-similar boundary layers are solved numerically using a very efficient finite-difference method known as the Keller-box scheme. Numerical results are presented for different values of the material and mixed convection parameters K and λ, respectively, and with the Prandtl number Pr=0.7 and 7. It is found that assisting flow ( λ>0) delays separation of the boundary layer and can, if the assisting flow is strong enough, suppress it completely. The opposing flow ( λ<0), on the other hand, brings the separation point nearer to the lower stagnation point of the sphere and for sufficiently strong opposing flows there will not be a boundary layer on the sphere. Some results were given in the form of tables. Such tables are very important and they can serve as a reference against which other exact or approximate solutions can be compared in the future.

Laminar mixed convection flow in a vertical tube

A computational study is conducted to quantify the buoyancy effects on laminar forced flow of air in a heated/cooled vertical tube. Buoyancy assisting and buoyancy opposing flow cases are considered for heating/cooling rates that provide either uniform wall temperature or uniform heat flux conditions. The nature of the observed effects of various heating/cooling rates and configurations on the velocity and temperature development, as well as on flow reversal, is explained. Critical buoyancy parameters that signal the onset of flow reversal, as well as axial locations where flow reversal first occurs, are determined in the study. The effects of the buoyancy parameter on friction factors, Nusselt numbers, and flow and thermal entry lengths are documented.