Transient Mixed Convection Flow Research Articles

Reduced Gravity and Magnetohydrodynamic Effects on Transient Mixed Convection Flow Past a Magnetized Heated Cone Embedded in Porous Medium

The effects of reduced gravity on the periodic behavior of convective heat transfer characteristics of fluid flow along the magnetized heated cone embedded in porous medium is studied in the current contribution. The mathematical form of the nonlinear partial differential equations subject to the boundary conditions for the proposed unsteady model is presented. By employing appropriate dimensionless quantities, the mathematical equations are transformed into dimensionless form to get the numerical solutions of the proposed model. The dimensionless form is further condensed to a form that is more straightforward for smooth numerical computations. Later, large simulations are run using the implicit finite difference method for appropriate range of parameters values included in the flow model. The effect of reduced gravity parameter R g , the Richardson parameter or mixed convection parameter λ , the Prandtl number Pr, and the porosity parameter Ω , on chief physical quantities, that is, velocity profile, temperature distribution, magnetic intensity, transient skin friction, transient rate of heat transfer, and transient current density are simulated and highlighted graphically. Additionally, via careful examination and intentional discussion of physical reasoning, the physical impacts of various factors on the material qualities are examined. Applications that motivate the present work is the reduced gravity effects due to which the other nongravity forces such as thermal volume expansion, density difference, and magnetic field can induce the fluid motion.

Theoretical Analysis of the Effects of Exothermic Catalytic Chemical Reaction on Transient Mixed Convection Flow along a Curved Shaped Surface.

The present problem addressed the transient behavior of convective heat and mass transfer characteristics across a curved surface under the influence of exothermic catalytic chemical reactions. The governing non-linear mathematical model wastransformed into a convenient form with the help of a primitive variable formulation. The final primitive formed model wassolved numerically by applying the finite difference method. The analysis of the above said computed numerical data in terms of oscillatory heat transfer, skin friction, and oscillatory mass transfer for various emerging parameters, such as the mixed convection parameter λT, modified mixed convection parameter λc, index parameter n, activation energy parameter E, exothermicparameter β, temperature relative parameter γ, chemical reaction parameter λ, and Schmidt number Sc is plotted in graphical form. An excellent agreement is depicted for oscillatory heat transfer behavior at the large value of activation energy E. The amplitude of heat transfer and prominent fluctuating response in mass transfer with a certain height is found at each value of the index parameter n with a good alteration. An increase in the activation energy led to an increase in the surface temperature, which yielded more transient heat transfer in the above-said mechanism. The main novelty of the current study is that first, we ensured the numerical results for the steady state heat and fluid flow and then these obtained results wereused in the unsteady part to obtain numerical results for the transient behavior of the heat and mass transfer mechanism.

Influence of chemical kinetic exponent on transient mixed convective hydromagnetic flow in vertical channel with convective boundary condition

A flow that is subject to the influence of both thermal buoyancy and pressure gradient is called mixed convection. This kind of flow can be found in a wide variety of scientific and infrastructural functionalities, such as sunlight transceivers that are open to the airflow, digital devices that are kept cool by fans, nuclear reactors that are cooled during emergency shutdowns, and heat exchangers that are placed in low-velocity environments. This paper present MHD coupled convection flow of chemical reaction of an exothermic and chemical kinetic fluid with Newtonian heating in a vertical channel. chemical reaction (λ), magnetohydrodynamics ( Ha ), Navier slip (Γ), and Newtonian heating ( Br ) are all taken into consideration, in addition to the chemical kinetic exponent ( m ). Homotopy perturbation techniques and implicit finite difference scheme are used to find the steady-state solution and transient state solution for the set of dimensionless coupled governing equations. The rate of heat transfer and sheer stress were derived by differentiating the analytical solution obtained. Various pertinent parameters controlling the flow such as chemical reaction parameter (λ), MHD ( Ha ), Newtonian heating parameter ( Br ), chemical kinetic exponent ( m ) and Navier slip parameter (Γ) are illustrated graphically. Velocity and temperature fields are also demonstrated. The studies showed that a little rise in the Hartman number induces the Lorentz force, which streamlines the velocity boundary layer, decelerating the flow. A minor increase in the mixed convection parameter, on the other hand, resulted in significantly enhanced flow profiles, resulting in a greater flow rate during biomolecular kinds of chemical processes. Also during course of computation, the energy and velocity profiles improve with increase in (λ), ( Br ), ( m ),(γ) and ( Gre ). However, a graphical comparison of the transient solution and the steady state solution was also displayed, with an outstanding agreement.

Investigation of transport mechanism in transient mixed convective flow of magnetize Maxwell nanofluid subject to nonuniform source/sink

Nowadays, the heat transfer potential of the base fluids can also be improved by adding nanoparticles to them. These nanotechnology-based fluids, called nanofluid, have superior properties such as high thermal conductivity, large critical heat flux (CHF) and improved heat transfer coefficient. The purpose of this paper is to study the thermal effectiveness of nanoparticles in transient flow of Maxwell fluid together the properties of mixed convection and magnetic field. Thermal field is controlled with the novel aspects of variable conductivity and nonuniform heat sink/source. Additionally, the impact of Brownian and thermophoretic diffusions is considered caused by nanoparticles dispersion in the fluid. The appropriate conversions yield the governing nonlinear ordinary differential system. Homotopic approach has been utilized to attain the solution of differential system and results are envisioned graphically. This study explores that the buoyancy ratio and mixed convection parameters enhance the velocity field. Further, the heat transfer rate rises significantly as the thermophoretic and Brownian diffusion parameters increase. Moreover, the effect of nonuniform heat source/sink on temperature field is noticed to be an increasing trend of temperature profile.

Computational analysis of the transient mixed convective flow of nanofluid in the plume regions

Computer microchips and many other electrical devices that use microfluidics use nanofluids as coolants. Nanofluids have a higher thermal conductivity due to the volumetric proportion of nanoparticles. Thus, as the nanofluids in engineering and industrial process have a significant role, the current study aims to focus on the transient mixed convective flow of nanofluid in the plume regions. The numerical solutions for the transient mixed convection flow in the form of amplitude and phase angle are performed reasonably. The desired nonlinear mathematical model is created by incorporating periodic behavior into conservation equations and appropriate boundary conditions. Using appropriate scaling variables, the dimensioned equations are transformed into dimensionless ones. Solutions for the values of Prandtl number Pr, Schmidt number Sc, thermophoretic parameter Nt, Brownian motion parameter Nb and mixed convection parameters and show that the coupling between the fluid and heat transfer can have dramatic effects on the transient shear stress heat and mass transfer. The buoyancy force acting on the heated boundary layer of nanofluid can also have a significant impact on transient skin friction, heat and mass transfer. The governing process is accelerating or depending upon the position of the sphere.

Numerical simulation of a non-linear nanofluidic model to characterise the MHD chemically reactive flow past an inclined stretching surface

A computational approach is delineated for mass and heat transport enhancement/reduction process to control the drift of nanofluid. The fluid is drifting on the inclined stretched surface. This numerical study demands the resolution of fundamental (conservation momentum, mass transfer, and energy) equations and for which computational proficiency is a challenge. The time-dependent concentration and temperature on the periphery, together with stretched velocity, are the basis of the transient mixed convective laminar nanofluid flow. A similar transformations technique is imposed to adopt a system of time dominated non-linear fundamental equations and transformed it into a differential equation of the ordinary system. It is solved computationally by utilising the scheme of Nactsheim–Swigert shooting along with the iteration process, namely Runge–Kutta of order six. The obtained model depends on diversified natural parameters and is narrated on several profiles. Moreover, an explicit scheme has also been imposed to illustrate the developed visualisation of the fluid flow with the aid of streamlines and isothermal lines. Here, the stretching parameter demonstrates a provoking character on the momentum boundary layer, and the Prandtl number depicts an insignificant minimal impact on the mass transfer flow. The accuracy of this model is found satisfactory by validating with experimental data and comparing it with the previous numerical tests. This investigation has applications in engineering industries in thermal nano-technological materials processing and manufactures.

Influence of Chemical Kinetic Exponent on Transient Mixed Convective Hydromagnetic Flow in Vertical Channel with Convective Boundary Condition

Influence of Chemical Kinetic Exponent on Transient Mixed Convective Hydromagnetic Flow in Vertical Channel with Convective Boundary Condition

Heat transfer enhancement with pressure drop optimisation in a horizontal porous channel locally heated from below

In this work, transient mixed convection heat transfer and fluid flow in a horizontal porous layer bounded by two impermeable plates with a localised heating from below is numerically studied. The study is conducted using the Brinkman–Forchheimer-extended Darcy model and the one-equation energy model based on the assumption of local thermal equilibrium. The effects of porosity (ɛ = 0.7−0.95) and permeability represented by Darcy number (Da = 0.1−100) are investigated for the following ranges of Richardson (Ri = 1−100) and Reynolds (Re = 0.1−50) numbers. The results show that the existence of the porous material increases Nusselt number, but does not change its trend with Reynolds number for all Richardson numbers. Interestingly, it is shown that unstable, oscillatory flow and temperature fields are generated in both empty and porous channels at higher Richardson number and/or higher Reynolds number. Also, both the heat transfer and the pressure drop are found to decrease as the porosity increases; however, the effect of Darcy number depends strongly on the range of Reynolds number.

Effects of Chemical Reaction on Transient MHD Flow with Mass Transfer Past an Impulsively Fixed Infinite Vertical Plate in the Presence of Thermal Radiation

The effects of chemical reaction on a transient MHD mixed convection flow with mass transfer past an impulsively fixed infinite vertical plate under the influence of a transverse magnetic field have been presented. The medium is considered to be non-scattering and the fluid to be non-gray having emitting-absorbing and optically thick radiation limit properties. The dimensionless governing equations of the flow and mass transfer with boundary conditions are solved numerically by using the Ritz finite element method. The numerical results for the velocity, temperature and the concentration profiles as well as the skin-friction coefficient for different values of physical parameters such as the radiation parameter, magnetic parameter, Schmidt number and chemical reaction parameter have been obtained and presented through graphs and tables. It has been found that there is a fall in the temperature and velocity for both air and water as the radiation parameter is increased. An increase in the Schmidt number and chemical reaction parameter results a decrease in the concentration and velocity profiles for both air and water. Furthermore, an increase in the radiation parameter, magnetic parameter, Schmidt number and chemical reaction parameter decreases the skin-friction.

CFD based investigations on the effects of blockage shapes on transient mixed convective nanofluid flow over a backward facing step

The separation and reattachment flow occurs in a backward-facing step (BFS) is available in various industrial applications such as gas turbine engines, combustors, aircraft, buildings and many other devices of heat transfer. It represents the pillar key of determining the flow structure and significantly affecting the heat transfer mechanism. This work studies numerically the effects of four various types of blockage shapes on transient laminar mixed convective nanofluid flow over a horizontal BFS placed in a duct. Nanoparticles of SiO2 with ethylene glycol as a base fluid at 2% of volume fraction and 20 nm of nanoparticle diameter are considered to examine the effect of different blockage shape on the thermal and flow fields at different time scales. The downstream of the step is kept at a constant heat flux of 500 W/m2, while other walls and sides of the duct are considered thermally insulated. The Reynolds number used in this study is in the range of 50–200. The relevant governing equations (continuity, momentum and energy) along with the boundary conditions are solved with the aid of finite volume method (FVM). The results reveal that after dimensionless time of τ = 5 the trend of nanofluid flow and recirculation area near the step and behind the blockage shape does not change significantly and this time is selected as a quasi-steady state time and the point of comparison. The velocity distributions for front facing triangular blockage decreased and this blockage shape has the highest value of skin friction coefficient beyond Re = 150. The results indicate that the front facing triangular blockage has the highest value of average Nusselt number and performance evaluation index while the trapezoidal blockage has the lowest value

Unsteady Flow of a Nanofluid over a Sphere with Nonlinear Boussinesq Approximation

A theoretical study is presented for transient mixed convection flow of a nanofluid in the forward stagnation region of a heated sphere that is rotating with time-dependent angular velocity, taking nonlinear Boussinesq approximation into account. The nanofluid is treated as a two-component mixture (i.e., nanoparticles distributed homogenously in a base fluid). The effects of the Brownian motion and thermophoresis are included for the nanofluid flow. The first and second laws of thermodynamics are employed to study thermophysics as well as heat and mass transfer phenomena. The governing equations are transformed into a system of dimensionless, nonlinear, coupled, differential equations using suitable transformation, which are then solved numerically by applying the Keller box method. The accuracy of the obtained numerical results is validated via comparison to previously published results for special cases. Primary shear stress is boosted with increasing mixed convection parameter and Brownian motion effect, whereas secondary shear stress is depressed. Temperatures are suppressed with increasing nonlinear temperature parameter, whereas nanoparticle concentrations are elevated.

Separation time analysis of transient magnetohydrodynamic mixed convection flow of nanofluid at lower stagnation point past a sphere

In this paper, the unsteady magnetohydrodynamics (MHD) mixed convection flow of nanofluid at lower stagnation point past a sphere is studied. Nanoparticles Cu and TiO2 with water as a base fluid are considered. The separation times of the flow as the boundary layer start to separate at the surface of the sphere are given attention. The governing boundary layer equations in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. Results of the separation times of boundary layer flow for viscous and nanofluid influenced by magnetic parameter and volume fraction are shown in tabular form and analysed. This study concluded that the separation times can be delayed by added more magnetic particles and small amount the volume fraction.

Homotopy analysis method for unsteady mixed convective stagnation-point flow of a nanofluid using Tiwari-Das nanofluid model

Purpose – The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting nanofluid over a vertical permeable stretching/shrinking sheet by means of Tiwari-Das nanofluid model. The purpose of this paper is to investigate the effects of the parameters governing the flow i.e. the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter on dimensionless velocity and temperature distributions, skin friction coefficient and local Nusselt number. Design/methodology/approach – The mathematical model has been formulated based on Tiwari-Das nanofluid model. Three different types of water-based nanofluid with copper, aluminum oxide (alumina) and titanium dioxide (titania) as nanoparticles are considered in this investigation. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved analytically by the well-know homotopy analysis method. The present simulations agree closely with the previous studies in the especial cases. Findings – The results show that by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter or reducing the velocity ratio parameter, the skin friction coefficient enhances. Furthermore, the local Nusselt number enhances with different rates by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter. Besides, the skin friction coefficient and the local Nusselt number are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Originality/value – Tiwari-Das nanofluid model has not been applied for the flow with these characteristics as mentioned in the paper. A comprehensive survey on boundary layer behavior has been presented. There are few studies regarding as analysis on thermal and hydrodynamics boundary layer. All plots presented in the paper are new and did not report in any other study. The effects of the parameters governing the flow on skin friction coefficient and local Nusselt number have been illustrated in the paper while there are some conflicts with previous published article that have been interpreted in details in the paper.

Transient Combined Convective Heat Transfer over a Stretching Surface in a Non-Newtonian Nanofluid Using Buongiorno’s Model

The present paper investigates the transient mixed convective boundary layer flow of an incompressible non-Newtonian quiescent nanofluid adjacent to a vertical stretching surface. The effects of the Brownian motion and thermophoresis are included for the nanofluid. Using appropriate non-similarity transformations the non-dimensional, coupled and highly non-linear system of equations is solved numerically using the efficient Keller-box implicit finite difference method for the whole transient from t=0 (initial state) to (final steady-state flow). The box method is unconditionally stable. Numerical results for dimensionless velocity (f’), micro-rotation (g), temperature (θ), nanoparticle volume fraction (Φ) at final steady state flow, skin friction function (), Nusselt number function () and Sherwood number function () have been presented on various parameters inform of tables and graphs. The results indicate that as Nb and Nt increase, the Nusselt number decreases whereas Sherwood number increases at initial and early state time but decreases at the final steady state time. As the K increases, the friction factor decreases whereas surface mass transfer rate and the surface heat transfer rates slightly increase. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work. The study has many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning and drawing plastic films.

A minimum residual projection to build coupled velocity–pressure POD–ROM for incompressible Navier–Stokes equations

The pressure term which appears in the ROM (reduced order model) associated to the incompressible Navier–Stokes equations, in particular for the shear flows, plays an important role on the velocity. The aim of this paper is to propose a Proper Orthogonal Decomposition based reduced order model (POD–ROM) to obtain both the velocity and pressure fields for incompressible flows. Two PODs are performed, one for the velocity and the other for the pressure. Contrary to existing projection methods available in the literature, the temporal velocity and pressure coefficients are sought by minimizing the residual of the momentum equation only, without the need of a Poisson equation. For the numerical test cases considered in this paper, the proposed minimum residual projection enables to obtain accurately the pressure field, and in turn to slightly improve the velocity one. The method is tested on two fluid flows: a transient mixed-convection flow and a periodic flow around a circular cylinder. In this last case, the drag, lift and pressure coefficients, as well as the Strouhal number are properly recovered compared to those of the full model.

Transient mixed convection flow of nanofluids in a vertical tube

Purpose – In the present work, a theoretical model based on the full Navier-Stokes and energy equations for transient mixed convection in a vertical tube is extended to nanofluids with nanoparticle volume fraction up to 5 percent to ensure a Newtonian fluid behaviour. The paper aims to discuss these issues. Design/methodology/approach – The nanofluids considered, alumina/water and CuO/water, flow inside a vertical tube of circular cross-section, which is subjected to convective heat exchange at the outer surface. The transient regime is caused by a sudden change of nanofluid temperature at the tube inlet. The range of the Richardson number (1.6=Ri=2.5) investigated in this study corresponds to classic cases of mixed convection flow. Findings – Results have shown a significant reduction in the size of the recirculation zone near the wall when the particle volume fraction increases. This may be attributed to the viscosity increase with the volume fraction. Moreover, the flow structure clearly changes when the convective heat transfer coefficient is modified. A decrease of the wall temperature along the tube was found when increasing the convective heat transfer coefficient imposed at the tube external surface. Research limitations/implications – The problem formulation in 2D axisymmetric geometry includes the continuity, the Navier-Stokes and energy equations and is based on the stream function and vorticity; the numerical solution of equations is carried out using a finite difference method. Practical implications – From an economic point of view, this research paper is innovative in the sense that it considers nanofluids as a new and more efficient way to transfer heat. This paper could find applications for heat exchange purposes of compact systems with high thermal loads. Originality/value – Across the world, a still growing number of research teams are investigating nanofluids and their properties. Investigations concern several aspects such as the preparation of the nanofluids, as well as the applications of these nanofluids for convective heat transfer purposes. The dynamical study will consist in the instantaneous and spatial characterization of the dynamic flow field for different nanoparticle volume fractions.

Numerical study of transient magnetohydrodynamic radiative free convection nanofluid flow from a stretching permeable surface

Transient mixed convective laminar boundary layer flow of an incompressible, viscous, dissipative, electrically conducting nanofluid from a continuously stretching permeable surface in the presence of magnetic field and thermal radiation flux is studied. The model used for the unsteadiness in the momentum, temperature, and concentration fields is based on the time-dependent stretching velocity and surface temperature and concentration. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum, thermal energy, and concentration to a system of nonlinear ordinary coupled differential equations with appropriate boundary conditions. The transformed model is shown to be controlled by a number of thermophysical parameters, namely the magnetic parameter, thermal convective parameter, mass convective parameter, suction parameter, radiation-conduction parameter, Eckert number, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, and the unsteadiness parameter. Numerical solutions are obtained with the robust Nactsheim–Swigert shooting technique together with Runge–Kutta sixth-order iteration schemes. Comparisons with previously published work are performed and are found to be in excellent agreement. The effects of selected parameters on velocity, temperature, and concentration distributions and furthermore on skin friction coefficients, heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) are presented graphically. The current study has applications in high-temperature nano-technological materials processing.

Transient mixed convective flow of reactive viscous fluid in vertical tube

The problem of fully-developed transient mixed convection flow of viscous reactive fluid in a vertical tube is analysed both analytically and numerically. The study reports the effect of several operating parameters on the flow hydrodynamics and thermal characteristics. The solutions for transient velocity and temperature fields are obtained by implicit finite difference method. To check the accuracy of the numerical solution steady-state solutions for temperature and velocity field are obtained by using perturbation series method. Skin-friction and Nusselt number at the surface of tube are determined. A selected set of graphical results illustrating the effects of the various parameters involved in the problem including mixed convection parameter, pressure gradient, reactant consumption parameter on the velocity and temperature profiles as well as flow reversal situations and Nusselt numbers are presented and discussed.

Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel

The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed. With the appropriate transformations, the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter. The asymptotic solutions are obtained for small and large values of the time-dependent mixed convection parameter. The results are discussed in terms of the skin friction, the heat transfer coefficient, the mass transfer coefficient, and the velocity, temperature, and concentration profiles for different values of the Prandtl number, the Schmidt number, the squeezing index, and the mixed convection parameter.

An optimal projection method for the reduced-order modeling of incompressible flows

A new method to build reduced order models (ROMs) for incompressible flows is addressed in this paper. Proper orthogonal decompositions (PODs) are used to efficiently represent both the fluid velocity and pressure fields with a small number of spatial modes. A minimum-residual projection is then developed for building the reduced models in which the velocity and pressure temporal coefficients are fully coupled. Comparisons of numerical calculations based on the proposed approach with results arising from the classical Galerkin projection are exposed on three fluid flows: a transient ventilated cavity, a periodic lid-driven cavity and a transient mixed convection flow. It is shown that both stability and accuracy of the ROMs are strongly enhance when the minimum-residual projection is used.