Some numerical methods for solving diffusion-convection equations in two dimensional space are formulated. Iterative scheme for each method is studied and numerical test to model problem is conducted. Comparison of methods is given in table form.
Beberapa kaedah berangka bagi menyelesaikan persamaan resapan-olakan dalam ruang dua dimensi telah dirumuskan. Skema lelaran untuk setiap satunya dikaji dan pengujian berangka kepada masalah model dilakukan. Perbandingan antara kaedah telah diberikan secara berjadual.
The linear stability theory is applied to investigate the effects of rotation and feedback control on the onset of steady and oscillatory thermocapillary convection in a horizontal fluid layer heated from below with a free-slip bottom. The thresholds and codimension-2 points for the onset of steady and oscillatory convection are determined. The effect of feedback control on the parameter space dividing the steady and oscillatory convection regions is demonstrated.
The paper reconsiders the problem of the mixed convection boundary layer flow near the lower stagnation point of a horizontal circular cylinder with a second order slip velocity model and a constant surface heat flux studied recently by RoKa et al. (2013). The ordinary (similarity) differential equations are solved numerically using the function bvp4c from Matlab for different values of the governing parameters. It is found that the similarity equations have two branches, upper and lower branch solutions, in a certain range of the mixed convection parameters. A stability analysis has been performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and therefore, not physically possible. This stability analysis is different by that presented by RoKa et al. (2013), who have presented a time-dependent analysis to determine the stability of the solution branches.
The unsteady mixed convection boundary layer flow near the forward stagnation point of a two-dimensional symmetric body prescribed by a uniform heat flux rate is studied in this paper. The main aim of the investigation is to identify situations in which dual solutions for the steady-state flow can be determined when the flow is opposing. It is also shown that there is a smooth transition from the unsteady initial flow (short time) to the final steady state flow (large time).
In this study, the numerical solution of stagnation point flow over a stretching surface, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is considered. The transformed boundary layer equations are solved numerically using the shooting method. Numerical solutions are obtained for the local heat transfer coefficient, the surface temperature and the temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number, stretching parameter and conjugate parameter are analyzed and discussed.
In this work we use an analytical technique to analyse the effect of a vertical uniform magnetic field on the onset of steady Benard-Marangoni convection in a horizontal layer of electrically conducting fluid subject to a uniform vertical temperature gradient in the asymptotic limit short waves. We found that in the limit of short waves, the leading order expression for the marginal curve is not affected by the magnetic field.
Dalam makalah ini kesan medan magnet menegak seragam ke atas lengkung sut permulaan olakan mantap Benard-Marangoni dalam lapisan bendalir mengufuk berpengalir elektrik dikaji tertakluk kepada kecerunan suhu yang seragam dalam had asimptot gelombang pendek. Kami dapati medan magnet tidak memberi kesan kepada sebutan utama lengkung sut dalam had gelombang pendek.
The effect of thermal dispersion on the steady free convection flow of a nanofluid in a vertical channel is investigated numerically using a single phase model. Considering the laminar and fully developed flow regime a simplified mathematical model is obtained. In the particular cases when solid phase and thermal dispersion effects are neglected the problem was solved analytically. The numerical solution is shown to be in excellent agreement with the close form analytical solution. Nusselt number enhancement with the Grashof number, volume fraction and thermal diffusivity constant increasing has been found.
We study and discuss the effect of thermal slip on steady free convection flow of a viscous, incompressible micropolar fluid past a vertical moving plate in a saturated porous medium. The effect of viscous dissipation is incorporated in the energy equation. The associated partial differential equations are transformed into a system of ordinary differential equations using similarity transformations generated by a group method and this system is then solved numerically. The effect of controlling parameters on the dimensionless velocity, angular velocity and temperature as well as friction factor, couple stress factor and heat transfer rate are shown graphically and discussed in detail. It is found that the dimensional velocity and angular velocity decrease whilst the temperature increases with velocity slip parameter. It is further found that thermal slip decreases the dimensional velocity and temperature but increases the dimensional angular velocity. Data from published work and our results are found to be in good agreement.
The effect of radiation on laminar and turbulent mixed convection heat transfer of a semitransparent medium in a square enclosure was studied numerically using the Finite Volume Method. A structured mesh and the SIMPLE algorithm were utilized to model the governing equations. Turbulence and radiation were modeled with the RNG k-ε model and Discrete Ordinates (DO) model, respectively. For Richardson numbers ranging from 0.1 to 10, simulations were performed for Rayleigh numbers in laminar flow (10⁴) and turbulent flow (10⁸). The model predictions were validated against previous numerical studies and good agreement was observed. The simulated results indicate that for laminar and turbulent motion states, computing the radiation heat transfer significantly enhanced the Nusselt number (Nu) as well as the heat transfer coefficient. Higher Richardson numbers did not noticeably affect the average Nusselt number and corresponding heat transfer rate. Besides, as expected, the heat transfer rate for the turbulent flow regime surpassed that in the laminar regime. The simulations additionally demonstrated that for a constant Richardson number, computing the radiation heat transfer majorly affected the heat transfer structure in the enclosure; however, its impact on the fluid flow structure was negligible.
Taking into account the effect of constant convective thermal and mass boundary conditions, we present numerical solution of the 2-D laminar g-jitter mixed convective boundary layer flow of water-based nanofluids. The governing transport equations are converted into non-similar equations using suitable transformations, before being solved numerically by an implicit finite difference method with quasi-linearization technique. The skin friction decreases with time, buoyancy ratio, and thermophoresis parameters while it increases with frequency, mixed convection and Brownian motion parameters. Heat transfer rate decreases with time, Brownian motion, thermophoresis and diffusion-convection parameters while it increases with the Reynolds number, frequency, mixed convection, buoyancy ratio and conduction-convection parameters. Mass transfer rate decreases with time, frequency, thermophoresis, conduction-convection parameters while it increases with mixed convection, buoyancy ratio, diffusion-convection and Brownian motion parameters. To the best of our knowledge, this is the first paper on this topic and hence the results are new. We believe that the results will be useful in designing and operating thermal fluids systems for space materials processing. Special cases of the results have been compared with published results and an excellent agreement is found.
Many studies have investigated natural convection heat transfer from the outside surface of horizontal and vertical cylinders in both constant heat flux and temperature conditions. However, there are poor studies in natural convection from inclined cylinders. In this study, free convection heat transfer was examined experimentally from the outside surface of a cylinder for glycerol and water at various heat fluxes. The tests were performed at 10 different inclination angles of the cylinder, namely, φ = 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°, and 90°, measured from the horizon. Our results indicated that the average Nusselt number reduces with the growth in the inclination of the cylinder to the horizon at the same heat flux, and the average Nusselt number enhanced with the growth in heat flux at the same angle. Also, the average Nusselt number of water is greater than that of glycerol. A new experimental model for predicting the average Nusselt number is suggested, which has a satisfactory accuracy for experimental data.
The migration process of magnetic nanoparticles and colloids in solution under the influence of magnetic field gradients, which is also known as magnetophoresis, is an essential step in the separation technology used in various biomedical and engineering applications. Many works have demonstrated that in specific situations, separation can be performed easily with the weak magnetic field gradients created by permanent magnets, a process known as low-gradient magnetic separation (LGMS). Due to the level of complexity involved, it is not possible to understand the observed kinetics of LGMS within the classical view of magnetophoresis. Our experimental and theoretical investigations in the last years unravelled the existence of two novel physical effects that speed up the magnetophoresis kinetics and explain the observed feasibility of LGMS. Those two effects are (i) cooperative magnetophoresis (due to the cooperative motion of strongly interacting particles) and (ii) magnetophoresis-induced convection (fluid dynamics instability originating from inhomogeneous magnetic gradients). In this feature article, we present a unified view of magnetophoresis based on the extensive research done on these effects. We present the physical basis of each effect and also propose a classification of magnetophoresis into four distinct regimes. This classification is based on the range of values of two dimensionless quantities, namely, aggregation parameter N* and magnetic Grashof number Grm, which include all of the dependency of LGMS on various physical parameters (such as particle properties, thermodynamic parameters, fluid properties, and magnetic field properties). This analysis provides a holistic view of the classification of transport mechanisms in LGMS, which could be particularly useful in the design of magnetic separators for engineering applications.
The three dimensional free convection boundary layer flow near a stagnation point region is embedded in viscous nanofluid with the effect of g-jitter is studied in this paper. Copper (Cu) and aluminium oxide (Al2O3) types of water base nanofluid are cho- sen with the constant Prandtl number, Pr=6.2. Based on Tiwari-Das nanofluid model, the boundary layer equation used is converted into a non-dimensional form by adopting non- dimensional variables and is solved numerically by engaging an implicit finite-difference scheme known as Keller-box method. Behaviors of fluid flow such as skin friction and Nusset number are studied by the controlled parameters including oscillation frequency, amplitude of gravity modulation and nanoparticles volume fraction. The reduced skin friction and Nusset number are presented graphically and discussed for different values of principal curvatures ratio at the nodal point. The numerical results shows that, in- crement occurs in the values of Nusset number with the presence of solid nanoparticles together with the values of the skin friction. It is worth mentioning that for the plane stagnation point there is an absence of reduced skin friction along the y-direction where as for axisymmetric stagnation point, the reduced skin friction for both directions are the same. As nanoparticles volume fraction increased, the skin friction increased as well as the Nusset number. The results, indicated that skin frictions of copper are found higher than aluminium oxide.
Unsteady mixed convection flow of Casson fluid towards a nonlinearly stretching sheet with the slip and convective boundary conditions is analyzed in this work. The effects of Soret Dufour, viscous dissipation and heat generation/absorption are also investigated. After using some suitable transformations, the unsteady nonlinear problem is solved by using Keller-box method. Numerical solutions for wall shear stress and high temperature transfer rate are calculated and compared with previously published work, an excellent arrangement is followed. It is noticed that fluid velocity reduces for both local unsteadiness and Casson parameters. It is likewise noticed that the influence of a Dufour number of dimensionless temperature is more prominent as compared to species concentration. Furthermore, the temperature was found to be increased in the case of nonlinear thermal radiation.
This paper looks at electrical power generation from solar concentrator using thermoelectric generator. An experiment was conducted on a concentrator thermoelectric generator (CTEG) utilising solar thermal energy. The CTEG used a parabolic dish as concentrator with thermoelectric device installed at the focal point to convert thermal energy to generate electricity. The investigation covered the cooling effect of the cold side of the thermoelectric generator using natural and forced convection cooling for optimum output. Forced convection cooling with a fan provided 69% more power output from the CTEG system as the temperature difference across the TEG was greater than the system cooled by natural convection. The outcome of this project showed maximum power output was obtained for the CTEG system cooled by forced convection cooling.
The steady laminar combined convective flow with heat and mass transfer of a Newtonian viscous incompressible fluid over a permeable flat plate with linear hydrodynamic and thermal slips has been investigated numerically. The velocity of the external flow, the suction/injection velocity and the temperature of the plate surface are assumed to vary nonlinearly following the power law with the distance along the plate from the origin. Lie group analysis is used to develop the similarity transformations and the governing momentum, the energy conservation and the mass conservation equations are converted to a system of coupled nonlinear ordinary differential equations with the associated boundary conditions. The resulting equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method. The effects of hydrodynamic slip parameter (a), thermal slip parameter (b), suction/injection parameter (fw), power law parameter (m), buoyancy ratio parameter (N), Prandtl number (Pr) and Schmidt number (Sc) on the fluid flow, heat transfer and mass transfer characteristics are investigated and presented graphically. We have also shown the effects of the Reynolds number (Re) and the power law parameter (m) on the velocity slip and the thermal slip factors. Good agreement is found between the numerical results of the present paper and published results.
A steady laminar mixed convection boundary layer flow about an isothermal solid sphere embedded in a porous medium filled with a nanofluid has been studied for both cases of assisting and opposing flows. The transformed boundary layer equations were solved numerically using an implicit finite-difference scheme. Three different types of nanoparticles, namely Cu, Al2O3 and TiO2 in water-based fluid were considered. Numerical solutions were obtained for the skin friction coefficient, the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the nanoparticle volume fraction and the mixed convection parameters were analyzed and discussed.
This paper delves into the problem of mixed convection boundary layer flow from a horizontal circular cylinder filled in
a Jeffrey fluid with viscous dissipation effect. Both cases of cooled and heated cylinders are discussed. The governing
equations which have been converted into a dimensionless form using the appropriate non-dimensional variables are solved
numerically through the Keller-box method. A comparative study is performed and authentication of the present results
with documented outcomes from formerly published works is excellently achieved. Tabular and graphical representations
of the numerical results are executed for the specified distributions, considering the mixed convection parameter, Jeffrey
fluid parameters and the Prandtl and Eckert numbers. Interestingly, boundary layer separation for mixed convection
parameter happens for some positive (assisting flow) and negative (opposing flow) values. Strong assisting flow means
the cylinder is heated, which causes the delay in boundary layer separation, whereas strong opposing flow means the
cylinder is cooled, which conveys the separation point close to the lower stagnation point. Contradictory behaviours
of both Jeffrey fluid parameters are observed over the velocity and temperature profiles together with the skin friction
coefficient and Nusselt number. The increase of the Prandtl number leads to the decrement of the temperature profile,
while the increase of the Eckert number results in the slight increment of the skin friction coefficient and decrement of
the Nusselt number. Both velocity and temperature profiles of Eckert number show no effects at the lower stagnation
point of the cylinder.
Antioxidant properties of both fresh and convection oven-dried guavas (Psidium guajava L.) were determined. Guava slices of 1.0 cm wide, 3.0 cm long and 0.5cm thick (20 g) were subjected to convection drying at 40°C for 9, 12 and 14 hours, respectively, and their water activity, total phenolic content (TPC) and antioxidant activities were measured. Guavas that had been subjected to drying for 9, 12 and 14 hours were shown to achieve the water activity of 0.36-0.49. Ascorbic Acid Equivalent Antioxidant Capacity (AEAC) of guava was found to decrease for all the drying durations. Convection oven-drying of guava for 12 and 14 hours showed a significant decrease in TPC (p < 0.01) and Ferric Reducing Power Assay (FRP) (p < 0.01). Nine hours of convection oven-drying was shown to retain most of the TPC, AEAC and FRP of guava.
This work analyses free convection flow of a nanofluid in an inclined square enclosure consisting of a porous layer and a nanofluid layer using the finite difference methodology. Sinusoidal temperature boundary conditions are imposed on the two opposing vertical walls. Nanofluids with water as base and Ag or Cu or Al2O3 or TiO2 nanoparticles are considered for the problem. The related parameters of this study are the Darcy number, nanoparticle volume fraction, phase deviation, amplitude ratio, porous layer thickness and the inclination angle of the cavity. A comparison with previously published work is performed and the results are in good agreement. Detailed numerical data for the fluid flow and thermal distributions inside the square enclosure, and the Nusselt numbers are presented. The obtained results show that the heat transfer is considerably affected by the porous layer increment. Several nanoparticles depicted a diversity improvement on the convection heat transfer.