Second law analysis of a disturbed flow in a thin slit with wall suction or injection

Fully-developed laminar flow in a horizontal thin slit having plates at different temperature is considered for the case of lower plate movement and/or the pressure gradient-and-upper plate movement. The flow under these conditions is analyzed in terms of entropy generations as function of the Prandtl number, the Eckert number, cross-flow Reynolds number and dimensionless temperature difference. In this context, the governing equations for distributions of temperature, the dimensionless entropy generation number and Bejan number are analytically derived with the aid of expressions for velocity distributions. The effect of each parameter on the temperature and the entropy generation are investigated by varying one of the parameters and keeping the rest of them constant for each flow case. The effects of viscous dissipation, rates of mass suction/injection and dimensionless temperature differences on the fluid temperature and entropy generation are examined. The magnitudes of mass suction and/or injection have a large influence on the temperature profile of the fluid. It is observed that the Prandtl number and the Eckert number affect fluid temperature in similar way. It is found that an increase in values of the cross-flow Reynolds number (mass suction/injection) enhances the entropy generation in boundary layer. The velocity profiles are found to be in agreement with the distributions of the dimensionless entropy generation number (N_S) for two flow cases.     

Velocity slip,chemical reaction,and suction/injection effects on two-dimensional unsteady MHD mass transfer flow over a stretching surface in the presence of thermal radiation and viscous dissipation

The purpose of this study is to analyze the impact of velocity slip, chemical reaction, and suction/injection on two-dimensional mass transfer effects on unsteady MHD flow over a stretching surface in the presence of thermal radiation and viscous dissipation. The governing time-dependent nonlinear partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformations. The converted equations are solved using the numerical technique with the help of Keller-Box method. The effect of nondimensional variables is studied and graphically illustrated on velocity, temperature, concentration, friction factor, Nusselt number, and Sherwood number. Concentration and temperature profiles are enhanced and the contrasting pattern for velocity profiles as increasing the velocity slip and magnetic parameter. The concentration profile is diminished as the Schmidt number (Sc) and chemical reaction (C_r) increase. The concentration, velocity, and temperature profiles display a reversal pattern, as the suction and unsteady parameter (A) increase. The findings of this study are very well-acknowledged with current research.     

Varying Heating Effect on Mixed Convection of Nanofluids in a Vented Horizontal Cavity with Injection or Suction

The problem of mixed convection heat transfer inside a horizontal vented enclosure through the lower and upper parts, respectively, of its left and right vertical walls is studied numerically using Al₂O₃-water nanofluid as working fluid. The bottom wall is subjected to a linearly varying (increasing or decreasing) heating temperature profiles, while the other boundaries are considered thermally insulated. The fresh fluid is admitted from the bottom part of the left vertical wall by injection or by the suction imposed on the opening of the right vertical wall. Based on numerical predictions, the conjugate effect of the Reynolds number and the nanoparticle concentration on fluid flow and heat transfer characteristics is studied. The obtained results demonstrate clearly the positive role of the nanoparticles addition on the improvement of the heat transfer rate and the mean temperature within the cavity. In addition, the flow structure and the temperature distribution inside the cavity are seen to be very sensitive to the variations of the Reynolds number, the imposed external flow mode, and the heating type. Results presented show that, in general, the decreasing heating mode is more favorable to the heat transfer in comparison with the case of the increasing heating mode. The cooling efficiency is found to be more pronounced by the injection/suction mode by applying the increasing/decreasing heating type.     

Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation

An analysis is carried out to study the effect of suction and injection on the flow and heat transfer characteristics for a continuous moving plate in a micropolar fluid in the presence of radiation. The boundary layer equations are transformed to non-linear ordinary differential equations. Numerical results are presented for the distribution of velocity, microrotation and temperature profiles within the boundary layer. The effects of varying the Prandtl number, Pr, the radiation parameter, N and porosity parameter, F_w, are determined.     

Variation of momentum and thermal boundary layers for oscillatory flows in a channel

Zero mean oscillatory flow over a heated plate mounted on the bottom wall of a channel, is analysed by solving two dimensional time dependent governing equations using control volume based pressure correction procedure. A uniform sinusoidally varying velocity profile is applied at the inlet, and temperature of the heated plate is kept constant. The numerical solutions are compared with experimental values and the effects of Reynolds and Wormersly numbers on the velocity and temperature profiles are presented for the same Prandtl number.     

Thermal transport analysis for natural convection in a porous corrugated rhombic enclosure

A numerical study of fluid flow and heat transfer, applying natural convection is carried out in a porous corrugated rhombic enclosure. A uniform heating source is applied from the bottom boundary wall while the inclined side walls are maintained to a constant cold temperature and the top corrugated wall is retained at insulated condition inside the enclosure. The heat transfer and flow features are presented for a wide spectrum of Rayleigh numbers (Ra), 10⁴ ≤ Ra ≤ 10⁶, and Darcy numbers (Da), 10^?3 ≤ Da ≤ 10^?2. The number of undulations (n) for the top and bottom walls have been varied from 1 to 13 keeping the amplitude of undulation fixed. It is revealed that the characteristics of heat transfer are conceivably modulated by changing the parameter of the undulation number on the enclosure walls, specifically at the bottom and top. The influencing control of n in altering the heat transfer rate is felt maximum on the left wall and minimum for the right wall, and there is a strong interplay between Ra and Da together with n on dictating the heat transfer characteristics. The critical value, where heat transfer rate is observed as maximum is at n = 11 and thereafter the values decrease.     

Double‐diffusive natural convection in a partially heated enclosure using a nanofluid

This paper analyzes numerically the effect of double‐diffusive natural convection of a water–Al₂O₃ nanofluid in a partially heated enclosure with Soret and Dufour coefficients. The top horizontal wall has constant temperature T_c, while the bottom wall is partially heated T_h, with T_h > T_c . The concentration in the top wall is maintained higher than the bottom wall C_c < C_h. The remaining bottom wall and the two vertical walls are considered adiabatic. Water is considered as the base fluid. The governing equations are solved by the Penalty Finite Element Method using Galerkin's weighted residual scheme. The effect of the parameters, namely, Rayleigh number and solid volume fraction of the nanoparticles on the flow pattern and heat and mass transfer has been depicted. Comprehensive average Nusselt and Sherwood numbers, average temperature and concentration, and mid‐height horizontal and vertical velocities at the middle of the cavity are presented as functions of the governing parameters mentioned above. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21010     

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

The influence of the external Rayleigh number, inclination angle, and internal Rayleigh number on natural convection within an air‐filled parallelogrammic enclosure containing a volumetric source has been investigated numerically. The left sidewall of the enclosure is subjected to a non‐uniformly hot temperature and the right sidewall experiences a uniform cold temperature while the remaining top and bottom walls are kept adiabatic. The physical problems are represented mathematically by various sets of governing equations along with the corresponding boundary conditions. Buoyancy forces are taken into account during the analysis of the present investigation. By using the finite volume method, the dimensionless governing equations are discretized numerically based on a non‐uniform collocated grid system. Results are obtained for a wide range of external Rayleigh numbers varying from 10³ to 10⁶ with internal Rayleigh numbers varying from (0) to (10⁸) while the left sidewall from vertical is varied as 0, 30, –30, 60, and ?60^°, respectively. In the present study, the obtained results are presented in terms of streamlines, isotherms, and average Nusselt number along the hot and cold sidewalls. Two pairs of rotating vortices are observed due to the non‐uniform heating process while the shape of this rotating vortices is sensitive to the inclination angle. Furthermore, the flow field circulation and the average Nusselt number increase remarkably with the increase in the external Rayleigh number. The results of the present work are compared with other published results and give excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 542–560, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21096     

Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing

A similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet in a porous medium subject to suction/blowing and in the presence of internal heat generation/absorption. A scaling group of transformations is applied to get the invariants. Using the invariants, a third and a second order ordinary differential equations corresponding to the momentum and energy equations are obtained respectively. Boundary layer velocity and temperature profiles are determined numerically for various values of the ratio of free stream velocity and stretching velocity, the permeability parameter, suction/blowing parameter, heat source/sink parameter, Prandtl number. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity (ax) and the stretching velocity (cx). The temperature decreases in this case. At a particular point of the porous stretching sheet, the non-dimensional fluid velocity decreases with the increase of the permeability of the porous medium and also with the increasing suction parameter when the free stream velocity is less than stretching velocity whereas fluid velocity increases with the increasing injection parameter. But when the free stream velocity is greater than the stretching velocity the opposite behaviour of horizontal velocity is noticed. The dimensionless temperature at a point of the sheet decreases due to suction but increases due to injection. The temperature at a point is found to decrease with the increasing Prandtl number.     

Cattaneo–Christov flux and entropy in thermofluidics involving shrinking surface

The paper examines radiative Casson boundary layer flow over an exponentially shrinking permeable sheet in a Cattaneo–Christov heat flux environment. The sheet is placed at the bottom of the fluid-saturated porous medium and suction is applied normally to the sheet to contain the vorticity. The radiative heat flux in the energy equation is assumed to follow the Rosseland approximation. Similarity transformation is performed to convert the governing partial differential equations into ordinary differential equations. The resulting boundary value problem is treated numerically employing Runge–Kutta fourth-order integration scheme along with the shooting method. The effects of pertinent parameters on quantities of interest are showcased graphically/in tabular form and are discussed. The dual profiles for velocity and temperature lead to a dual solution regime for entropy. It is found that critical mass suction rate and Nusselt number are substantially responsive to various parameters' values. Critical suction values decrease with a rise in Casson parameter β and permeability parameter K. Skin friction coefficient and Nusselt number show peculiar behavior for distinct branches of solutions.     

Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

Three-dimensional numerical analysis of the natural convection and entropy generation of MWCNTs-H2O and air as two immiscible fluids in a rectangular cuboid with fillet corners

A numerical investigation has been carried out to study the natural convection and entropy generation within the three-dimensional enclosure with fillets. There are two immiscible fluids of Multi-Walled Carbon Nano-Tubes (MWCNTs)-water and air in the enclosure, which is simulated as two discrete phases. There are two heaters with constant heat flux at the sides, and the top and bottom walls are kept at cold constant temperature. The finite volume approach is applied to solve the governing equations. Moreover, a numerical method is developed based on the three-dimensional solution of Navier–Stokes equations. The fluid flow, heat transfer, and total volumetric entropy generation due to natural convection are studied carefully in a three-dimensional enclosure. The effects of the corner radius of fillets (r?=?0, 0.15, 0.2, and 0.25), Rayleigh number (10³?Ra?6), and solid volume fraction (φ?=?0.002 and 0.01) of the nanofluid have been investigated on both natural convection characteristic and volumetric entropy generation.* The results show that the curved corner can be an effective method to control fluid flow and energy consumption, and three dimensional solutions render more accurate results.     

Upward Heat Flux Through the Horizontal Fluid Layer of Water with Sinusoidal Wall Temperature at the Top or Bottom Boundary

Either top or bottom wall temperature of an infinite horizontal fluid layer at Pr = 6 is sinusoidally oscillated with constant average temperature on the opposing horizontal wall. This is a system with no temperature difference between the top and bottom walls in a time-averaged sense, as studied by Kalabin et al. for a square channel. The fluid is water, and the Boussinesq approximation is made. The computational region of height 1 and horizontal width 1 is adopted and numerical computation is carried out. The results show that the fluctuating Nusselt numbers computed at both the top and bottom walls give positive time-averaged values for two different frequencies computed. Time-dependent convection plumes occur when the bottom wall temperature becomes higher than the top wall temperature. The time-averaged heat flux is always positive, i.e., upward, even if the time-averaged temperature difference is zero between the top and bottom walls. This holds even if the oscillating temperature is on either the top or bottom wall. Two periods of temperature oscillation give one period of oscillation in flow and Nu, at least for the parameters studied.     

Mixed convective flow in a bottom heated lid‐driven cubical cavity: Energy streamlines and field synergy

Analysis of three dimensional natural convective lid‐driven cavity flow is carried out numerically. The top wall is assumed to slide in its own plane at a constant speed. Isothermal temperature is maintained at horizontal walls in which the bottom wall is assumed to be at a higher temperature than the top wall. Governing equations of this problem, expressed in dimensionless form are solved by using the finite volume method. Numerical results are computed for the control parameters arising in the system, namely, the Reynolds number (Re) and Richardson number (Ri) in the range of 100 ≤ Re ≤ 1000 and 0.001 ≤ Ri ≤ 10. The contours of isotherms, streamlines, Vortex corelines, energy pathlines, and field synergy are used to visualize the flow and thermal characteristics. The simulated results are corroborated with those available in the literature. When Re = 100 and 400 with growth of Ri there are "free" energy streamlines and they exhibited symmetric nature near the boundaries. The participation of convective thermal energy and kinetic energy is insignificant compared to conductive thermal energy, where the velocity components are modest. When Re = 1000 with increase of Ri, "trapped" energy streamlines are detected. Energy streamlines occupy substantial part. This is due to the result of high Re, with increasing Ri, kinetic energy and convective thermal energy get dominated and hence "trapped" streamlines formed. As Re increases, synergy angle increases for distinct Ri values. So the synergy between temperature and velocity gets worse. The synergy angle of buoyant‐aiding flow is high while the buoyant‐opposing flow is significantly less than that of forced convection flow when Ri = 1. This gives the relation between temperature field and velocity at buoyant‐aiding flow, which is at the worst situation leading to increasing average Nusselt number.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

Natural Convection Heat Transfer Enhancement in a Square Cavity Periodically Cooled from Above

The present article reports numerical results of natural convection within an air filled square cavity with its horizontal walls submitted to different heating models. The temperature of the bottom horizontal surface (hot temperature) is maintained constant, while that of the opposite surface (cold temperature) is varied sinusoidally with time. The remaining vertical walls are considered adiabatic. The parameters governing the problem are the amplitude (0 ≤ a ≤ 0.8) and the period (τ ≥ 0.001) of the variable temperature, the Rayleigh number (10³ ≤ Ra ≤ 7 × 10⁶), and the Prandtl number (Pr = 0.71). In constant cooling conditions (a = 0), up to three different solutions (monocellular flow MF, bicellular vertical flow BVF, and bicellular horizontal flow BHF) are obtained. Their existence ranges are delineated and, in the limits of the existence range of each solution, the transitions observed are identified and described. In the variable cooling conditions, the effect of the amplitude and the period of the exciting temperature on fluid flow and heat transfer is examined in the case of the MF, and BHF for specific values of Ra. Results are presented in terms of Ψ _max (t), Ψ _min (t), Nu(t) and streamlines, heatlines, and isotherms during the evolutions of selected flow cycles. In comparison with the constant heating conditions, it is found that the variable cooling temperature could lead to a drastic change in the flow structure and the corresponding heat transfer, especially at specific low periods of the cold variable temperature. This leads to a resonance phenomenon characterized by an important increase in heat transfer by about 46.1% compared to the case of a constant cold temperature boundary condition.     

Combined free and forced convection flow past a vertial porous plate

Local similarity solutions of the forced and free convection flow past a semi-infinite vertical porous plate have been obtained numerically. Velocity and temperature profiles are shown for air (Pr = 0.72) and for different values of Gr (Gr > 0, cooling of the plate and Gr<0, heating of the plate) (Grashof number), E (Eckert number) and f_w (f_w>0, suction, f_w <0, injection). the effects of these parameters are discussed.     

Numerical Study on Heat Transfer Between Turbulent Flow and Porous Rectangular Cylinders with Uniform Injection or Suction

The heat transfer characteristics of the flow around rectangular cylinders having various aspect ratios with uniform injection or suction through the rear, top, bottom, and all surfaces have been studied numerically. The effects of injection or suction on heat transfer have been linked to the analysis via wall functions of the velocity and temperature sublayers. The computational code employed in the present study was verified with a typical benchmark problem of the flow around a square cylinder. The results show that the heat transfer between the main flow and rectangular cylinders is substantially influenced by injection or suction—that is, suction enhances the heat transfer, while injection through the rear surface provides some thermal protection.