Unsteady Forced Convection Research Articles

Thermal lattice Boltzmann approach-based numerical study of nanofluid magnetohydrodynamic forced convection in a back-facing stepped porous channel

Unsteady laminar magnetohydrodynamic forced convection and entropy generation inside a backward-facing step (BFS) porous channel with Cu-H2O nanofluid under a tilted magnetic field is numerically handled using a thermal lattice Boltzmann method (TLBM) with two distribution functions. The Darcy-Brinkman-Forchheimer (DBF) equations filled up with the energy equation (with local thermal equilibrium assumption) have been drawn up as the governing equations model. Their numerical solutions unveiled streamlines, Nusselt number, pumping power, performance index and entropy generation, and impacts of influential parameters (Hartmann number (Ha = 0; 10; 20; 100, 200), Darcy number (Da = 10−3; 10−2; 10−1), magnetic tilt angle (γ = 0, π∕4, π∕2), nanoparticles’ volume fraction (φ = 1 − 4%), medium porosity (ε = 0.6, 0.7, 0.8). The irreversibility analysis is also addressed to highlight the flow behavior. Regarding the validation of the modeling approach deemed, a consensus has been achieved with results available in the literature. Computations revealed that the volume fraction provides a fair performance rating with moderate pumping power. Likewise, the average Nusselt number, the average entropy generation, the pumping power and the performance index have a direct relationship with the Hartmann number, the nanoparticles volume fraction and the magnetic field tilt. Moreover, it can be stated the Cu-H2O nanofluid that seems worthwhile in terms of heat transfer efficiency compared to other examined nanofluids. Entropy generation due to the magnetic field was identified as the main source of irreversibility processes in all cases. Based on the outcomes, it is thought that applying a magnetic field can help minimize entropy generation in practical applications.

Numerical investigation of mixed convection from rectangular cylinders subjected to upper cross flow

Unsteady combined natural and forced convection heat transfer from a rectangular cylinder subjected to upward cross flow is investigated numerically. The working fluids are air (Pr = 0.7) and water (Pr = 7), and the flow is laminar. The governing flow and energy equations are solved using a fractional step finite-difference scheme. The effects of the cylinder aspect ratio (a = L/D), Reynolds and Richardson numbers on the flow and heat transfer characteristics are investigated. Numerical simulations were carried out for the cylinders with aspect ratios of a = 0.5, 1, and 2, while the Richardson and Reynolds numbers varied between 0 to 10, and 100 to 200, respectively. The mean drag, mean rms lift coefficients, as well as the Strouhal number and the mean Nusselt number were computed for each simulation to determine the quantitative effects on flow and heat transfer. Steady flow is observed for Pr = 0.7, Ri = 0.5, and a = 0.5 or for Re ≥ 150 and Ri ≥ 1. For Ri = 10 and Re = 200, the flow becomes unsteady in the downstream region and trigger vortex street formation for a = 0.5, 1, and 2. Decreasing the aspect ratio, as well as increasing Reynolds number, increases the heat transfer from the cylinder. The rms lift coefficient decreases sharply at Ri < 1 for Pr = 0.7, Ri < 2 for Pr = 7 due to vortex breakdown. Further increase in the Richardson leads to a slight increase in rms lift coefficient except for Re = 200 where the sharp increase is observed due to triggered vortex formation again. For air, the increase in the mean Nusselt number in Ri = 10 case with respect to the forced convection case (Ri = 0) was 54–65% and 80–98%, respectively, for a = 0.5 and 2, while these values for water were realized as 50–68% and 53–63%, respectively. Using the computed data and nonlinear regression, the mean Nusselt number and the drag coefficients were developed.

Unsteady forced convection flow and heat transfer past a blunt headed semicircular cylinder at low Reynolds numbers

A numerical analysis is performed to study the forced convective fluid flow and heat transfer past an unconfined semicircular cylinder. The two-dimensional simulations are carried out for Reynolds number ranging 10 ≤ Re ≤ 200 and operating fluid is air (Pr = 0.71) for Newtonian constant property fluid. Continuity, Navier-Stokes, and energy equations with appropriate boundary conditions are solved using computational fluid dynamics solver Ansys Fluent. Various parameters flow such as lift, drag, skin friction coefficient, pressure coefficient, Nusselt (Nu) number, Strouhal (St) number, and vortex strength are calculated. The transition from steady to time periodic flow occurs between Re = 60 and 80. The effect of Reynolds number on heat transfer is discussed. Finally, a developed correlation of Nu and St numbers are presented.

Effect of Heat Generation/Absorption and Radiation on Two-Dimensional Unsteady Magnetohydrodynamic Heat and Mass Transfer Nanofluid Boundary Layer Flow Over a Permeable Shrinking Sheet

The objective of this research is to look into the impact of heat generation/absorption and radiation on twodimensional unsteady magnetohydrodynamic forced convection heat and mass transfer nanofluid boundary layer flow over a permeable shrinking sheet. Similarity transformations are used to translate the governing time-dependent nonlinear PDEs into nonlinear ODEs. The Keller box method is used to solve the transformed equations. The effect of non-dimensional variables is studied and graphically illustrated on velocity, temperature, and concentration. The friction factor, Nusselt, and Sherwood numbers are also investigated and arranged for different values of Unsteadiness parameter, effective Prandtl number, thermophoresis parameter, magnetic field, Grashof number, Modified Grashof number, Lewis number, Heat Source/Sink, and Suction in tabular form. The velocity profiles for dual solutions have improved as the Thermal Grashof number and Modified Grashof number have amplified, but the temperature and concentration profiles have shown the reverse pattern. Temperature profiles are increasing as improving the Heat source/sink. The temperature and concentration profiles decline in the first and opposite pattern in the second solution with improved values of the magnetic field. The findings of this study are very well-acknowledged with current research.

Particle resolved numerical modeling of unsteady forced convection of nanofluid around a porous cuboid with sinusoidal inlet velocity

Abstract In this research, the laminar, incompressible, unsteady oscillatory flow and convective heat transfer of nanofluid around a porous cuboid were studied two-dimensionally using particle resolved calculations. Several cuboids of different sizes and porosities and with a constant temperature were subjected to a nanofluid flow with a sinusoidal velocity profile. The effects of the Reynolds number (Re = 100–900), the volume fraction of nanoparticles, the aspect ratio of the porous cuboid, the Darcy number and the amplitude and frequency of the inlet velocity on the flow field and heat transfer were investigated. To evaluate the system’s optimal performance, performance evaluation criteria (PEC) were also investigated. The results showed that increasing the Reynolds number improved thermal performance. Increasing the volume fraction of nanoparticles increased the Nusselt number; however, the pressure drop coefficient increased more strongly. The heat transfer and pressure drop coefficient increased in line with the growth of the porous cuboid aspect ratio. When the Darcy number was increased, the Nusselt number first increased and then decreased and the pressure drop coefficient continuously decreased. A higher amplitude of the inlet velocity profile augmented the heat transfer and pressure drop coefficient. An increase in the amplitude and frequency of the inlet velocity profile widened the range of drag and lift coefficients. Furthermore, flow at different inlet velocity frequencies (f * = 0–10) behaved differently; as a result, the maximum rate of heat transfer and pressure drop was obtained at f *=5. However, considering the ratio of the Nusselt number to the pressure drop coefficient and PEC parameter, the optimum frequency was f *=9.

Numerical Investigation of Metal Foam Pore Density Effect on Sensible and Latent Heats Storage through an Enthalpy-Based REV-Scale Lattice Boltzmann Method

In this work, an unsteady forced convection heat transfer in an open-ended channel incorporating a porous medium filled either with a phase change material (PCM; case 1) or with water (case 2) has been studied using a thermal lattice Boltzmann method (TLBM) at the representative elementary volume (REV) scale. The set of governing equations includes the dimensionless generalized Navier–Stokes equations and the two energy model transport equations based on local thermal non-equilibrium (LTNE). The enthalpy-based method is employed to cope with the phase change process. The pores per inch density (10≤PPI≤60) effects of the metal foam on the storage of sensible and latent heat were studied during charging/discharging processes at two Reynolds numbers (Re) of 200 and 400. The significant outcomes are discussed for the dynamic and thermal fields, the entropy generation rate (Ns), the LTNE intensity, and the energy and exergy efficiencies under the influence of Re. It can be stated that increasing the PPI improves the energy and exergy efficiencies of the latent heat model, reduces energy losses, and improves the stored energy quality. Likewise, at a moderate Re (=200), a low PPI (=10) would be suitable to reduce the system irreversibility during the charging period, while a high value (PPI = 60) might be advised for the discharging process. As becomes clear from the obtained findings, PPI and porosity are relevant factors. In conclusion, this paper further provides a first analysis of entropy generation during forced convection to improve the energy efficiency of various renewable energy systems.

Unsteady forced convection heat transfer of a stationary and rotating sphere: Experimental Investigation

Unsteady forced convection heat transfer of a stationary and rotating sphere in an open-loop air system was experimentally investigated with an aim to evaluate the influence of sphere rotation rate on the heat transfer enhancement. A special-purpose conical diffuser having a circular cross-section with constant divergence angle has been carefully designed and adopted as a passive rotating technique. The effect of inlet Re number, non-dimensional rotational speed, and initial surface temperature on heat transfer enhancement are examined. It is observed from the comparison made that there are significant differences between the stationary and rotating sphere of heat transfer behavior. The experimental results of heat transfer behavior in terms of heat flux q and Nusselt number Nu, respectively, expose that q decreases with increase of non-dimensional rotational speed, while Nu increases with the increase of non-dimensional rotational speed around 600%.

Insight into Foam Pore Effect on Phase Change Process in a Plane Channel under Forced Convection Using the Thermal Lattice Boltzmann Method

In this work, the two-dimensional laminar flow and the heat transfer in an open-ended rectangular porous channel (metal foam) including a phase change material (PCM; paraffin) under forced convection were numerically investigated. To gain further insight into the foam pore effect on charging/discharging processes, the Darcy–Brinkmann–Forchheimer (DBF) unsteady flow model and that with two temperature equations based on the local thermal non-equilibrium (LTNE) were solved at the representative elementary volume (REV) scale. The enthalpy-based thermal lattice Boltzmann method (TLBM) with triple distribution function (TDF) was employed at the REV scale to perform simulations for different porosities (0.7≤ε≤0.9) and pore per inch (PPI) density (10≤PPI≤60) at Reynolds numbers (Re) of 200 and 400. It turned out that increasing Re with high porosity and PPI (0.9 and 60) speeds up the melting process, while, at low PPI and porosity (10 and 0.7), the complete melting time increases. In addition, during the charging process, increasing the PPI with a small porosity (0.7) weakens the forced convection in the first two-thirds of the channel. However, the increase in PPI with large porosity and high Re number limits the forced convection while improving the heat transfer. To sum up, the study findings clearly evidence the foam pore effect on the phase change process under unsteady forced convection in a PCM-saturated porous channel under local thermal non-equilibrium (LTNE).

On the unsteady forced convection in porous media subject to inlet flow disturbances-A pore-scale analysis

Heat convection response of a porous medium to the harmonic disturbances in the inlet flow is investigated in a configuration consisting of several obstacles. Navier Stokes and energy equations are solved computationally and the average Nusselt number around the obstacles is favourably compared against the existing empirical data. The Nusselt number fluctuations are then examined, revealing that the dynamical relations between the inlet flow fluctuations as the input and those of Nusselt number as the output, can be nonlinear. The extent of encountered nonlinearity is determined quantitatively through introduction of a measure of nonlinearity. It is shown that increases in the pore-scale Reynolds number can strengthen the nonlinearity. However, this is not a global trend and further increases in Reynolds number may push the system dynamics back to linear. Application of the concept of transfer function to the identified linear cases reveals that the frequency response of the Nusselt number closely resembles a classical low-pass filter. Further, through a statistical analysis, it is shown that thermal response of the porous medium is strongly dominated by those of the first few obstacles. This highlights the importance of taking pore-scale approach in the dynamical problems that involve heat convection in porous media.

A pore-scale assessment of the dynamic response of forced convection in porous media to inlet flow modulations

An increasing number of technologies require prediction of unsteady forced convection in porous media when the inlet flow is unsteady. To gain further insight into this problem, the unsteady equations of continuity, Navier Stokes and energy are solved within the pores formed by several cylindrical flow obstacles. The system is modulated by sine waves superimposed on the inlet flow velocity, and the spatio-temporal responses of the flow and temperature fields are calculated. The results are then utilised to assess the linearity of the thermal response represented by the Nusselt number on the obstacles. It is shown that for linear cases, a transfer function can be devised for predicting the dynamic response of the Nusselt number. It is further argued that such a transfer function can be approximated by a classic low-pass filter which resembles the average response of the individual obstacles. This indicates that there exists a frequency threshold above which the thermal system is essentially insensitive to flow modulations. The results also show that changes in Reynolds number and porosity of the medium can push the dynamic response of the system towards non-linearity. Yet, there appears to be no monotonic change in the linearity of the response with respect to the Reynolds number and porosity. In general, it is found that for low Reynolds numbers, the dynamics of heat convection can be predicted decently by taking a transfer function approach. The findings of this study can enable further understanding of unsteady forced convection in porous media subject to time-varying inlet flows.

Numerical investigations of turbulent multiple jet impingement on a heated square block in a confined channel

The analysis of fluid flow and heat transfer characteristics of turbulent single and multiple jets impinging on a square block in a confined channel has been studied numerically. The study of jet impingement on a square block is important as it is directly relevant to the cooling process of food products by jet impingement and present results would be useful in understanding this process. Two-dimensional unsteady state incompressible turbulent forced convection flow is considered for the present analysis. Turbulence is modelled by Reynolds Averaged Navier-Stokes (RANS) equation with a standard k-∊ model and enhanced wall treatment at the wall. The governing equations are solved using a finite volume-based commercial solver. The second-order upwind scheme is used for non-linear terms and the SIMPLE algorithm is used for the pressure-velocity decoupling problem. Effects of a single jet, double jet, 3 jets, and 4 jets, the center distance between jets, block size and height between the block and bottom jets on flow and heat transfer characteristics are reported. The better enhancement of heat transfer is observed from all surfaces of the block with multiple jet impingement compared with a single jet due to multiple recirculation zones than a single jet. The enhancement of heat transfer on the right surface of the block for 4 jets impingement is 113.3% compared to single jet impingement. The overall heat transfer rate is increased by 72.74% with an increase in center distance between jets from 2 to 6. Present results are validated with experimental results available in the literature.

Analytical solutions for unsteady forced convection pulsating flow in a microchannel in the presence of EDL effects

A forced convection flow driven in a microchannel by an applied pressure gradient that fluctuates with small amplitude harmonically in time in the presence of electrical double layer effects is investigated. An analytical expression for the electrostatic potential is obtained via Poisson’s equation. Based on this solution, we further obtain analytical solutions for velocity and temperature for both the cases Pr ≠ 1 and Pr = 1. Results show that they match each other as Pr → 1− and Pr → 1+. The explicit expression of the transient Nusselt number is derived. We notice that the Debye–Hückel parameter γ and the angular velocity Ω are key factors for flow behaviours. Our proposed study adds some new insights by including the time-dependent pressure term that is usually overlooked in previous works. It is expected that this work could help to understand the transportal mechanisms of forced convection flow in microfluidic equipment and instruments.

A numerical study on heat transfer enhancement via mechanical aids

The work deals with an experimental and numerical analysis on disturbed thermal boundary layer obtained in a heat exchanger by two rotating blades (scrapers). A three-dimensional numerical model of unsteady forced convection in an analyzed device is proposed and taken into consideration. The model allows for the transient nature of the processes occurring in a very efficient in terms of heat transfer the Scraped Surface Heat Exchanger (SSHE) and the impacts on the body forces such as gravity, centrifugal and Coriolis forces on processes. In order to validate the model, a specially constructed experimental test stand was designed and manufactured. The series of experiments for the Reynolds number equal to 1100 and the Nusselt number in the range of 10–25 were performed and compared with numerical results achieving satisfactory agreement, with the error smaller than 5% for temperature and 9% for the heat flux values. The set of governing equations of conservation of mass, momentum, and energy was solved within the framework of the Finite Volume Method (FVM). The movement of the scrapers was incorporated into the model with the use of the Sliding Mesh Method (SMM). The distributions of temperature and velocity were elaborated and scrutinized. It was found that in the analyzed flow regime, the gap width between the stator wall and the scraping blade tip highly affects the Nusselt number. Moreover, the numerical results were compared with other mathematical models available in the literature and the discrepancy between the conventionally used model based on penetration theory was found.

Unsteady MHD forced convection over a backward facing step including a rotating cylinder utilizing Fe3O4-water ferrofluid

Abstract In this paper, the unsteady magnetohydrodynamic forced convection of Fe 3 O 4 -water ferrofluids inside the backward facing step benchmark is investigated. A rotating cylinder with fixed dimensions is located inside the flow domain and one phase model is used to simulate the ferrofluid. The dimensionless governing equations are discretized using the Galerkin finite element method in space and the Crank-Nicolson scheme in time. The discrete system of equations in each time level is treated with the help of Newton’s method and the resulting linearized problems are computed using multigrid approach. Wide ranges of the governing parameters are considered such as the Hartmann number 0 ⩽ Ha ⩽ 100 , the magnetic field inclination angle 0 ° ⩽ γ ⩽ 90 ° , the angular velocity - 75 ⩽ Ω ⩽ 75 , the Reynolds number 10 ⩽ Re ⩽ 200 and the nanoparticle volume fraction 0 ⩽ ϕ ⩽ 0.15 . It is observed that the average Nusselt number and lift coefficient are enhanced by the increase in either nanoparticle volume fraction or Reynolds number, while the drag coefficient takes its minimum in case of the fixed cylinder ( Ω = 0 ). In addition, the lift coefficient takes its minimum at value of the magnetic field inclination angle equals π / 6 . Moreover, the electromagnetic force slowdown the ferrofluid flow but the drag coefficient is enhanced. Also, the average Nusselt number decreases with ratio 53.12% as the Hartmann number increases from 0 to 100.

Implicit heat flux correction-based immersed boundary-finite volume method for thermal flows with Neumann boundary conditions

In the frameworks of immersed boundary method (IBM) and finite volume method (FVM), an implicit heat flux correction-based IB-FVM is proposed for thermal flows with Neumann boundary conditions. With the use of a fractional-step technique, the preconditioned Navier–Stokes (N–S) equations are solved by the FVM to obtain the intermediate solution in the prediction step and the heat flux is corrected by enforcing the Neumann condition in the correction step. Different from existing IBMs, the cell face centers are defined as the Eulerian points due to the heat flux computation at each face in the FVM. The Neumann condition is implemented in such a way that the interpolated temperature gradient is equal to the specified boundary value at the same point when the corrected gradient field is interpolated from the face centers to the Lagrangian points. To achieve an implicit algorithm, the temperature derivative corrections at the Lagrangian points are set as unknowns and a system of algebraic equations is established by constructing hybrid thin-plate splines (TPS) interpolation/delta function distribution. In the derivative interpolation process, the much more accurate TPS is introduced because the use of cosine delta function yields a less accurate solution. After the distribution process, the heat flux correction of a fluid cell is evaluated by using the solved temperature derivative corrections at the face centers, but that of a solid cell is calculated by using their additive inverses to supplement the same amount of heat flux into the solid domain as that flowing into the fluid domain across the boundary. Finally, the heat flux of a cell is corrected by adding the correction to the intermediate value and the corrected heat flux is utilized to solve the N–S equations in the prediction step. As compared with the available implicit IBMs for Neumann conditions, the present method avoids the introduction of auxiliary layers of Lagrangian points as well as the approximate conversion from the Neumann to Dirichlet condition and thus is suitable for an arbitrary geometry. The proposed method is verified by simulating several benchmark thermal flows with Neumann conditions, the natural convection in an annulus and the steady or unsteady forced convection over a stationary or oscillating cylinder. All the computed results agree well with the literature data.

Heat Transfer Enhancement of Forced Convection in Horizontal Channel with Heated Block due to Oscillation of Incoming Flow

The study in question consists to amplify the hydrodynamic and thermal instabilities by imposed pulsation during forced convection of air cooling of nine identical heated blocks simulate electronic components mounted on horizontal channel. The finite volume method has been used to solve the governing equations of unsteady forced convection. This approach uses control volume for velocities that are staggered with respect to those for temperature and pressure. The numerical procedure called SIMPLER is used to handle the pressure-velocity coupling. The results show that the time averaged Nusselt number for each heated block depends on the pulsation frequencies and is always larger than in the steady-state case. The new feature in this work is that we obtained a short band of frequencies which the enhancement of heat transfer of all electronic components is greater than 20 % compared with steady non pulsation flow. In addition, the gain in heat transfer Emax attainted the maximum value for the central blocks. Our numerical results were compared with other investigations and found to agree well with experimental data.

Outflow velocity for SIMPLE algorithm for unsteady forced convection flows with variable density

The SIMPLE algorithm for the pressure-velocity coupling has been adopted by many commercial and non-commercial CFD codes. The SIMPLE algorithm requires all normal velocities at the boundaries before solving the pressure correction equation. These velocities must imply an overall mass balance. In this paper, a new procedure to recalculate the outflow velocity for the Neumann type outflow boundary for forced convection with variable density is proposed. As an example of the utilization of this procedure, the outflow normal velocity of a circular duct was computed and the results were compared with the results using the new modified procedure.

Effect of Radiation and Heat Generation on Unsteady MHD Flow of Non-Newtonian Fluid Along a Stretching Vertical Surface

In this paper, the unsteady forced convection boundary-layer flow of a non-Newtonian fluid along a continuously moving stretching sheet with thermal radiation and heat generation or absorption in the presence of magnetic field has been studied. First, the governing equations have been nondimensionalized by usual transformations to obtain the similar solutions. Then, the obtained equations have been solved by an implicit finite difference method. The convergency of explicit and implicit finite difference method has also been discussed. The results are presented for the effect of various parameters such as magnetic parameter (M), radiation parameter (N), heat source parameter (Q), Prandtl number (Pr) and power-law fluid index (n). The effects of these parameters on skin-friction coefficient (Cf) and the local Nusselt number (NuL) which are of physical and engineering interest have also been studied and presented graphically.GANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 7-17

Geometry effect on flow fluctuation and heat transfer in unsteady forced convection over backward and forward facing steps

This study presents a direct numerical simulation of the geometry effect on fluid flow and heat transfer characteristics in the transitional flow over backward and forward facing steps. A computer program of FORTRAN code is used to solve the governing equations according to finite volume method. The effects of the bottom wall length and the step height are investigated. With the increase of bottom wall length, a fundamental frequency of flow fluctuation appears at Lb = 10 h and then disappears at Lb = 14 h. This fundamental fluctuating frequency decreases with the increase of step height. The fact that the heat transfer performance is better in the reattachment region at Lb = 12 h and S = h indicates that the periodic flow fluctuation with a larger fluctuating velocity has positive effects on heat transfer enhancement. The results of the relationship between flow fluctuation and heat transfer enhancement are significant for certain practical applications of energy conversion.

Unsteady Magnetoconvective Flow of Bionanofluid with Zero Mass Flux Boundary Condition

Induced magnetic field stagnation point flow for unsteady two-dimensional laminar forced convection of water based nanofluid containing microorganisms along a vertical plate has been investigated. We have incorporated zero mass flux boundary condition to get physically realistic results. The boundary layer equations with three independent variables are transformed into a system of ordinary differential equations by using appropriate similarity transformations. The derived equations are then solved numerically by using Maple which use the fourth-fifth order Runge-Kutta-Fehlberg algorithm to solve the system of similarity differential equations. The effects of the governing parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction, density of motile microorganisms, skin friction coefficient, local Nusselt number and motile density of microorganisms transfer rate are illustrated graphically and tabular form. It is found that the controlling parameters strongly affect the fluid flow and heat transfer characteristics. We compare our numerical results with published results for some limiting cases and found excellent agreement.