A numerical investigation on the fluid flow and heat transfer in the confined impinging slot jet in the low Reynolds number region for different channel heights

The numerical solution is obtained for unsteady two-dimensional fluid flow and heat transfer in a confined impinging slot jet using the finite volume method. In order to consider the effect of Reynolds number and height ratio on the flow and temperature fields in the channel, the numerical simulations were performed for different Reynolds numbers of 50–500 and different height ratios of 2–5. The critical Reynolds number, beyond which the flow and thermal fields change their state from steady to unsteady, depends on the Reynolds number and height ratio. The unsteadiness gives a big impact on the flow and temperature fields and as a result the pressure coefficient, skin friction coefficient and Nusselt number in the unsteady region show different characteristics from those in the steady region.     

MHD flow and heat transfer in a backward-facing step

The laminar flow of a viscous incompressible electrically conducting fluid in a backward-facing step is investigated under the usual magnetohydrodynamic (MHD) hypothesis. Numerical simulations are performed for Reynolds numbers less then Re = 380 in the range of 0 ≤ N ≤ 0.2, where N is the Stuart number or interaction parameter which is the ratio of electromagnetic force to inertia force. Heat transfer is investigated for Prandtl number ranging from Pr = 0.02 corresponding to liquid metal, to Pr = 7 corresponding to water. It is found through the calculation of the reattachment length that external magnetic field acts to decrease the size of the recirculation zone. Velocity profiles show that, out of the recirculation zone, the basic flow is damped by the magnetic induced force, whereas flow near the walls channel is accelerated. Heat transfer is significantly enhanced by the magnetic field in the case of fluids of high Prandtl numbers.     

Conjugated heat transfer investigation with racetrack-shaped jet hole and double swirling chamber in rotating jet impingement

A numerical study is performed to investigate the effects of jet hole shape and channel geometry on impingement cooling for both stationary and rotating condition. Two hole shapes and two channel geometries are introduced to counteract the adverse effects of centrifugal force and Coriolis force which are induced by rotation. Both the fluid and solid part are considered for realizing the conjugate heat transfer simulation. The unsteady k-ω SST turbulence model was employed to obtain the time-averaged Nusselt number distributions, time-averaged temperature and temperature gradient fields and the turbulent flow structure. The results show that the cooling jet from the racetrack-shaped hole can effectively withstand the intensive streamwise crossflow to enhance the heat transfer. The double swirling chamber (DSC) channel significantly improves the heat transfer characteristics on the cambered surface and diminishes the adverse effects of the Coriolis force. The high Nu number region is expanded while the temperature uniformity is improved. The combination of the racetrack-shaped hole and DSC channel provides the highest heat transfer among the four cases. The averaged Nu numbers on both the leading and trailing sides for all tested cases show obvious downtrend as rotation number increases, especially at high Reynolds number.     

Simulation of free surface MHD‐flow and heat transfer around a cylinder

Magnetohydrodynamic (MHD) free‐surface flow and heat transfer of liquid metal around a cylinder under different Reynolds numbers were simulated numerically. The effects of the application of a magnetic field on wake and vortex shedding were analyzed. The characteristics of flow fields and temperature as well as Lorentz forces under two different Reynolds numbers were presented. The results showed that magnetic field could not only change substantially the flow pattern, but also suppress turbulent viscosity and surface renewal, which degraded heat transfer. Under the same Hartmann numbers, compared with the MHD‐flow and heat transfer of lower Reynolds numbers, the turbulence intensity and interaction between free surface and wake were still stronger for higher Reynolds numbers; consequently, the heat transfer was still high. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(1): 11–19, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20189     

Effect of wall proximity on forced convection in a plane channel with a built-in triangular cylinder

A numerical investigation has been carried out to analyze the effect of wall proximity of a triangular cylinder on the heat transfer and flow field in a horizontal channel. Computations have been carried out for Reynolds numbers (based on triangle width) range of 100–450 and gap widths (a/h) 0.5, 0.75 and 1. Results are presented in the form of instantaneous contours of temperature, vorticity, with some characteristics of fluid flow and heat transfer; such as time-averaged and instantaneous local Nusselt number, skin friction coefficient along bottom channel's wall, and drag coefficient. Results show that approaching triangular cylinder in the wall, removes vortex shedding and subsequently the heat transfer rate decreases at low Reynolds number. By decreasing the vortex shedding, drag coefficient decrease as triangular cylinder approaches the wall of the channel. The variation of vortex formation has a more significant suppression effect on the skin friction coefficient than the Nusselt number.     

Visualization of heat flow in a vertical channel with fully developed mixed convection

A study on visualization of heat flow in three channels with laminar fully developed mixed convection heat transfer is performed. The first channel is filled with completely pure fluid; the second one is completely filled with fluid saturated porous medium. A porous layer exists in the half of the third channel while another half is filled with pure fluid. The velocity, temperature and heat transport fields are obtained both by using analytical and numerical methods. Analytical expression for heat transport field is obtained and presented. The heatline patterns are plotted for different values of Gr/Re, thermal conductivity ratio, Peclet and Darcy numbers. It is found that the path of heat flow in the channel strongly depends on Peclet number. For low Peclet numbers (i.e., Pe = 0.01), the path of heat flow is independent of Gr/Re and Darcy numbers. However, for high Peclet numbers (i.e., Pe = 5), the ratio of Gr/Re, Darcy number and thermal conductivity ratio influence heatline patterns, considerably. For the channels with high Peclet number (i.e., Pe = 5), a downward heat flow is observed when a reverse flow exits.     

Wall–bounded flow and heat transfer around a circular cylinder at low Reynolds and Hartmann numbers

A two–dimensional numerical simulation is performed following a finite volume approach to analyze the forced convection heat transfer for the hydromagnetic flow around a circular cylinder at low Reynolds numbers. The cylinder is placed within a rectangular channel subjected to externally applied magnetic fields and acted upon by the magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conductive fluid. The magnetic field is applied either along the streamwise or transverse directions. The simulation is carried out for the range of Reynolds number 10 ≤ Re ≤ 80 with Hartmann number 0 ≤ Ha ≤ 10 and for different Prandtl numbers, Pr = 0.02 (liquid metal), 0.71 (air), and 7 (water) for a blockage ratio β = 0.25. The flow is steady for the above range of conditions. Apart from the channel wall, the magnetic field provides additional stability to the flow as a result of which the recirculation region behind the obstacle reduces with increasing magnetic field strength for a particular Reynolds number. The rate of heat transfer is found almost invariant at low Re whereas it increases slightly for higher Re with the applied magnetic field. The heat transfer increases as usual with the Reynolds number for all Hartmann numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21025     

Stability analysis of MHD radiative mixed convective flow in vertical cylindrical annulus: Thermal nonequilibrium approach

In the present study, the influence of the induced magnetic field on the MHD mixed convective electrically conducting fluid flow inside the vertical cylindrical annulus is analyzed numerically. The heat transfer is presumed to be due to a combination of mixed convection and radiation. The stability of the flow is examined when the solid and fluid phases are not in local thermal equilibrium. The governing equations are solved numerically by both finite difference and finite element methods. To control the flow formation rate more accurately the induced magnetic field is also considered in this study. As the magnetic Prandtl number (Pm) and Hartmann number (M) get enhanced, the velocity and induced magnetic fields get retarded in the annulus due to the presence of drag-like force, namely, the Lorentz force. When there is an increase in the mixed convection parameter the induced magnetic field gets enhanced. An increase in radiation parameter tends to decline the fluid temperature and reverse the behavior of the solid temperature. Increment in Pm decreases the wall shear stress near the conducting cylinder. Increasing values of porous, magnetic, and radiation parameters lead to an unstable system with smaller heat transfer coefficient values but the system gets stabilized for larger values of heat transfer coefficient. The results could be used as first-hand information for comprehending and developing the thermal flow phenomenon in porous media. The obtained numerical results are in good accordance with the existing results. Using an artificial neural network, heat transfer characteristics are analyzed through mean square error and regression analysis.     

Effect of magnetic field on near-wall coherent structures and heat transfer in magnetohydrodynamic turbulent channel flow of low Prandtl number fluids

A numerical study is carried out of the magnetic field effects on the coherent structures and the associated heat transfer in a turbulent channel flow with constant temperature at the bottom (cold) and top (hot) walls. Results from direct numerical simulations are conditionally sampled in order to extract the dominant coherent structures in the near-wall region for flows with and without a uniform external magnetic field in the wall-normal direction. The Reynolds number based on the bulk velocity and the wall distance is 5600, while only a representative small Stuart number of 0.01 is explored. Two fluids with Prandtl numbers of 0.01 and 0.71 are studied. It is shown that the conditionally averaged quasi-streamwise vortices are modified by the magnetic field with their size being increased and their strength decreased. The underlying organized fluid motions are damped by the Lorentz force and the turbulent heat transfer related to the action of quasi-streamwise vortices is decreased by the magnetic field. For the higher Prandtl number fluid, a similarity between the coherent temperature and the coherent streamwise velocity fluctuations is observed for both types of flow. This is diminished for the lower Prandtl number fluid, especially in the magnetohydrodynamic flow, inhibiting the intrusion of cold (hot) fluid from the cold (hot) wall towards the central region.     

Flow patterns and heat transfer enhancement in low-Reynolds–Rayleigh-number channel flow

This paper presents an experimental study on buoyancy-induced flow patterns and heat transfer characteristics of airflow through a horizontal rectangular channel. The channel had an aspect ratio of six, and its bottom and sidewalls were heated, whereas the top of the channel was cooled. The experiments were conducted at the Reynolds numbers 40 and Rayleigh numbers ranging from 100 to 4200. The Nusselt number and the temperature distributions on the top surface of the channel were measured simultaneously at different thermal/flow conditions, and the heat transfer characteristics of the channel was evaluated, together with the flow patterns in the channel. The results showed that due to the heated sidewalls, which was an `imperfect' factor comparing with the classic Rayleigh–Bénard channel, the longitudinal vortex rolls can occur at the Rayleigh number Ra=100, starting with number of rolls N=2 and then N=4 as the Ra increases, rather than the N=6 mode for the same channel with `perfect' sidewalls. In the present study, the six-roll mode occurred at Ra=1730 and above, but an initial trigger was required. Otherwise the four-roll mode would continue to be the dominant flow pattern at high Rayleigh numbers. It was demonstrated that significant heat transfer enhancement could be achieved in low Reynolds and Rayleigh number flow if the longitudinal vortex rolls were excited in the channel.     

Wall‐Confined Flow and Heat Transfer Around a Square Cylinder at Low Reynolds and Hartmann Numbers

This article discusses the results obtained through a two‐dimensional numerical simulation following a finite volume approach on the forced convection heat transfer for the hydromagnetic flow around a square cylinder at low Reynolds and Hartmann numbers. The magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conducting fluid is assumed to take place in a rectangular channel subjected to externally imposed magnetic fields and the cylinder is fixed within the channel. The magnetic fields may be applied either along the streamwise or transverse directions. Simulations are performed for the range of kinetic Reynolds number 10 ≤ Re ≤ 60 with Hartmann number 0 ≤ Ha ≤ 15 and for different thermal Prandtl numbers, Pr = 0.02 (liquid metal), 0.71 (air), and 7 (water) for a blockage ratio β = 0.25. A steady flow can be expected for the above range of conditions. Besides the channel wall, the magnetic field imparts additional stability to the flow as a consequence of which the recirculation region behind the obstacle reduces with increasing magnetic field strength for a particular Re. The critical Hartmann numbers for the complete suppression of flow separation in the case of a transversely applied magnetic field are computed. The rate of heat transfer is found almost invariant at low Re whereas it increases moderately for higher Re with the applied magnetic field. The heat transfer increases in general with the Reynolds number for all Hartmann numbers. Finally, the influence of obstacle shape on the thermohydrodynamic quantities is noted. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 459–475, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21091     

Steady mixed convective flow and heat transfer from tandem square cylinders in a horizontal channel

The two-dimensional laminar steady mixed convective flow and heat transfer around two identical tandem square cylinders confined in a horizontal channel are simulated by the high-accuracy multidomain pseudo-spectral method. The blockage ratio of the channel is chosen as 0.1, whereas the spacing between the cylinders is fixed with four widths of the cylinder. The Prandtl number is fixed at 0.7, the Reynolds number (Re) is studied in the range 5?≤?Re?≤?60, and the Richardson number (Ri) demonstrating the influence of thermal buoyancy ranges from 0 to 1. Numerical results reveal that, with the thermal buoyancy effect, the mixed convective flow remains steady. The variations of the overall drag and lift coefficients and the Nusselt numbers, are presented and discussed. Furthermore, the influence of thermal buoyancy on fluid flow and heat transfer is discussed and analyzed.     

Periodic laminar flow and heat transfer in a channel with 45° staggered V-baffles

A numerical investigation has been carried out to examine periodic laminar flow and heat transfer characteristics in a three-dimensional isothermal wall channel of aspect ratio, AR = 2 with 45° staggered V-baffles. The computations are based on the finite volume method, and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers based on the hydraulic diameter of the channel ranging from 100 to 1200. To generate two pair of main streamwise vortex flows through the tested section, V-baffles with an attack angle of 45° are mounted in tandem and staggered arrangement on the lower and upper walls of the channel. Effects of different baffle heights on heat transfer and pressure drop in the channel are studied and the results of the V-baffle pointing upstream are also compared with those of the V-baffle pointing downstream. It is apparent that in each of the main vortex flows, a pair of streamwise twisted vortex (P-vortex) flows can induce impinging flows on a sidewall and a wall of the interbaffle cavity leading to drastic increase in heat transfer rate over the channel. In addition, the rise in the V-baffle height results in the increase in the Nusselt number and friction factor values. The computational results reveal that the optimum thermal enhancement factor is around 2.6 at baffle height of 0.15 times of the channel height for the V-baffle pointing upstream while is about 2.75 at baffle height of 0.2 times for the V-baffle pointing downstream.     

Investigation of a Confined Laminar Impinging Jet on a Plate with a Porous Layer Using the Preconditioned Density-Based Algorithm

The preconditioned density-based algorithm and two-domain approach were used to investigate the fluid flow and heat transfer characteristics of a confined laminar impinging jet on a plate covered with porous layer. In the porous zone, the momentum equations were formulated by the Darcy-Brinkman-Forchheimer model; the thermal nonequilibrium model was adopted for the energy equation. At the porous/fluid interface, the applicability and influence of different hydrodynamic and thermal interfacial conditions were analyzed for the problem. The governing equations were solved by the preconditioned density-based finite-volume method, with preconditioning matrix for equations of porous domain adopted, aiming to eliminate the equation stiffness of porous seepage flows. The effects of Reynolds number, porosity, Darcy number, thermal conductivity ratio, Biot number, and porous layer thickness on the flow pattern and local heat transfer performance were studied. Results indicate that the Reynolds number and porosity don't strongly influence the flow pattern of porous channel, while the Darcy number and porous layer thickness have obvious influence on the flow pattern. The heat transfer performance are greatly influenced by the parameters studied.     

Fluid flow characteristics and convective heat transfer improvement on a gas turbine blade

The flow field features and heat transfer enhancement are investigated on a gas turbine blade by applying the jet impingement cooling method. The distribution of the flow field and the Nusselt number (Nu) was determined on the targeted surface in the cooling channel. The injection holes of different shapes, such as circular, square, and rectangular were considered. The Reynolds numbers (Re) of the airflow in the range of 2000–5000 and aspect ratios of 0.5–2 were particularly focused. The flow vortices and recirculation in the cooling channel and their influence on the heat transfer enhancement were analyzed in detail under different airflow and geometric conditions. Decreasing the ratio of the distance between jet-to-target plate to the diameter of the jet orifice (H/d) increased the heat transfer rate and produced high-intensity vortices and recirculation zones. It was noticed that the formation and generation of vortices and recirculation have important effects on the convective heat transfer rate at the impingement surface. Local Nusselt number, formation of complex vortices, and airflow recirculation in the cooling channel decreased with the increase in the distance between the jet hole and the targeted surface. It was found that with the increase in the Reynolds number of the jet, heat transfer between cold airflow and the targeted surface increased. Moreover, it was observed that the cooling performance of the round and square jet holes was better than the rectangular holes.     

Laminar periodic flow and heat transfer in square channel with 45° inline baffles on two opposite walls

A numerical investigation has been carried out to examine laminar flow and heat transfer characteristics in a three-dimensional isothermal wall square channel with 45°-angled baffles. The computations are based on the finite volume method, and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers based on the hydraulic diameter of the channel ranging from 100 to 1000. To generate a pair of mainstreamwise vortex flows through the tested section, baffles with an attack angle of 45° are mounted in tandem and inline arrangement on the lower and upper walls of the channel. Effects of different baffle heights on heat transfer and pressure loss in the channel are studied and the results of the 45° inline baffle are also compared with those of the 90° transverse baffle and the 45° staggered baffle. It is apparent that in each of the main vortex flows, a pair of streamwise twisted vortex (P-vortex) flows created by the 45° baffle exist and help to induce impinging flows on a sidewall and wall of the baffle cavity leading to drastic increase in heat transfer rate over the channel. In addition, the rise in the baffle height results in the increase in the Nusselt number and friction factor values. The computational results reveal that numerical results of both the 45° inline and staggered baffles are nearly the same. The optimum thermal enhancement factor is at the 45° baffle height of 0.2 times of the channel height for both arrays. The maximum thermal enhancement factor of the 45° baffle in the Re range studied is found to be about 2.6 or twice higher than that of the 90° transverse baffle.     

Heat and fluid flow across a rotating cylinder dissipating uniform heat flux in 2D laminar flow regime

Free-stream flow and forced convection heat transfer across a rotating cylinder, dissipating uniform heat flux, are investigated numerically for Reynolds numbers of 20–160 and a Prandtl number of 0.7. The non-dimensional rotational velocity (α) is varied from 0 to 6. Finite volume based transient heatline formulation is proposed. For Re = 100, the reasons for the onset/suppression of vortex shedding at a critical rotational velocity is investigated using vorticity dynamics. At higher rotational velocity, the Nusselt number is almost independent of Reynolds number and thermal boundary conditions. Finally, a heat transfer correlation is proposed in the 2D laminar flow regime. Cylinder rotation is an efficient Nusselt number reduction or cylinder-surface temperature enhancement technique.     

Effect of Thermal Buoyancy on Fluid Flow and Heat Transfer Across a Semicircular Cylinder in Cross-Flow at Low Reynolds Numbers

The influence of superimposed thermal buoyancy on hydrodynamic and thermal transport across a semicircular cylinder is investigated through numerical simulation. The cylinder is fixed in an unconfined medium and interacted with an incompressible and uniform incoming flow. Two different orientations of the cylinder are considered: one when the curved surface is exposed to the incoming flow and the other when the flat surface is facing the flow. The flow Reynolds number is varied from 50 to 150, keeping the Prandtl number fixed (Pr = 0.71). The effect of superimposed thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ Ri ≤ 2. The unsteady two-dimensional governing equations are solved by deploying a finite volume method based on the PISO (Pressure Implicit with Splitting of Operator) algorithm. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds and Richardson numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag, lift and pressure coefficients, and Nusselt numbers are presented and discussed. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. Additionally, intriguing effects of thermal buoyancy can be witnessed. It is established that heat transfer rate differs significantly under the superimposed thermal buoyancy condition for the two different orientations of the obstacle.