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     

Unsteady free convection MHD flow past a vertical cylinder with heat and mass transfer

Heat and mass transfer characteristics and the flow behavior on the MHD flow past a vertical cylinder are studied. The equations of conservation of mass, momentum, energy and concentration which govern the flow and heat and mass transfer are obtained. The nondimensional governing equations are solved by an efficient, more accurate, unconditionally stable and fast converging implicit scheme. The unsteady effects of material parameters such as Prandtl number, Schmidt number, buoyancy ratio parameter and magnetic parameter on the velocity, temperature and concentration are discussed. The local and average skin-friction, Nusselt number and Sherwood number are also presented graphically. The numerical predictions have been compared with the existing information in the literature and good agreement is obtained.     

Total and local heat transfer from a smooth circular cylinder in cross-flow at high reynolds number

The total and local heat transfer from a smooth circular cylinder to the cross flow of air has been measured over the Reynolds number range 3 × 10⁴ < Re < 4 × 10⁶. The interaction between flow and heat transfer is discussed. In particular, the boundary-layer effects on the heat transfer, such as transition from laminar to turbulent flow or boundary-layer separation, are considered in conjunction with the distributions of local static pressure and skin friction.     

Unsteady wake dynamics and heat transfer in forced and mixed convection past a circular cylinder in cross flow for high Prandtl numbers

This paper investigates the combined effect of Prandtl number and Richardson number on the wake dynamics and heat transfer past a circular cylinder in crossflow using a SUPG based finite element method. The computations are carried out for 80 < Re < 180, 0.7 < Pr < 100 and $0?\mathrm{Ri}?2$. The results have been presented for both forced and mixed convection flows. In the case of forced convection, crowding of temperature contours with reduced spatial spread is observed for increasing Prandtl numbers. The local and average Nusselt numbers are found to increase with increasing Reynolds number and Prandtl number. The average Nusselt number and Colburn factor are found to vary as Re^0.548 Pr ^0.373 and Re^?0.452, respectively. The extrapolated results of the average Nusselt number for low and high Reynolds numbers are found to match quite well with the available results in literature. Effect of Prandtl number shows various interesting phenomena for the mixed convective flows. Increasing the Prandtl numbers resulted in decreasing deflection and strength in the wake structures. The effect of baroclinic vorticity production during vortex shedding has been demonstrated at the vicinity of the cylinder and near wake. The Strouhal number is found to decrease with increasing Prandtl number, in the case of buoyancy induced flow. The effect of increasing Prandtl number is manifested as the stabilizing effect in the flow. This is, perhaps, the first time that such behavior for the Prandtl number is being reported. Additionally it is observed that the average Nusselt number decreases with increasing Richardson number.     

Stokes flow and heat transfer past a circular cylinder in a square cavity with suction/injection on sidewalls

The laminar viscous fluid flow past a circular cylinder placed in a square cavity of a uniform cross‐section is generated by applying injection/suction at the adjacent sidewalls. The temperature on the side walls without suction and on the boundary of the cylinder is kept constant, and constant heat flux is maintained on the walls with suction. The streamline flow pattern and isothermal lines are drawn. The flow is assumed to be Stokesian. Hence, the resulting biharmonic equation is solved for stream function by expressing it in two coupled equations, and a 5‐point formula is used to solve these equations. Fictitious nodes are introduced for derivative boundary conditions for stream function by using a central difference scheme, and a 3‐point backward difference formula is used for derivative boundary conditions on temperature.     

Unsteady MHD flow and heat transfer with viscous dissipation past a stretching sheet

In this paper a study is carried out to analyze the unsteady heat transfer effects of viscous dissipation on the steady boundary layer flow past a stretching sheet with prescribed constant surface temperature in the presence of a transverse magnetic field. The sheet is assumed to stretch linearly along the direction of the fluid flow. The assumed initial steady flow and temperature field neglecting dissipation effects becomes transient by accounting dissipation effects when time t′ > 0. The temperature and the Nusselt number are computed numerically using an implicit finite difference method. The obtained steady temperature field with dissipation is of practical importance.     

Waviness effect of a wavy circular cylinder on the heat transfer at a Reynolds number of 300

The present study investigates three-dimensional characteristics of fluid flow and heat transfer around a wavy cylinder which has the sinusoidal variation in the cross sectional area along the spanwise direction. The three different wavelengths of π/4, π/3 and π/2 at the fixed wavy amplitude of 0.1 have been considered to investigate the effect of waviness on especially the forced convection heat transfer around a wavy cylinder when the Reynolds and Prandtl numbers are 300 and 0.71, respectively. The numerical solution for unsteady forced convective heat transfer is obtained using the finite volume method. The immersed boundary method is used to handle the wavy cylinder in a rectangular grid system. The present computational results for a wavy cylinder are compared with those for a smooth cylinder. The fluid flow and heat transfer around the wavy cylinder depends on both the location along the spanwise direction and the wavelength. The time- and total surface-averaged Nusselt number for a wavy cylinder with λ = π/2 is larger than that for a smooth cylinder, whereas that with λ = π/4 and π/3 is smaller than that for a smooth cylinder. However, because the surface area exposed to heat transfer for a wavy cylinder is larger than that for a smooth cylinder, the total heat transfer rate for a wavy cylinder with different wavelengths of λ = π/4,π/3 and π/2 is larger than that for a smooth cylinder.     

Characteristics for flow and heat transfer around a circular cylinder near a moving wall in wide range of low Reynolds number

The present study numerically investigates two-dimensional laminar fluid flow and heat transfer past a circular cylinder near a moving wall. Numerical simulations to calculate the fluid flow and heat transfer past a circular cylinder are performed for different Reynolds numbers varying in the range of 60–200 and a fixed Prandtl numbers of 0.7 (air) in the range of 0.1 ? G/D ? 4, where G/D is the ratio of the gap between the cylinder and a moving wall, G and the cylinder diameter, D. The flow and thermal fields become the steady state below the critical gap ratios of 0.8, 0.4 and 0.2 for the Reynolds numbers of 60, 80 and 100, respectively. As the gap ratio decreases, the magnitude of lift coefficient for all Reynolds numbers increased significantly with diminishing G/D due to the ground effect. The cases of Reynolds numbers of 60, 80 and 100 revealed the sharp slope of drag coefficient in the range of the gap ratio where the flow transfers from the unsteady state to the steady state. As the Reynolds number decreases, the variation of Nusselt is much significant and increases considerably with decreasing G/D.     

Fluid flow and heat transfer in the duct of an MHD power generator

A numerical solution of the equations governing the flow of an electrically conducting, viscous, compressible gas with variable fluid properties in the presence of a uniform magnetic field is obtained. The velocity and temperature distributions for subsonic and supersonic flows as these occur in the duct of an M HD generator are analysed.     

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.     

MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity and hall effect

In the present paper the laminar fully developed MHD flow and heat transfer through a rectangular duct of a viscous incompressible electrically conducting fluid is studied. A constant pressure gradient and an external uniform magnetic field are applied and the Hall effect is taken into consideration. The fluid viscosity is assumed to be temperature dependent with the assumption of constant wall heat flux axially and constant wall temperature peripherally. A numerical solution for the governing non-linear partial differential equations is obtained. The effect of the Hall term and the variable viscosity on the velocity and temperature fields is examined.     

Effect of arc-shaped vertical control plate on heat and mass transfer in uniform flow past an isothermally heated circular cylinder

The current work investigates the effect of an arc-shaped vertical control plate on the heat and mass transfer in uniform flow past an isothermally heated circular cylinder. The control plate is positioned downstream at various distances from the circular cylinder's surface. The governing equations are discretized by the higher order compact (HOC) finite difference scheme, and then this system of discretized equations is solved by using a bi-conjugate gradient stabilized iterative method for Prandtl number $Pr=0.7$, Reynolds number $Re=150$. To investigate the effect of an arc-shaped control plate on heat and mass transfer, we consider a range of nondimensional distances between the circular cylinder and the control plate, $0.5\le d∕R_0\le 8$, where $d$ is the control plate's distance and $R_0$ is the cylinder's radius. The exact timing and location of the bifurcation points are calculated by using topological aspect-based structural bifurcation analysis. Significant effects of various locations of the control plate on periodic wake and heat transfer are observed. It is found that the increasing distance of the control plate from the cylinder delays the occurrence of the structural bifurcation and shifts the bifurcation points upwards in the upper half and downwards in the lower half of the cylinder. Our study shows that the specific location of the control plate can fully suppress the vortex shedding. Time-averaged total Nusselt number can be drastically reduced by increasing the distance between the control plate and the cylinder. With proper positioning, the vertical control plate can lessen the time-averaged drag force by up to $22.5\%$ when compared to a cylinder without a control plate. Overall, this work presents many new phenomena that have not been reported before.     

Forced and mixed convective heat transfer from accelerated flow past an elliptic cylinder

Investigated in this paper are the initial stages of the laminar, two-dimensional, thermal-fluid problem of forced and mixed convective heat transfer from accelerated flow past an elliptic cylinder. The cylinder is taken to be inclined at an angle η with the horizontal and the viscous incompressible Boussinesq fluid accelerates uniformly from rest past it. Two types of solutions are presented. The first type takes the form of an approximate analytical solution valid for small times and large Reynolds numbers. The second type is a numerical solution obtained by numerically integrating the full Navier-Stokes and energy equations using a spectral-finite difference procedure.     

Numerical investigation of fluid flow and heat transfer around a solid circular cylinder utilizing nanofluid

In this study, flow-field and heat transfer through a copper–water nanofluid around circular cylinder has been numerically investigated. Governing equations containing continuity, N–S equation and energy equation have been developed in polar coordinate system. The equations have been numerically solved using a finite volume method over a staggered grid system. SIMPLE algorithm has been applied for solving the pressure linked equations. Reynolds and Peclet numbers (based on the cylinder diameter and the velocity of free stream) are within the range of 1 to 40. Furthermore, volume fraction of nanoparticles (φ) varies within the range of 0 to 0.05. Effective thermal conductivity and effective viscosity of nanofluid have been estimated by Hamilton–Crosser and Brinkman models, respectively. The effect of volume fraction of nanoparticles on the fluid flow and heat transfer characteristics are investigated. It is found that the vorticity, pressure coefficient, recirculation length are increased by the addition of nanoparticles into clear fluid. Moreover, the local and mean Nusselt numbers are enhanced due to adding nanoparticles into base fluid.