Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure

 A collocated, non-orthogonal grid based finite volume technique has been applied for investigating the two dimensional natural convective flow and heat transfer around a heated cylinder kept in a square enclosure. The effects of different enclosure wall thermal boundary conditions, fluid Prandtl number and the ratio between enclosure and cylinder dimensions (aspect ratio) upon the flow and thermal features, have been systematically studied. It is observed that the patterns of recirculatory flow and thermal stratification in the fluid are significantly modified, if any of these parameters is varied. The overall heat transfer rates are also affected due to the changes in the flow and temperature patterns. The study presents useful observations regarding the variation of local Nusselt number along each wall, for the different cases considered. Received on 2 August 2000 / Published online: 29 November 2001     

MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure

This study looks at MHD natural convection flow and heat transfer in a laterally heated enclosure with an off-centred partition. Governing equations in the form of vorticity–stream function formulation are solved using the polynomial differential quadrature (PDQ) method. Numerical results are obtained for various values of the partition location, Rayleigh, Prandtl and Hartmann numbers. The results indicate that magnetic field significantly suppresses flow, and thus heat transfer, especially for high Rayleigh number values. The results also show that the x-directional magnetic field is more effective in damping convection than the y-directional magnetic field, and the average heat transfer rate decreases with an increase in the distance of the partition from the hot wall. The average heat transfer rate decreases up to 80% if the partition is placed at the midpoint and an x-directional magnetic field is applied. The results also show that flow and heat transfer have little dependence on the Prandtl number.     

The conjugate heat transfer of the partially heated microchannels

In this paper, the conjugate heat transfer of the water flow inside the microtube (D _i/D _o = 0.1/03 and 0.1/0.5 mm) was investigated. The laminar regime was considered with Re up to 200, input heat transfer rate of Q ₀ = 0.1 W and variable thermophysical properties of the water. Two different cases of the partial joule heating were considered for the tube wall. In the first case the tube wall was heated near the inlet of the tube (upstream heating) while, in the second case, the outlet portion of the wall was heated (downstream heating). In order to investigate the influence of the tube material on the heat transfer behavior and limits of the axial conduction inside the wall, three different tube wall materials were considered, stainless steel (k = 15.9 W/m K), silicon (k = 189 W/m K) and copper (k = 398 W/m K).     

An experimental study of fluid flow and heat transfer in decaying swirl through a heated annulus

The mean and turbulent structures of turbulent swirling flow in a heated annulus have been measured. Both forced and free vortex swirling flows were generated, and the outer wall of the test section was heated uniformly. The maximum swirl number was 1.39, Reynolds numbers were up to 200000, and heat input was 10.5 kW. Mean and turbulent velocity components, air and wall temperatures, and wall static pressures were all measured. Hot-film techniques were developed to measure turbulence. From these parameters, the flow and temperature fields, pressure distribution, and heat transfer coefficients were determined. The mechanisms of heat transfer were identified.     

Numerical simulation of MHD stagnation point flow and heat transfer of a micropolar fluid towards a heated shrinking sheet

A comprehensive study of magneto hydrodynamics two‐dimensional stagnation flow with heat transfer characteristics towards a heated shrinking sheet immersed in an electrically conducting incompressible micropolar fluid in the presence of a transverse magnetic field is analyzed numerically. The governing continuity, momentum, angular momentum and heat equations together with the associated boundary conditions are first reduced to a set of self similar nonlinear ordinary differential equations using a similarity transformation and are then solved by a method based on finite difference discretization. Some important features of the flow and heat transfer in terms of normal and streamwise velocities, microrotation and temperature distributions for different values of the governing parameters are analyzed, discussed and presented through tables and graphs. The results indicate that the reverse flow caused due to shrinking of the sheet can be stopped by applying a strong magnetic field. The magnetic field enhances the shear stresses and decreases the thermal boundary layer thickness. The heat loss per unit area from the sheet decreases with an increase in the shrinking parameter. Micropolar fluids exhibit reduction in shear stresses and heat transfer rate as compared with Newtonian fluids, which may be beneficial in the flow and thermal control of polymeric processing. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of fluid flow and heat transfer in a channel with intermittent heated porous blocks

A numerical study of forced convection enhancement in a channel intermittently heated is presented in this work. The use of porous blocks mounted on the heated parts of the channel to improve thermal performance is investigated. In order to account for the inertia, drag and boundary effects, the Brinkman-Forchheimer-extended Darcy model is adopted for the flow inside the porous regions. The effects of several parameters such as Darcy number, the block dimensions, the number of blocks and the thermal conductivity ratio are documented. The results show that the blocks may alter substantially the flow pattern depending on the permeability of the porous medium, and may improve the heat transfer and reduce the wall temperature under certain circumstances. Received on 9 June 1997     

Numerical study of the flow and heat transfer in a Reiner-Rivlin fluid on a rotating porous disk

An unsteady flow and heat transfer to an infinite porous disk rotating in a Reiner—Rivlin non-Newtonian fluid are considered. The effect of the non-Newtonian fluid characteristics and injection (suction) through the disk surface on velocity and temperature distributions and heat transfer is considered. Numerical solutions are obtained over the entire range of the governing parameters.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 85–95, January–February, 2005.     

Convective magnetohydrodynamic two fluid flow and heat transfer in an inclined channel

 The problem of fully developed free convection two fluid magnetohydrodynamic flow in an inclined channel is investigated. The governing momentum and energy equations are coupled and highly nonlinear due to dissipation terms, solutions are found employing perturbation technique for small values of Pr · Ec (=ɛ) the product of Prandtl number and Eckert number. Effects of Grashof number, Hartmann number, inclination angle, the ratios of electrical conductivities, viscosities and heights of two fluids on the flow are explored. It is observed that the flow can be controlled effectively by suitable adjustment of the values for the ratios of heights, electrical conductivities and viscosities of the two fluids. Received on 10 December 1999     

Numerical and experimental study of the heat transfer and fluid flow by thermocapillary convection around gas bubbles

 At liquid–gas or liquid–liquid interfaces thermocapillary or Marangoni convection develops in the presence of a temperature or concentration gradient along the interface. This convection was not paid much attention up to now, because under terrestrial conditions it is superimposed by the strong buoyancy convection. In a microgravity environment, however, it is the remaining mode of natural convection. During boiling in microgravity it was observed at subcooled conditions. Therefore the question arises about its contribution to the heat transfer. Thus the thermocapillary convection was intensively studied at single gas bubbles in various liquids both experimentally and numerically. Inside a temperature gradient chamber, the overall heat transfer around single bubbles of different volume was measured with calorimetry and the liquid flow with PIV and LDV. In parallel to the experiment, a 2-dimensional mathematical model was worked out and the coupled heat transfer and fluid flow was simulated with a CV-FEM method both under earth gravity level and under microgravity. The results are described in terms of the dimensionless Nusselt-, Peclet-, Marangoni-, Bond- and Prandtl-number. Received on 23 August 1999     

Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system

We consider turbulent flows in a differentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of [Elena and Schiestel, 1996] and [Schiestel and Elena, 1997] widely validated in various rotor-stator cavities with throughflow ( [Poncet, 2005], [Poncet et al., 2005] and [Haddadi and Poncet, 2008]) and heat transfer (Poncet and Schiestel, 2007). To show the capability of the present code, our numerical predictions are compared very favorably to the velocity measurements of Escudier and Gouldson (1995) in the isothermal case, for both the mean and turbulent fields. The RSM model improves, in particular, the predictions of the k-ε model of Naser (1997). Then, the second order model is applied for a large range of rotational Reynolds (3744 ? Re_i ? 37,443) and Prandtl numbers (0.01 ? Pr ? 12), flow rate coefficient (0 ? C_w ? 30,000) in a very narrow cavity of radius ratio s = R_i/R_o = 0.961 and aspect ratio L = (R_o − R_i)/h = 0.013, where R_i and R_o are the radii of the inner and outer cylinders respectively and h is the cavity height. Temperature gradients are imposed between the incoming fluid and the inner and outer cylinders. The mean hydrodynamic and thermal fields reveal three distinct regions across the radial gap with a central region of almost constant axial and tangential mean velocities and constant mean temperature. Turbulence, which is weakly anisotropic, is mainly concentrated in that region and vanishes towards the cylinders. The mean velocity distributions are not clearly affected by the rotational Reynolds number and the flow rate coefficient. The effects of the flow parameters on the thermal field are more noticeable and considered in details. Correlations for the averaged Nusselt numbers along both cylinders are finally provided according to the flow control parameters Re_i, C_w, and Pr.     

A study on Brinkman number variation on water based nanofluid heat transfer in partially heated tubes

Even if the variation of Nusselt number with Reynolds number has been observed before, little to no studies are concerning nanofluids. The present numerical data in the laminar regime were also found to correlate well with the Brinkman number for the individual sets and much better globally, by combining all the data sets for nanofluids and water.Thus, this work proposes a new correlation between heat transfer rate and Brinkman number which is a nondimensional number of viscosity, flow velocity and temperature. The results showed a good empirical equation that Nu/(Re^0.62 Pr^0.33) is dependent on a power law function to the Brinkman number in laminar flow regime. The proposed correlation can be applied both to water and nanofluid flow, with respect to the nanoparticle loading. It is expected that the equation suggested by this work can be useful to design heating/cooling devices.     

Buoyancy-induced flow and convective heat transfer in an inclined arc-shape enclosure

Numerical and experimental investigations have been conducted to study the flow and heat transfer characteristics for the buoyancy-induced flow inside an inclined arc-shape enclosure. Mathematical model in form of a stream function-vorticity formulation representing the laws of conservation in mass, momentum, and energy is expressed in a curvilinear coordinate frame and solved by a finite-volume discretization method. Heat transfer and flow pattern are predicted at various Grashof numbers and inclination angles. Meanwhile, an experimental system is developed and a flow-visualization technique using smoke is employed to observe the flow pattern. Results show that only when the Grashof number is higher than 10⁵, the increase in natural convection heat transfer becomes appreciable. Both the strength and the pattern of the buoyancy-induced vortex are found to be greatly dependent on the inclination angle. The range of the Grashof number considered in this study is up to 10⁷ and the inclination angle is varied from 0 to π.     

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.     

Axisymmetric flow and heat transfer of the Carreau fluid due to a radially stretching sheet: Numerical study

The prime objective of this article is to study the axisymmetric flow and heat transfer of the Carreau fluid over a radially stretching sheet. The Carreau constitutive model is used to discuss the characteristics of both shear-thinning and shear-thickening fluids. The momentum equations for the two-dimensional flow field are first modeled for the Carreau fluid with the aid of the boundary layer approximations. The essential equations of the problem are reduced to a set of nonlinear ordinary differential equations by using local similarity transformations. Numerical solutions of the governing differential equations are obtained for the velocity and temperature fields by using the fifth-order Runge–Kutta method along with the shooting technique. These solutions are obtained for various values of physical parameters. The results indicate substantial reduction of the flow velocity as well as the thermal boundary layer thickness for the shear-thinning fluid with an increase in the Weissenberg number, and the opposite behavior is noted for the shear-thickening fluid. Numerical results are validated by comparisons with already published results.     

Convective heat transfer in a locally heated plane incompressible fluid layer

The problem of convection in a plane horizontal layer of incompressible fluid with rigid boundaries when the temperature is constant on the lower boundary and has a parabolic profile on the upper boundary can be reduced to solution of a system of time-dependent one-dimensional equations. An analytic solution of the problem is obtained directly at the extremum point. Together with the wellknown solutions which describe heat transfer for the linear temperature distribution on the boundaries, the results obtained make it possible to calculate the heat flux through a thin slit for an arbitrary given heating of a thin fluid layer between heat-conducting bodies.     

Numerical investigation of heat transfer and fluid flow characteristics inside a wavy channel

The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed for Prandtl number 0.7, and Reynolds number ranging from 100 to 1,100 on non-orthogonal non-staggered grid systems, based on SIMPLER algorithm in the curvilinear body-fitted coordinates. Effects of wavy heights, lengths, wavy pitches and channel widths on fluid flow and heat transfer were studied. The results show that overall Nusselt numbers and friction factors increase with the increase of Reynolds numbers. According to the local Nusselt number distribution along channel wall, the heat transfer may be greatly enhanced due to the wavy characteristics. In the geometries parameters considered, friction factors and overall Nusselt number always increase with the increase of wavy heights or channel widths, and with the decrease of wavy lengths or wavy pitches. Especially the overall Nusselt number significantly increase with the increase of wavy heights or channel widths, where the flow may become into transition regime with a penalty of strongly increasing in pressure drop. An erratum to this article can be found at     

Analysis of heat and fluid flow in partially divided fluid saturated porous cavities

Fluid flow and heat transfer phenomena in partially divided cavities filled with porous media have been numerically studied in this research. A non-Darcy generalized formulation is applied to describe the behavior of fluid flow in porous media. A splitting semi-implicit finite element method is adopted to solve the governing equations. The range of Ra involved in this study is between 10⁴ and 10⁶. Three different locations of dividers are investigated to probe the geometrical effect on heat and fluid flow. The results of Da = 10⁻² display a trend similar to the non-porous medium, but those of Da = 10⁻⁴ show dramatic decrease in flow strength, as well as heat transfer rate. A different location of divider may change the local and average Nusselt numbers. Received on 10 August 1999     

Numerical investigation of fully developed turbulent fluid flow and heat transfer in a square duct

Three-dimensional fully developed turbulent fluid flow and heat transfer in a square duct are numerically investigated with the author's anisotropic low-Reynolds-number k-ε turbulence model. Special attenton has been given to the regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, instead of the common wall function approach, the no-slip boundary condition at the wall is directly used. Velocity and temperature profiles are predicted for fully developed turbulent flows with constant wall temperature. The predicted variations of both local wall shear stress and local wall heat flux are shown to be in close agreement with available experimental data. The present paper also presents the budget of turbulent kinetic energy equation and the systematic evaluation for existing wall function forms. The commonly adopted wall function forms that are valid for two-dimensional flows are found to be inadequate for three-dimensional turbulent flows in a square duct.     

Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (Re = 2,000–5,500), angles of V corrugated plates (θ = 20°, 40°, 60°), and constant heat fluxs (q″ = 580, 830, 1,090 W/m²). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (θ) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.     

3D Numerical heat transfer and fluid flow analysis in plate-fin and tube heat exchangers with electrohydrodynamic enhancement

Three-dimensional laminar fluid flow and heat transfer over a four-row plate-fin and tube heat exchanger with electrohydrodynamic (EHD) wire electrodes are studied numerically. The effects of different electrode arrangements (square and diagonal), tube pitch arrangements (in-line and staggered) and applied voltage (V_E=0–16 kV) are investigated in detail for the Reynolds number range (based on the fin spacing and frontal velocity) ranging from 100 to 1,000. It is found that the EHD enhancement is more effective for lower Re and higher applied voltage. The case of staggered tube pitch with square wire electrode arrangement gives the best heat transfer augmentation. For V_E=16 kV and Re = 100, this study identifies a maximum improvement of 218% in the average Nusselt number and a reduction in fin area of 56% as compared that without EHD enhancement.