Effects of Reynolds and Prandtl numbers on heat transfer from a square cylinder in the unsteady flow regime

The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 ? Re ? 160 and 0.7 ? Pr ? 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.     

A numerical study on the forced convection heat transfer from an isothermal and isoflux sphere in the steady symmetric flow regime

The effects of Reynolds and Prandtl numbers on the heat transfer characteristics of an unconfined sphere for different thermal boundary conditions (isothermal and isoflux) on the sphere surface have been investigated numerically by using a finite volume method for the range of conditions as 5 ⩽ Re ⩽ 200 and 0.7 ⩽ Pr ⩽ 400 (the maximum value of Peclet number being 2000). Based on the numerical results obtained herein, heat transfer correlations are developed for the constant temperature and the constant heat flux boundary conditions on the solid sphere surface in the steady symmetric flow regime. The variation of local Nusselt number on the sphere surface shows the effect of Prandtl number on heat transfer from a sphere in this flow regime. In addition, this work also demonstrates an approach to solve such flow problems using the Cartesian form of the field equations.     

Steady forced convection heat transfer from a heated circular cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated circular cylinder in the steady cross-flow regime has been investigated numerically by solving the momentum and thermal energy equations using a finite volume method and the QUICK scheme on a non-uniform Cartesian grid. The dependence of the average Nusselt number on the Reynolds number (5 ⩽ Re ⩽ 40), power-law index (0.6 ⩽ n ⩽ 2) and Prandtl number (1 ⩽ Pr ⩽ 1000) has been studied in detail. The numerical results are used to develop simple correlations as functions of the pertinent dimensionless variables. In addition to the average Nusselt number, the effects of Re, Pr and n on the local Nusselt number distribution have also been studied to provide further physical insights. The role of the two types of thermal boundary conditions, namely, constant temperature and uniform heat flux on the surface of the cylinder has also been presented.     

Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers

In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re = 1–40 and Richardson number, Ri = 0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re = 1–2, between Re = 2–3 and between Re = 3–4 for Ri = 0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

A numerical study of natural convection around a square,horizontal, heated cylinder placed in an enclosure

In this paper, natural convection around a tilted heated square cylinder kept in an enclosure has been studied in the range of 10³ ⩽ Ra ⩽ 10⁶. Streamfunction-vorticity formulation of the Navier–Stokes equation is solved numerically using finite-difference method in non-orthogonal body-fitted coordinate system. Detailed flow and heat transfer features for two different thermal boundary conditions are reported. Effects of the enclosure geometry has been assessed using three different aspect ratio placing the square cylinder at different heights from the bottom. The concept of heatfunction has been employed to trace the path of heat transport. It is found that the uniform wall temperature heating is quantitatively different from the uniform wall heat flux heating. Flow pattern and thermal stratification are modified, if aspect ratio is varied. Overall heat transfer also changes for different aspect ratio.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Effect of power-law fluid behavior on momentum and heat transfer characteristics of an inclined square cylinder in steady flow regime

The governing equations describing the momentum and heat transfer phenomena of power-law non-Newtonian fluids over a heated square cylinder at 45° of incidence in the two-dimensional (2-D) steady flow regime are solved numerically. Extensive results on the detailed structure of the flow and temperature fields as well as on the gross engineering parameters are presented over the following ranges of conditions: 0.2 ? n ? 1; 0.1 ? Re ? 40 and 0.7 ? Pr ? 100. At low Reynolds numbers, the flow remains attached to the surface of the cylinder. This seems to occur for all values of power-law index, at least up to about Re = 1. On the other hand, twin standing vortices were seen to form at Re = 10 for all values of power-law index considered herein. The influence of the Reynolds number and power-law index is delineated on the detailed structure of the flow field (streamlines), wake characteristics and surface pressure distribution as well as on the value of drag coefficients. Similarly, the effect of Prandtl number is studied on forced convective heat transfer for the two commonly encountered boundary conditions, namely, constant temperature or constant heat flux prescribed on the surface of the cylinder. Using the computed numerical results, simple heat transfer correlations are obtained in terms of the Nusselt number as a function of the pertinent governing parameters thereby enabling the prediction of the rate of heat transfer between the fluid and the immersed cylinder. In addition, variation of the local Nusselt number on the surface of the inclined of square cylinder and representative isotherm plots are also presented to elucidate the effect of Reynolds number, Prandtl number and power-law index on the heat transfer phenomenon.     

Experiments on heat transfer enhancement from a heated square cylinder in a pulsating channel flow

Experiments have been performed to investigate heat transfer enhancement from a heated square cylinder in a channel by pulsating flow. For all the experiments, the amplitude of the pulsating flow is fixed at A = 0.05. The effects of the Reynolds number based on the mean flow velocity (Re = 350 and 540), the pulsating frequency (0 Hz < f_p < 60 Hz) and the blockage ratio of the square cylinder (β = 1/10, 1/8, and 1/6) on convective heat transfer are examined. The measured Strouhal numbers of shedding vortices for non-pulsating (A = 0) steady inlet flow are compared with the previously published data, and good agreement is found. The “lock-on” phenomenon is clearly observed for a square cylinder in the present flow pulsation. When the pulsating frequency is within the lock-on regime, heat transfer from the square cylinder is substantially enhanced. In addition, the influence of the Reynolds number and the blockage ratio on the lock-on occurrence is discussed in detail.     

Electrohydrodynamic enhancement of in-tube convective condensation heat transfer

An experimental investigation of electrohydrodynamic (EHD) augmentation of heat transfer for in-tube condensation of flowing refrigerant HFC-134a has been performed in a horizontal, single-pass, counter-current heat exchanger with a rod electrode placed in the centre of the tube. The effects of varying the mass flux (55 kg/m² s ⩽ G ⩽ 263 kg/m² s), inlet quality (0.2 ⩽ x_in ⩽ 0.83) and the level of applied voltage (0 kV ⩽ V ⩽ 8 kV) are examined. The heat transfer coefficient was enhanced by a factor up to 3.2 times for applied voltage of 8 kV. The pressure drop was increased by a factor 1.5 at the same conditions of the maximum heat transfer enhancement. The improved heat transfer performance and pressure drop penalty are due to flow regime transition from stratified flow to annular flow as has been deduced from the surface temperature profiles along the top and bottom surfaces of the tube.     

Numerical prediction of flow and heat transfer of power-law fluids in a plane channel with a built-in heated square cylinder

Structure of unsteady laminar flow and heat transfer of power-law fluids in two-dimensional horizontal plane channel with a built-in heated square cylinder is studied numerically. The governing equations are solved using a control volume finite element method (CVFEM) adapted to the staggered grid. Computations are performed over a range of Reynolds and Richardson numbers from Re = 20 to 200 and from Ri = 0 to 8, respectively at fixed Prandtl number Pr = 50 and blockage ratio value β′ = 1/8. Three different values of the power-law index (n = 0.5, 1 and 1.4) are considered in this study to show its effect on the value of the critical Reynolds number defining the transition between two different flow regimes (symmetrical and periodic flows), the variations of Strouhal number, drag and lift coefficients and the heat transfer from the square cylinder as function of Reynolds number. Heat transfer correlations are obtained through forced convection. A discussion about the buoyancy effect on the flow pattern and the heat transfer for different power-law index is also presented.     

Jet impingement interaction with cross flow in horizontal porous layer under thermal non-equilibrium conditions

In the present article the jet impingement cooling of heated portion of a horizontal surface immersed in a thermally non-equilibrium porous layer is considered for investigation numerically with the presence of a cross flow. The mathematical model is derived for steady, two-dimensional laminar flow based on Darcy model and two-energy equation for fluid and solid phases. A parametric study is carried out by varying the following parameters: cross flow to jet flow velocity ratio parameter (0 ⩽ M ⩽ 1); porosity scaled thermal conductivity ratio parameter (0.1 ⩽ K_r ⩽ 1000); heat transfer coefficient parameter (0.1 ⩽ H ⩽ 1000); Péclet number (1 ⩽ Pe ⩽ 1000) and Rayleigh number (10 ⩽ Ra ⩽ 100). The total average Nusselt number is defined based on the overall thermal conductivity, which is assumed to be the arithmetic mean of the porosity scaled thermal conductivity of the fluid and solid phases. The total average Nusselt number as well as the average Nusselt number for both fluid and solid phases is presented for different governing parameters. It is found that the presence of a weak cross flow in a jet impinging jet may degrade the heat transfer. The results show that the average Nusselt number calculated from the thermal equilibrium model are the maximum possible values and these values can be reproduced by large values of H × K_r.     

Numerical simulation of natural convection heat transfer in a porous cavity heated from below using a non-Darcian and thermal non-equilibrium model

The present paper investigates the numerical simulation of steady laminar incompressible natural convection heat transfer in an enclosed cavity that is filled with a fluid-saturated porous medium. The bottom wall is subjected to a relatively higher temperature than the top wall while the vertical walls are considered to be insulated. The flow field is modeled upon incorporating different non-Darcian effects, such as the convective term, Brinkman effect and Forchhiemer quadratic inertial effect. Moreover the two-equation model is used to separately account for the local fluid and solid temperatures. The numerical solution is obtained through the application of the finite volume method. The appraisals of the sought objectives are performed upon identifying key dimensionless groups of parameters. These dimensionless groups along with their operating domains are: Rayleigh number 1 ⩽ Ra ⩽ 400, Darcy number 10⁻⁴ ⩽ Da ⩽ 10⁻³, effective fluid-to-solid thermal conductivity ratio 0.1 ⩽ κ ⩽ 1.0, and the modified Biot number 1 ⩽ χ ⩽ 100. The non-Darcian effects are first examined over a broad range of Rayleigh number. Next, the implications of the group of parameters on the flow circulation intensity, local thermal non-equilibrium (LTNE) and average Nusselt number are highlighted and pertinent observations are documented.     

Heat transfer of impinging jet-array over convex-dimpled surface

A detailed heat transfer measurement over a convex-dimpled surface of impinging jet-array with three eccentricities (E/H) between jet-centre and dimple-centre is performed. These surface dimples considerably modify heat transfers from smooth-walled scenarios due to different impinging topologies for jet array with modified inter-jet reactions. Heat transfer variations caused by adjusting jet Reynolds number (Re) and separation distance (S/D_j) over the ranges of 5000 ⩽ Re ⩽ 15,000 and 0.5 ⩽ S/D_j ⩽ 11 with three eccentricities of E/H = 0, 1/4 and 1/2 are examined. A selection of experimental data illustrates the isolated and interactive influences of Re, S/D_j and E/H on local and spatially averaged heat transfers. In conformity with the experimentally revealed heat transfer physics, a regression-type analysis is performed to generate a set of heat transfer correlations, which permit the evaluations of spatially averaged Nusselt numbers over central jet region of dimpled impinging surface.     

Oscillatory double-diffusive mixed convection in a two-dimensional ventilated enclosure

By starting from a steady flow configuration based on the work of Deng et al. [Qi-Hong Deng, Jiemin Zhou, Chi Mei, Yong-Ming Shen, Fluid, heat and contaminant transport structures of laminar double-diffusive mixed convection in a two-dimensional ventilated enclosure, Int. J. Heat Mass Transfer 47 (2004) 5257–5269], a numerical investigation was conducted to analyse the unsteady double-diffusive mixed convection in two-dimensional ventilated room due to heat and contaminant sources. Owing to the large number of parameters, the results are reported only for a constant buoyancy ratio N equal to 1. The flow is found to be oscillatory for a fixed Reynolds number (700 ⩽ Re ⩽ 1000) when the Grashof number is varied in a wide range (10³ ⩽ Gr ⩽ 10⁶). Results of the simulations show that the onset of the oscillatory indoor airflow occurs for couples (Re, Gr) values that can be correlated as Re = aGr^b.     

Convective heat transfer on a rotating finned cylinder with transverse airflow

The present experimental investigation relates to the convective heat transfer determination around annular fins mounted on a rotating cylinder with air crossflow. The mean convective heat transfer coefficient can be identified by solving the inverse conduction heat transfer problem during the fin cooling process. We used an inverse method, based on the mean squared error, to develop a model of mean convective heat transfer, taking lateral conduction into account. Tests were carried out for rotational Reynolds numbers Re_ω between 2150 and 17,200, air crossflow Reynolds numbers Re_U between 0 and 39,600, and fin spacings u in the range 10 mm to ∞, u = ∞ corresponding to the single disk case. For each fin spacing, the relative influences of the rotational and airflow forced convections on the heat transfer were analyzed and correlations of the mean Nusselt number on the fin, relative to both Reynolds numbers, are proposed. Moreover, an efficiency definition, that allows optimal geometrical configurations of the finned cylinder to be identified for the given operating conditions, is proposed.     

Effect of temperature-dependent viscosity on forced convection heat transfer from a cylinder in crossflow of power-law fluids

The steady, two-dimensional and incompressible flow of power-law fluids across an unconfined isothermal heated circular cylinder is investigated numerically to ascertain the effect of temperature-dependent viscosity on the flow and forced convection heat transfer phenomena. Extensive numerical results elucidating the variation of the heat transfer characteristics and drag coefficient on the severity of temperature dependence of viscosity (0 ? b ? 0.5), power law index (0.6 ? n ? 1.6), Prandtl number (1 ? Pr ? 100) and Reynolds number (1 ? Re ? 30) are presented. The coupled momentum and energy equations are expressed in the stream function/vorticity formulation and solved using a second-order accurate finite difference method to determine the local and surface-averaged Nusselt numbers, the drag coefficient, and to map the flow domain in terms of the temperature and flow fields near the cylinder. The variation of viscosity with temperature is shown to have a substantial effect on both the local and surface-averaged values of the Nusselt number. As expected, the results also suggest that the rate of heat transfer shows positive dependence on the Reynolds number and Prandtl number. Furthermore, stronger the dependence of viscosity on the temperature, the greater is the enhancement in the rate of heat transfer. Finally, all else being equal, shear-thinning fluid behaviour facilitates heat transfer while the shear-thickening behaviour has deleterious effect on heat transfer.     

Steady natural convection flows in a square cavity with linearly heated side wall(s)

The present numerical study deals with natural convection flow in a closed square cavity when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Non-linear coupled PDEs governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Numerical results are obtained for various values of Rayleigh number (Ra) (10³ ⩽ Ra ⩽ 10⁵) and Prandtl number (Pr) (0.7 ⩽ Pr ⩽ 10). Results are presented in the form of streamlines, isotherm contours, local Nusselt number and the average Nusselt as a function of Rayleigh number.     

Steady natural convection flow in a square cavity filled with a porous medium for linearly heated side wall(s)

In this paper natural convection flows in a square cavity filled with a porous matrix has been investigated numerically when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Darcy–Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for a range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.2 ⩽ Pr ⩽ 100) in terms of stream functions and isotherm contours, and local and average Nusselt numbers.     

Effect of flow geometry parameters on transient heat transfer for turbulent flow in a circular tube with baffle inserts

The effect of the flow geometry parameters on transient forced convection heat transfer for turbulent flow in a circular tube with baffle inserts has been investigated. The characteristic parameters of the tubes are pitch to tube inlet diameter ratio H/D = 1, 2 and 3, baffle orientation angle β = 45°, 90° and 180°. Air, Prandtl number of which is 0.71, was used as working fluid, while stainless steel was considered as pipe and baffle material. During the experiments, different geometrical parameters such as the baffle spacing H and the baffle orientation angle β were varied. Totally, nine types of baffle inserted tube were used. The general empirical equations of time averaged Nusselt number and time averaged pressure drop were derived as a function of Reynolds number corresponding to the baffle geometry parameters of pitch to diameter ratio H/D, baffle orientation angle β, ratio of smooth to baffled cross-section area S_o/S_a and ratio of tube length to baffle spacing L/H were derived for transient flow conditions. The proposed empirical correlations were considered to be applicable within the range of Reynolds number 3000 ⩽ Re ⩽ 20,000 for the case of constant heat flux.