Laminar mixed convection in a channel with a built-in semi-circular cylinder under the effect of cross-buoyancy

Effects of cross-buoyancy mixed convection on flow and heat transfer characteristics of a long semi-circular cylinder (long in neutral direction) in a confined channel have been investigated in the laminar regime. The numerical results have been presented and discussed for the range of conditions as Reynolds number (Re) = 1–40, Richardson number (Ri) = 0–4, Prandtl number (Pr) = 0.71–50 and blockage ratio (β) = 16.67%–50%. The drag coefficient increases with increasing Richardson number and/or blockage ratio. The average Nusselt number is showing a maximum relative enhancement of approximately 45% for Ri = 4 with respect to corresponding forced convection value (Ri = 0). The average Nusselt number increases with increase in Prandtl number and shows a maximum relative enhancement of approximately 1136% for Pr = 50 with respect to corresponding value at Pr = 0.71. On the other hand, the maximum relative variation of the total drag coefficient is found to be approximately 55% for Ri = 4 with respect to corresponding value at Ri = 0. Finally, the simple heat transfer correlation is obtained for the proceeding range of control parameters.     

Large-eddy simulation of combined forced and natural convection in a vertical plane channel

A combined forced and natural convective flow between two vertical plates with different temperatures is studied using large eddy simulation. The numerical simulations were performed with a Grashof number of Gr = 9.6 × 10⁵ and Reynolds number of Re_τ = 150 (based on the wall friction velocity and half channel width). Two sets of dynamic subgrid-scale (SGS) models were tested in the simulation; namely, the set of linear SGS models consisting of the dynamic Smagorinsky SGS stress model (DM) and dynamic eddy diffusivity SGS heat flux model (DEDM-HF), and the set of nonlinear SGS models consisting of the dynamic nonlinear SGS stress model (DNM) and dynamic tensor diffusivity SGS heat flux model (DTDM-HF). The numerical results are compared with the reported direct numerical simulation data. It is found that the resolved and SGS quantities related to the temperature field are noticeably influenced by the choice of SGS models. In general, the set of dynamic nonlinear SGS models yields better prediction of the flow than the set of dynamic linear SGS models.     

Effect of nano-particles on forced convection in sinusoidal-wall channel

In this paper heat transfer and flow field in a wavy channel with nano-fluid is numerically studied. The temperature of input fluid (T_c) is taken less than that of the wavy horizontal walls (T_w). The governing equations are numerically solved in the domain by the control volume approach based on the SIMPLE technique. Copper–water nano-fluid is considered for simulation. A wide spectrum of numerical simulations has been done over a range of Reynolds number, Re_H, 5 ≤ Re_H ≤ 1500, nano-fluid volume fraction, ?, 0 ≤ ? ≤ 20% and the wave amplitude, α, 0 ≤ α ≤ 0.3. The effects of these parameters are investigated on the local and average Nusselt numbers and the skin friction coefficient. Simulations show excellent agreement with the literature. From this study, it is concluded that heat transfer in channels can enhance by addition of nano-particles, and usage of wavy horizontal walls. These can enhance the heat transfer by 50%. The present work can provide helpful guidelines to the manufacturers of the compact heat exchangers.     

Effect of yaw on forced convection heat transfer from a circular cylinder

Wind tunnel experiments encompassing ten angles of yaw between 0 (crossflow) and 60° yielded Nusselt numbers extending over the range of free stream Reynolds numbers from 9000 to 70,000. Supplementary experiments were also performed in which the heating pattern at the surface of the cylinder was varied and in which major alterations were made in the boundary layer on the wind tunnel wall. These experiments established that the measured Nusselt numbers were truly representative of the uniform wall temperature boundary condition and were independent of the characteristics of the wind tunnel boundary layer. It was found that as the cylinder was yawed relative to the crossflow orientation, the Nusselt number at first decreased, attained a minimum at a yaw angle of 15°, and then increased to a broad maximum which occurred in the range of yaw angles between 30 and 45°. Thereafter, the Nusselt number decreased with increasing yaw. Furthermore, the data did not obey the so-called Independence Principle, according to which the Nusselt number is supposed to be a unique function of the Reynolds number based on the component of the free stream velocity normal to the cylinder. As a further supplement to the heat transfer experiments, the pattern of fluid flow adjacent to the cylinder surface was visualized by means of the oil-lampblack technique.     

Heat transfer enhancement in a channel with a built-in square cylinder

A two dimensional numerical investigation of the unsteady laminar flow pattern and forced convective heat transfer in a channel with a built-in square cylinder is presented. The channel in the entrance region has a length to plate spacing of ten. The computations were made for several Reynolds number and two square cylinder sizes. Hydrodynamic behavior and heat transfer results are obtained by solution of the complete Navier-Stokes and energy equation. The results show that these flow exhibits laminar self-sustained oscillations for Reynolds numbers above the critical one. This study shows that oscillatory separated flows result in a significant heat transfer enhancement but also in a significant pressure drop increase.     

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.     

The coupling of conduction with forced convection in a plane duct

In this paper an analytical solution of the energy equation for laminar convection problems in plane ducts, taking into account the coupling with wall conduction, is presented.The solution is obtained by means of an asymptotic representation of the temperature Laplace transform that enables one to apply the stationary phase method. This entrance solution holds for values of the axial abscissa so high as to permit the calculation of the temperature by means of a few terms of the usual expansion in eigenfunctions. The accuracy of the results, for any coupling parameter, is proved by comparison with those obtained by using an expansion in terms of 120 eigenfunctions.     

Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow

An analytical solution is investigated for forced convection heat transfer from a laminar plane wall jet as conjugate case. For Re ? 1, boundary layer theory is used for the investigation. The problem has been solved for two classic cases such as Pr ? 1 and Pr ? 1. The conjugate model consists of considering the full Navier-Stokes equation in the fluid medium and coupling of energy equations in the fluid and the slab through the interface boundary conditions. Closed-form relations are found for Nusselt number (Nu), average Nusselt number and conjugate interface boundary temperature (θ_b). The effects of the Reynolds number (Re), the Prandtl number (Pr), the thermal conductivity ratio (k) between the slab and the fluid medium and the slab aspect ratio (λ) are investigated on the heat transfer characteristics. The analytical results are compared with the full numerical results.     

Buoyancy-aided momentum and heat transfer in a vertical channel with a built-in square cylinder

This study focuses on the confined upward flow and heat transfer around a square cylinder under the effect of aiding buoyancy (Richardson number, Ri=0–1) in the vertical channel for Reynolds number (Re)=1–40 and blockage ratio (BR)=25–50% for the air as working fluid. Flow is found to be steady and symmetric for the range of settings. For Re≤2, no separation zone occurs for BR=25% and 30%. However, for BR=50%, no wakes are observed for Re≤3. The onset of flow separation takes place between Re=2 and 3 for BR=25% and 30%; whereas, for BR=50%, it exists between Re=3 and 4, irrespective of the value of Ri. Heat transfer correlations have also been obtained at different values of Re, BR and Ri.     

Laminar Forced Convection in Curved Channel with Vortex Structures

Theoretical and experimental investigations of heat transfer in flat curvilinear channel have been carried out. Linear and non-linear effects of Dean vortexes on intensity of heat transfer were taken into account. The linear effect, which describe harmonic (sinuous) variation of the heat transfer coefficient near the concave surface of the channel and the non-linear effect causes the general increase of the heat transfer coefficient due to augmentation of heat transfer engendered by the Dean vortexes. For both effects, mathematical relations were obtained in the form of quadratures. These numerical results were modified to the form convenient in engineering calculations. The investigations have shown that both linear and nonlinear components grow up with the Dean number. Nonlinear component Q0T increases more abruptly, while the linear one Q1T is more conservative. This is a confirmation of stability of vortex structures.     

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.     

Laminar forced convection from a rotating horizontal cylinder in cross flow

The influence of non-dimensional rotational velocity, flow Reynolds number and Prandtl number of the fluid on laminar forced convection from a rotating horizontal cylinder subject to constant heat flux boundary condition is numerically investigated. The numerical simulations have been conducted using commercial Computational Fluid Dynamics package CFX available in ANSYS Workbench 14. Results are presented for the non-dimensional rotational velocity α ranging from 0 to 4, flow Reynolds number from 25 to 40 and Prandtl number of the fluid from 0.7 to 5.4. The rotational effects results in reduction in heat transfer compared to heat transfer from stationary heated cylinder due to thickening of boundary layer as consequence of the rotation of the cylinder. Heat transfer rate increases with increase in Prandtl number of the fluid.     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Validation of thermal equilibrium assumption in forced convection steady and pulsatile flows over a cylinder embedded in a porous channel

The validity of the local thermal equilibrium assumption in the forced convection steady and pulsatile flows over a circular cylinder heated at constant temperature and embedded in a horizontal porous channel is investigated. For this purpose, the Darcy–Brinkman–Forchheimer momentum and the local thermal non-equilibrium energy models are solved numerically using a spectral element method. Numerical solutions obtained over broad ranges of representative dimensionless parameters are utilized to present conditions at which the local thermal equilibrium assumption can or cannot be employed. For steady flow, the circumstances of a higher Reynolds number, a higher Prandtl number, a lower Darcy number, a lower microscopic and macroscopic frictional flow resistance coefficient, a lower Biot number, a lower solid-to-fluid thermal conductivity ratio, a lower cylinder-to-particle diameter ratio and a lower porosity, are identified as unfavorable circumstances for the local thermal equilibrium LTE condition to hold. For oscillatory flow, the degree of non-equilibrium can be decreased as pulsating amplitude increases or pulsating frequency decreases; however, such flows do not have a significant influence on satisfying the LTE.     

Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder

Forced convection heat transfer characteristics of a cylinder (maintained at a constant temperature) immersed in a streaming power-law fluids have been studied numerically in the two-dimensional (2-D), unsteady flow regime. The governing equations, namely, continuity, momentum and thermal energy, have been solved using a finite volume method based solver (FLUENT 6.3) over wide ranges of conditions (power law index, 0.4 ? n ? 1.8; Reynolds number, 40 ? Re ? 140; Prandtl number, 1 ? Pr ? 100). In particular, extensive numerical results elucidating the influence of Reynolds number, Prandtl number and power-law index on the isotherm patterns, local and average Nusselt numbers and their evolution with time are discussed in detail. Over the ranges of conditions considered herein, the nature of flow is fully periodic in time. The heat transfer characteristics are seen to be influenced in an intricate manner by the value of the Reynolds number (Re), Prandtl number (Pr) and the power-law index (n). Depending upon the value of the power-law index (n), though the flow transits from being steady to unsteady somewhere in the range ～33 < Re < 50, the fully periodic behavior is seen only beyond the critical value of the Reynolds number (Re). As expected, the average Nusselt number increases with an increase in the values of Reynolds and/or Prandtl numbers, irrespective of the value of the flow behavior index. A strong influence of the power-law index on both local and time-averaged Nusselt numbers was observed. Broadly, all else being equal, shear-thinning behavior (n < 1) promotes heat transfer whereas shear-thickening behavior (n > 1) impedes it. Furthermore, this effect is much more pronounced in shear-thinning fluids than that in shear-thickening fluids.     

Bifurcated three-dimensional forced convection in plane symmetric sudden expansion

Simulations of bifurcated three-dimensional laminar forced convection in horizontal duct with plane symmetric sudden expansion are presented to illustrate the effects of flow bifurcations on temperature and heat transfer distributions. The stable bifurcated flow that develops in this symmetric geometry leads to non-symmetric temperature and heat transfer distributions in the transverse direction, but symmetric distributions with respect to the center width of the duct in the spanwise directions for the Reynolds number of 400-800. A strong downwash develops at the corner of the step and a smaller reverse flow region develops adjacent to the lower stepped wall than the one that develops adjacent to the upper stepped wall. The downwash and the “jet-like” flow that develop near the sidewall create a strong swirling spanwise flow in the primary recirculating flow regions downstream from the sudden expansion. The magnitude of maximum Nusselt number that develops on the lower stepped walls is higher than the one that develops on the upper stepped wall. The locations of these maximum Nusselt numbers on the stepped walls are near the sidewalls and are upstream of the “jet-like” flow impingement regions. Results reveal that the locations where the streamwise component of wall shear stress is zero on the stepped walls do not coincide with the outer edge of the recirculation flow region near the sidewalls. Velocity, temperature, Nusselt number, and friction coefficient distributions are presented.     

Effects of a porous medium on forced convection of a reciprocating curved channel

Enhancement of heat transfer rates of a reciprocating curved channel partially installed by a porous medium is investigated numerically. The distribution of heat transfer rates on the heat surface of the reciprocating curved channel is rather non-uniform that easily causes a thermal damage to destroy the channel. A method of using the porous medium to enhance heat transfer rates of the channel is then developed to solve the thermal damage. The arbitrary Lagrangian–Eulerian method is firstly modified for treating a moving boundary problem of the porous medium. Main parameters of Reynolds numbers, porosities, frequencies and amplitudes are examined. The results show that the enhancements of heat transfer rates of most porous medium situations are achieved. However, heat transfer rates of a few porous medium situations are unexpectedly inferior to those of without porous medium situations.     

Confined flow and heat transfer across a triangular cylinder in a channel

In this paper, fluid flow and heat transfer across a long equilateral triangular cylinder placed in a horizontal channel is studied for Reynolds number range 1–80 (in the steps of 5) and Prandtl number of 0.71 for a fixed blockage ratio of 0.25. The governing Navier-Stokes and energy equations along with appropriate boundary conditions are solved by using a commercial CFD solver FLUENT (6.3). The computational grid is created in a commercial grid generator GAMBIT. The flow and temperature fields are presented by stream-line and isotherm profiles, respectively. The wake/recirculation length, mean drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions studied here. The critical value of the Reynolds number (i.e., transition to transient) is found to lie between Re = 58 and Re = 59. The average Nusselt number and the wake length increase with increasing value of the Reynolds number; however, the mean drag coefficient decreases with increasing value of the Reynolds number. Finally, simple correlations for wake length, mean drag coefficient and average Nusselt number are obtained for the range of conditions studied here.     

Mass-transfer to a channel wall downstream of a cylinder

The electrochemical method is used to measure the mass-transfer to a channel wall downstream of a cylinder. For Reynolds numbers based on cylinder diameter Re > 50, the flow is unsteady, and the mass-transfer rate is a function of time. When 50 < Re < 200, the mass-transfer rate is periodic with a frequency in the range of 1–3 Hz. When the ratio of cylinder diameter d to channel height h is 0.25, the Strouhal number is measured to be 0.27±0.02, and when d/h = 0.51, the Strouhal number is 0.49±0.01. The average mass-transfer rate at various positions downstream of the cylinder is reported. Experiments are compared to two-dimensional numerical simulations. The simulated and experimental variations of Nusselt number with position and Re contain similar features, but exact agreement is not found.