Forced convection heat transfer from an elliptical cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated elliptical cylinder in the steady, laminar cross-flow regime has been studied numerically. In particular, the effects of the power-law index (0.2 ? n ? 1.8), Reynolds number (0.01 ? Re ? 40), Prandtl number (1 ? Pr ? 100) and the aspect ratio of the elliptic cylinder (0.2 ? E ? 5) on the average Nusselt number (Nu) have been studied. The average Nusselt number for an elliptic cylinder shows a dependence on the Reynolds and Prandtl numbers and power-law index, which is qualitatively similar to that for a circular cylinder. Thus, heat transfer is facilitated by the shear-thinning tendency of the fluid, while it is generally impeded in shear-thickening fluids. The average Nusselt number values have also been interpreted in terms of the usual Colburn heat transfer factor (j). The functional dependence of the average Nusselt number on the dimensionless parameters (Re, n, Pr, E) has been presented by empirically fitting the numerical results for their easy use in process design calculations.     

Experimental investigation of mixed convection heat transfer in a rectangular channel with discrete heat sources at the top and at the bottom

Mixed convection heat transfer in a top and bottom heated rectangular channel with discrete heat sources has been investigated experimentally for air. The lower and upper surfaces of the channel were equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux. Sidewalls, the lower and upper walls were insulated and adiabatic. The experimental study was made for an aspect ratio of AR = 6, Reynolds numbers 955 ≤ Re_Dh ≤ 2220 and modified Grashof numbers Gr* = 1.7 × 10⁷ to 6.7 × 10⁷. From experimental measurements, surface temperature and Nusselt number distributions of the discrete heat sources were obtained for different Grashof numbers. Furthermore, Nusselt number distributions were calculated for different Reynolds numbers. Results show that surface temperatures increase with increasing Grashof number. The row-averaged Nusselt numbers first decrease with the row number and then, due to the increase in the buoyancy affected secondary flow and the onset of instability, they show an increase towards the exit as a result of heat transfer enhancement.     

Investigation of mixed convection heat transfer in a horizontal channel with discrete heat sources at the top and at the bottom

Mixed convection heat transfer from arrays of discrete heat sources inside a horizontal channel has been investigated experimentally. Each of the lower and upper surfaces of the channel was equipped with 8 × 4 flush mounted heat sources subjected to uniform heat flux. Sidewalls, lower and upper walls are insulated and adiabatic. The experimental parametric study was made for aspect ratios of AR = 2, 4 and 10, at various Reynolds and Grashof numbers. From the experimental measurements, row-average surface temperature and Nusselt number distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these numbers were investigated. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that top and bottom heater surface temperatures increase with increasing Grashof number. The top heater average-surface temperatures for AR = 2 are greater than those of bottom ones. For high values of Grashof numbers where natural convection is the dominant heat transfer regime (Gr¹/Re² ≫ 1), temperatures of top heaters can have much greater values. The variation of the row-average Nusselt numbers for the aspect ratio of AR = 4, show that with the increase in the buoyancy affected secondary flow and the onset of instability, values of Nusselt number level off and even rise as a result of heat transfer enhancement especially for low Reynolds numbers.     

Natural convection effects on heat and mass transfer in a curvilinear triangular cavity

Finite element method is used in this study to analyze the effects of buoyancy ratio and Lewis number on heat and mass transfer in a triangular cavity with zig-zag shaped bottom wall. Buoyancy ratio is defined as the ratio of Grashof number of solutal and thermal. Inclined walls of the cavity have lower temperature and concentration according to zig-zag shaped bottom wall. Enclosed space consists mostly of an absorber plate and two inclined glass covers that form a cavity. Both high temperature and high concentrations are applied to bottom corrugated wall. Computations were done for different values of buoyancy ratio (?10 ? Br ? 10), Lewis number (0.1 ? Le ? 20) and thermal Rayleigh number (10⁴ ? Ra_T ? 10⁶). Streamlines, isotherms, iso-concentration, average Nusselt and Sherwood numbers are obtained. It is found that average Nusselt and Sherwood numbers increase by 89.18% and 101.91% respectively as Br increases from ?10 to 20 at Ra_T = 10⁶. Also, average Nusselt decreases by 16.22% and Sherwood numbers increases by 144.84% as Le increases from 0.1 to 20 at this Rayleigh number.     

Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in unconfined flowing Newtonian fluids have been investigated numerically. The governing equations, namely, continuity, Navier–Stokes and energy, have been solved in the steady flow regime over wide ranges of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr ? 100). Prior to the investigation of drag and heat transfer phenomena, the critical values of the Reynolds number for wake formation (0.55 < Re^c < 0.6) and for the onset of vortex shedding (39.5 < Re_c < 40) have been identified. The corresponding values of the lift coefficient, drag coefficient, and Strouhal number are also presented. After establishing the limit of the steady flow regime, the influence of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr = 0.72, 1, 10, 50 and 100) on the global flow and heat transfer characteristics have been elucidated. Detailed kinematics of the flow is investigated in terms of the streamline and vorticity profiles and the variation of pressure coefficient in the vicinity of the cylinder. The functional dependence of the individual and total drag coefficients on the Reynolds number is explored. The Nusselt number shows an additional dependence on the Prandtl number. In addition, the isotherm profiles, local Nusselt number (Nu_L) and average Nusselt number (Nu) are also presented to analyze the heat transfer characteristic of a semi-circular cylinder in Newtonian media.     

Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media

Numerical simulations have been carried out to investigate the turbulent heat transfer enhancement in the pipe filled with porous media. Two-dimensional axisymmetric numerical simulations using the k–? turbulent model is used to calculate the fluid flow and heat transfer characteristics in a pipe filled with porous media. The parameters studied include the Reynolds number (Re = 5000–15,000), the Darcy number (Da = 10^?1–10^?6), and the porous radius ratio (e = 0.0–1.0). The numerical results show that the flow field can be adjusted and the thickness of boundary layer can be decreased by the inserted porous medium so that the heat transfer can be enhanced in the pipe. The local distributions of the Nusselt number along the flow direction increase with the increase of the Reynolds number and thickness of the porous layer, but increase with the decreasing Darcy number. For a porous radius ratio less than about 0.6, the effect of the Darcy number on the pressure drop is not that significant. The optimum porous radius ratio is around 0.8 for the range of the parameters investigated, which can be used to enhance heat transfer in heat exchangers.     

Experimental investigation of mixed convection heat transfer for thermally developing flow in a horizontal circular cylinder

An experimental investigation is presented on mixed (free and forced) convection to study the local and average heat transfer for hydrodynamically fully developed, thermally developing and thermally fully developed laminar air flow in a horizontal circular cylinder. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L/D = 30), is subjected to a constant wall heat flux boundary condition. The investigation covers Reynolds number range from 400 to 1600, the heat flux varied from 60 W/m² to 400 W/m² and with cylinder inclination angle of θ = 0° (horizontal). The hydrodynamically fully developed condition is achieved by using an aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 180 cm (L/D = 60), another one with length of 240 cm (L/D = 80) and two short calming sections with lengths 60 cm (L/D = 20), 120 cm (L/D = 40). The surface temperature variation along the cylinder surface, the local and average Nusselt number variation with the dimensionless axial distance Z⁺ were presented. For all entrance sections, it was found an increase in the Nusselt number values as the heat flux increases. It was concluded that the free convection effects tended to decrease the heat transfer results at low Re while to increase the heat transfer results for high Re. The combined convection regime could be bounded by a suitable selection of Re number ranges and the heat flux ranges. The obtained Richardson numbers (Ri) range varied approximately from 0.13 to 7.125. The average Nusselt numbers were correlated with the (Rayleigh numbers/Reynolds numbers). The proposed correlation has been compared with available literature and showed satisfactory agreement.     

Non-Newtonian power-law flow and heat transfer across a pair of side-by-side circular cylinders

Flow and heat transfer of non-Newtonian power-law fluids across a pair of identical circular cylinders in side-by-side arrangement are investigated numerically by solving the continuity, momentum and energy equations along with the appropriate boundary conditions. The numerical calculations are performed in an unconfined computational domain for the following range of physical parameters: Reynolds number, Re = 1–40 and power-law index, n = 0.4–1.8 (covering shear-thinning, n < 1; Newtonian, n = 1 and shear-thickening, n > 1 behaviors) for gap ratio, T/D = 1.5–4.0 at a constant Prandtl number of 50. The global characteristics such as drag coefficients and average Nusselt number, etc. are calculated and the representative streamline and isotherm contours are presented for the above range of conditions. It has been found that the individual and overall drag coefficients decrease and the average Nusselt number increases with Reynolds number for all T/D and n considered here. The heat transfer is found higher in shear-thinning fluids than Newtonian fluids and followed by shear-thickening fluids for 1.5 ? T/D ? 4.0 and 1 ? Re ? 40.     

Momentum and heat transfer phenomena of spheroid particles at moderate Reynolds and Prandtl numbers

The momentum and heat transfer phenomena of spheroid particles in an unbounded Newtonian fluid have been numerically investigated by solving governing conservation equations of the mass, the momentum and the energy. The numerical solution methodology has been benchmarked by performing comparisons between present results with those reported in the literature. Further, extensive new results have been obtained to elucidate effects of pertinent dimensionless parameters such as the Reynolds number (Re), the Prandtl number (Pr) and the aspect ratio (e) on the flow and heat transfer behaviour of spheroid particles in the range of parameters: 1 ? Re ? 200; 1 ? Pr ? 1000 and 0.25 ? e ? 2.5. Regardless of the value of the Reynolds number, the total and individual drag coefficients of oblate spheroids (e < 1) are smaller than those of spheres (e = 1) and opposite trend has been observed for prolate spheroids (e > 1). Irrespective of values of Reynolds and Peclet numbers, the average Nusselt number is large for prolate particles as compared to spheres and opposite trend has been observed for the case of oblate particles. Major contribution of this work is the development of simple correlations for the total drag coefficient and the average Nusselt number of unconfined isolated spheroid particles based on present numerical results which can be used in new applications.     

A general correlation for the stagnation point Nusselt number of an axisymmetric impinging synthetic jet

Whereas the heat transfer mechanisms in steady impinging jets are well understood, the available knowledge of heat transfer to impinging synthetic jets remains inconsistent. This paper provides an objective comparison of the stagnation point heat transfer performance of axisymmetric impinging synthetic jets versus established steady jet correlations. Furthermore, a general correlation for the stagnation point Nusselt number is proposed including the effect of all appropriate scaling parameters: Reynolds number (500 ? Re ? 1500), jet-to-surface spacing (2 ? H/D ? 16) and stroke length (2 ? L₀/D ? 40). Based on the ratio of stroke length to jet-to-surface spacing L₀/H, four heat transfer regimes are identified.     

Combined convection heat transfer for thermally developing aiding flow in an inclined circular cylinder with constant heat flux

Experiments have been conducted to study the local and average heat transfer by mixed convection for hydrodynamically fully developed, thermally developing and thermally fully developed laminar air flow in an inclined circular cylinder. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L/D = 30), is subjected to a constant wall heat flux boundary condition. The investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m² to 400 W/m² and cylinder angles of inclination including 30°, 45° and 60°. The hydrodynamically fully developed condition has been achieved by using aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 180 cm (L/D = 60), another one with length of 240 cm (L/D = 80) and two short calming sections with lengths of 60 cm (L/D = 20), 120 cm (L/D = 40). The results present the surface temperature distribution along the cylinder length, the local and average Nusselt number distribution with the dimensionless axial distance Z⁺. For all entrance sections, the results showed an increase in the Nusselt number values as the heat flux increases and as the angle of cylinder inclination moves from θ = 60° inclined cylinder to θ = 0° horizontal cylinder. The mixed convection regime has been bounded by the convenient selection of Re number range and the heat flux range, so that the obtained Richardson numbers (Ri) is varied approximately from 0.13 to 7.125. The average Nusselt numbers have been correlated with the (Rayleigh numbers/Reynolds numbers) in empirical correlations.     

Heat transfer behavior in a rotating aluminum foam heat sink with a circular impinging jet

This work experimentally studied heat transfer associated with an impinging jet onto a rotating heat sink. Air was used as the impinging coolant, and a square Al-foam heat sink was adopted. The variable parameters were the jet Reynolds number (Re), the relative nozzle-to-foam tip distance (C/d), the rotational Reynolds number (Re_r) and the relative side length of the square heat sink (L/d). The effects of Re, C/d, Re_r and L/d on the dimensionless temperature distributions and the average Nusselt number were considered. For a stationary system, the results reveal that the average Nusselt number (Nu₀) with Al-foam was two to three times that without Al-foam. Nu₀ increased with Re. A larger L/d responded to a larger Nu₀ based on the same jet flow rate. The effect of C/d on Nu₀ was negligible herein. For a rotating system, when Re and L/d were small and C/d was large, the average Nusselt number (Nu_Ω) increased considerably with Re_r. Additionally, for Nu_Ω/Nu₀ ? 1.1, the results suggest that rotation was substantial at Re_r/Re ? 1.13 when L/d = 4.615 with C/d = 0–5 and at Re_r/Re ? 1.07 when L/d = 3.0 with C/d = 0–5. For L/d = 2.222, rotation was substantial at Re_r/Re ? 1.44 when C/d = 0 and was always substantial when C/d ? 1.     

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.     

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.     

A porous model for the square pin-fin heat sink situated in a rectangular channel with laminar side-bypass flow

This work illustrates the compact heat sink simulations in forced convection flow with side-bypass effect. Conventionally, the numerical study of the fluid flow and heat transfer in finned heat sinks employs the detailed model that spends a lot of computational time. Therefore, some investigators begin to numerically study such problem by using the compact model (i.e. the porous approach) since the regularly arranged fin array can be set as a porous medium. The computations of the porous approach model will be faster than those of the detailed mode due to the assumption of the volume-averaging technique. This work uses the Brinkman–Forchheimer model for fluid flow and two-equation model for heat transfer. A configuration of in-line square pin-fin heat sink situated in a rectangular channel with fixed height (H = 23.7 mm), various width and two equal-spacing bypass passages beside the heat sink is successfully studied. The pin-fin arrays with various porosities (ε = 0.358–0.750) and numbers of pin-fins (n = 25–81), confined within a square spreader whose side length (L) is 67 mm, are employed. The numerical results suggest that, within the range of present studied parameters (0.358 ? ε ? 0.750, 25 ? n ? 81 and 1 ? W/L ? 5), the pin-fin heat sink with ε = 0.750 and n = 25 is the optimal cooling configuration based on the maximum ratio of Nusselt number to dimensionless pumping power (Nu/(ΔP × Re³)). Besides, based on medium Nu/(ΔP × Re³) value and suitable channel size, W/L = 2–3 is suggested as the better size ratio of channel to heat sink.     

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.     

Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: Mixed convection regime

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions with the limitation of the Darcy model. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Péclet number (1 ? Pe ? 1000), Rayleigh number (10 ? Ra ? 100), half jet width (0.1 ? D ? 1.0), and the distance between the jet and the heated portion (0.1 ? H ? 1.0). It is found that the average Nusselt number increases with increase in either Rayleigh number or jet width for high values of Péclet number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The correlation for Nu_avg in the forced convection regime is suggested. It is shown that mixed convection mode can cause minimum average Nusselt number unfavorably due to counteraction of jet flow against buoyancy driven flow. Hence, careful consideration must be given while designing a system of jet impingement cooling through porous medium.     

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.     

Buoyancy-induced flow and heat transfer in a partially divided square enclosure

The present investigation addressed buoyancy-induced heat transfer in a partially divided square enclosure. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used was ascertained by comparing our results with previously published results. Results were obtained in terms of streamlines, isotherms, and Nusselt number for various geometrical parameters specifying the height, width and position of the heater. The effect of Rayleigh number in the range of 10⁴ ? Ra ? 5 × 10⁷ was highlighted in the proposed work. The results revealed that all the parameters related to the geometrical dimensions of the heater were significant on the flow field, isotherms, and heat transfer. The examined dimensionless geometric dimensions employed along with their respective ranges were: heater width (0.005 ? W ? 0.5), heater height (0.005 ? H ? 0.5), and heater location (0 ? D ? 0.5). The investigation revealed that increased heater height, width, and location has enhanced the heat transfer due to increasing the surface area of the heater.     

Natural convection in a rectangular enclosure containing an oval-shaped heat source and filled with Fe3O4/water nanofluid

This work concerns with the study of natural convection heat transfer in rectangular cavities with an inside oval-shaped heat source filled with Fe₃O₄/water nanofluid. The finite element method is employed to solve the governing equations for this problem. Average Nusselt numbers are presented for a wide range of Rayleigh number (10³ ≤ Ra ≤ 10⁵), volume fraction of nanoparticles (0 ≤ ϕ ≤ 14%), and four different size and shapes of the heat source. Depending on concentration of the nanoparticle, geometry of the heat source, and the value of Rayleigh number different behaviors are monitored for average Nusselt numbers. Configuration of the heat source dictates a significant change on the behavior of the average Nusselt number, while addition of the nanoparticles has a negative effect on the magnitude of Nusselt number for this problem.