Numerical studies of simultaneously developing laminar flow and heat transfer in microtubes with thick wall and constant outside wall temperature

The effects of wall axial heat conduction in a conjugate heat transfer problem in simultaneously developing laminar flow and heat transfer in straight thick wall of circular tube with constant outside wall temperature are numerically investigated. The results show that the heat transfer process is most sensitive to wall-to-fluid conductivity ratio k_sf, and when k_sf ? 25 the increasing tube thickness and the decreasing k_sf could make the inner wall surface approaching the uniform heat flux condition. It turns out that the basic function of the wall axial heat conduction for the cases studied is to unify the inner wall surface heat flux.     

Use of porous baffles to enhance heat transfer in a rectangular channel

An experimental investigation was carried out to measure module average heat transfer coefficients in uniformly heated rectangular channel with wall mounted porous baffles. Baffles were mounted alternatively on top and bottom of the walls. Heat transfer coefficients and pressure loss for periodically fully developed flow and heat transfer were obtained for different types of porous medium (10, 20, and 40 pores per inch (PPI)) with two window cut ratios (B_h/D_h=1/3 and 2/3) and two baffle thickness to channel hydraulic diameter ratios (B_t/D_h=1/3 and 1/12). Reynolds number (Re) was varied from 20,000 to 50,000. To compare the effect of foam metal baffle, the data for conventional solid-type baffle were obtained for (B_t/D_h=1/3). The maximum uncertainties associated with module Nusselt number and friction factor were 5.8% and 4.3% respectively. The experimental procedure was validated by comparing the data for the straight channel with no baffles (B_h/D_h=0) with those in the literature [Publications in Engineering, vol. 2, University of California, Berkeley, 1930, p. 443; Int. Chem. Eng. 16 (1976) 359]. The use of porous baffles resulted in heat transfer enhancement as high as 300% compared to heat transfer in straight channel with no baffles. However, the heat transfer enhancement per unit increase in pumping power was less than one for the range of parameters studied in this work. Correlation equations were developed for heat transfer enhancement ratio and heat transfer enhancement per unit increase in pumping power in terms of Reynolds number.     

Analysis on the heat transfer in a square cavity with a semitransparent wall: Effect of the roof materials

A theoretical study on conjugated heat transfer (natural convection, radiation and conduction) in a square cavity with turbulent flow is presented. The cavity is a representation of a room, where the left wall is isothermal, the right wall is semitransparent (glass), the lower wall is considered as insulated and on the upper opaque wall heat conduction is present. Both conductive walls (opaque and semitransparent) interact with the ambient. The semitransparent wall is subject to a constant heat flux (G₂ = 736 W/m²) whereas on the opaque wall a constant heat flux (G₁ = 875 W/m²) falls perpendicularly. The sizes of the cavity under study were 5.0, 4.0, 3.0 and 2.0 m. The upper opaque wall was considered as a mixture of concrete and a composite material (concrete–expanded polystyrene) with different thicknesses and diverse types of water-repellent coatings on top of it. From the results, it was found that the white coating on top of the opaque wall significantly reduces the amount of energy towards the inside of the cavity. It was also determined that the opaque wall with a 20 cm thickness shows the best thermal performance and it is the most adequate to reduce thermal gains inside the cavity. Correlations for the total heat transfer as a function of the cavity size, the type of coating and material of the opaque upper wall are proposed.     

Numerical study on coupled fluid flow and heat transfer process in parabolic trough solar collector tube

A unified two-dimensional numerical model was developed for the coupled heat transfer process in parabolic solar collector tube, which includes nature convection, forced convection, heat conduction and fluid-solid conjugate problem. The effects of Rayleigh number (Ra), tube diameter ratio and thermal conductivity of the tube wall on the heat transfer and fluid flow performance were numerically analyzed. The distributions of flow field, temperature field, local Nu and local temperature gradient were examined. The results show that when Ra is larger than 10⁵, the effects of nature convection must be taken into account. With the increase of tube diameter ratio, the Nusselt number in inner tube (Nu₁) increases and the Nusselt number in annuli space (Nu₂) decreases. With the increase of tube wall thermal conductivity, Nu₁ decreases and Nu₂ increases. When thermal conductivity is larger than 200 W/(m K), it would have little effects on Nu and average temperatures. Due to the effect of the nature convection, along the circumferential direction (from top to down), the temperature in the cross-section decreases and the temperature gradient on inner tube surface increases at first. Then, the temperature and temperature gradients would present a converse variation at θ near π. The local Nu on inner tube outer surface increases along circumferential direction until it reaches a maximum value then it decreases again.     

Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli

Forced and free convective heat transfer for thermally developing and thermally fully developed laminar air flow inside horizontal concentric annuli in the thermal entrance length has been experimentally investigated. The experimental setup consists of a stainless steel annulus having a radius ratio of 2 and an inner tube with a heated length of 900 mm subjected to a constant wall heat flux boundary condition and an adiabatic outer annulus. The investigation covers Reynolds number range from 200 to 1000, the Grashof number was ranged from 6.2 × 10⁵ to 1.2 × 10⁷. The entrance sections used were long tube with length of 2520 mm (L/D_h = 63) and short tube with length of 504 mm (L/D_h = 12.6). The surface temperature distribution along the inner tube surface, and the local Nusselt number distribution versus dimensionless axial distance Z_t were presented and discussed. It is inferred that the free convection effects tended to decrease the heat transfer at low Re number while to increase the heat transfer for high Re number. This investigation reveals that the Nusselt number values were considerably greater than the corresponding values for fully developed combined convection over a significant portion of the annulus. The average heat transfer results were correlated in terms of the relevant dimensionless variables with an empirical correlation. The local Nusselt number results were compared with available literature and show similar trend and satisfactory agreement.     

Conjugate-mixed convection heat transfer in a lid-driven enclosure with thick bottom wall

Conjugate heat transfer by mixed convection and conduction in lid-driven enclosures with thick bottom wall has been studied by a numerical method. The enclosure is heated from the bottom wall isothermally. Temperature of the top moving wall, which has constant flow speed, is lower than that of the outside of bottom wall. Vertical walls of the enclosure are adiabatic. Governing parameters are solved for a wide range of Richardson numbers (0.1 ≤ Ri ≤ 10), ratio of height of bottom wall to enclosure height (0.1 ≤ h/H ≤ 0.5) and thermal conductivity ratio (0.01 ≤ λ_f/λ_s ≤ 10). Obtained results showed that heat transfer decreases with increasing of λ_f/λ_s ratio, Richardson number and thickness ratio of the wall. Flow strength is affected for only higher values of λ_f/λ_s ratio.     

Heat transfer characteristics of two-phase He I (4.2 K) thermosiphon flow

In the framework of the cryogenic cooling system design of a large superconducting magnet under construction at CERN-Geneva, heat transfer in two-phase He I natural circulation loop has been investigated experimentally. The experiments were conducted on a 2 m thermosiphon loop with copper tube of 10 mm inner diameter uniformly heated over a length of 0.95 m. All data were obtained near atmospheric pressure. Evolution of the exit vapour quality and wall superheat as a function of heat flux are presented and analyzed. A comparison between the two-phase heat transfer coefficient h_TP determined in our study and the most relevant correlations available in literature is made. Further, we predict h_TP with a correlation based on the combining effects of forced convection and nucleate boiling by a power-type asymptotic model. Finally, we present the boiling crisis study and we propose a critical heat flux correlation as a function of channel height to diameter ratio (z/D) to model our experimental results.     

Effects of buoyancy and conjugate heat transfer on non-Darcy mixed convection about a vertical slender hollow cylinder embedded in a porous medium with high porosity

This study investigates mixed convection heat transfer about a vertical slender hollow cylinder in the buoyancy and conjugate heat transfer effects in the porous medium with high porosity. The non-similar solutions using the Keller box method are obtained. The wall conduction parameter p, the porous medium parameter k₁, the Forchheimer parameter F∗ and the Richardson number are the main parameters. For various values of these parameters the local skin friction and local heat transfer parameters are determined. The validity of the methodology is checked by comparing the results with those available in the open literature and a fairly good agreement is observed. Finally, it is determined that the local skin friction and the local heat transfer coefficients increase with an increase buoyancy parameter Ri, porous medium parameter k₁, Forchheimer parameter F∗ and decrease with conjugate heat transfer parameter p.     

Hybrid formulation and solution for transient conjugated conduction–external convection

This work presents a hybrid numerical–analytical solution for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the fluid–solid interface. This conjugated conduction–convection problem is first reformulated through the employment of the coupled integral equations approach (CIEA) to simplify the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, an improved lumped partial differential formulation for the transversally averaged wall temperature is obtained, while a third kind boundary condition is achieved for the fluid from the heat balance at the solid–fluid interface. From the available steady velocity distributions, a hybrid numerical–analytical solution based on the generalized integral transform technique (GITT), under its partial transformation mode, is then proposed, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve. The interface heat flux partitions and heat transfer coefficients are readily determined from the wall temperature distributions, as well as the temperature values at any desired point within the fluid. A few test cases for different materials and wall thicknesses are defined to allow for a physical interpretation of the wall participation effect in contrast with the simplified model without conjugation.     

Heat transfer and bubble characteristics in a fluidized bed with immersed horizontal tube bundle

The effect of gas velocity on the average and local heat transfer coefficients between a submerged horizontal tube (25.4 mm-OD) and a fluidized bed has been determined in a fluidized-bed-heat-exchanger (0.34×0.50×0.6 m-high) of silica sand particles. The heat transfer coefficients and the properties of bubble and emulsion phases were simultaneously measured at the same location around the tube circumference by thermocouples and an optical probe. The average heat transfer coefficient (h_avg) exhibits a maximum value with variation of gas velocity (U_g). The local heat transfer coefficient (h_i) exhibits maximum values at the side of the tube (0°). Bubble frequency (f_b) increases and the emulsion contacting time (t_e) decreases with increasing U_g. The h_i increases with increasing f_b and decreasing t_e. The f_b exhibits higher values and t_e is shorter at the bottom (under each side) than those at the top section of the tube. The t_e and bubble fraction (δ_b) have been correlated with Froude number. The predicted h_avg values of small particles based on the packet renewal model and the emulsion contacting characteristics around the tube well accord to the experimental data.     

A unified heat transfer model in a pressurized volumetric solar receivers

In the present work, we developed an overall mathematical model adequately describing the main heat transfer processes in a pressurized volumetric receiver. The key components, a windowed cavity, incorporating with the irradiated surface of the absorber, were theoretically modeled as a closed diffuse-gray surfaces system. Accordingly, a boundary condition for the absorber concerning its porous structure surface was developed using net radiation method (NRM) under local thermal non-equilibrium (LTNE) condition. The same method is also applied to the back cavity. Then a modified P1 approximation with collimated irradiation was introduced to incorporate the radiation transfer penetrating in the absorber. The major characteristic of the heat transfer behavior combining radiation, thermal conduction, and convection in the windowed cavity, absorber and the back cavity, are detailedly presented. Also, the key design parameters, such as those relating to pore structure (φ and d_p), the volumetric heat transfer coefficient h_v, the emissivity ε for window and absorber, and their thickness L_a and L_g were systematically analyzed. Optimization design can be carried out for both of the solar thermal system and the receiver itself in the future work based on our model.     

Visualization of heat flow due to natural convection within triangular cavities using Bejan’s heatline concept

Natural convection and flow circulation within a cavity has received significant attention in recent times. The wide range of applicability of flow inside a cavity (food processing industries, molten metal industries, etc.) requires thorough understanding for cost efficient processes. This paper is based on comprehensive analysis of heat flow pattern using Bejan’s heatline concept. The key parameters for our study are the Prandtl number, Rayleigh number and Nusselt number. The values of Prandtl number (0.015, 0.026, 0.7 and 1000) have been chosen based on wide range of applicability. The Rayleigh number has been varied from 10² to 10⁵. Interesting results were obtained. For low Rayleigh number, it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction. But as Ra increases, flow slowly becomes convection dominant. It is also observed that multiple secondary circulations are formed for fluids with low Pr whereas these features are absent in higher Pr fluids. Multiple circulation cells for smaller Pr also correspond multiple cells of heatlines which illustrate less thermal transport from hot wall. On the other hand, the dense heatlines at bottom wall display enhanced heat transport for larger Pr. Further, local heat transfer (Nu_l, Nu_t) are explained based on heatlines. The comprehensive analysis is concluded with the average Nusselt number plots. A correlation for average heat transfer rate and Ra has been developed and the range of Rayleigh number is also found, to depict the conduction dominant heat transfer.     

Effects of fin geometry on boiling heat transfer from silicon chips with micro-pin-fins immersed in FC-72

Experiments were performed to study the effects of the height and thickness of square micro-pin-fin on boiling heat transfer from silicon chips immersed in a pool of degassed or gas-dissolved FC-72. Six kinds of micro-pin-fins with the dimensions of 30 × 60, 30 × 120, 30 × 200, 50 × 60, 50 × 200 and 50 × 270 μm² (thickness, t × height, h) were fabricated on the surface of a square silicon chip with the dimensions of 10 × 10 × 0.5 mm³ by using the dry etching technique. The fin pitch was twice the fin thickness. The experiments were conducted at the liquid subcooling, ΔT_sub, of 0, 3, 25 and 45 K under the atmospheric condition. The results were compared with previous results for a smooth chip and three chips with enhanced heat transfer surfaces. The micro-pin-finned chips showed a considerable heat transfer enhancement in the nucleate boiling region and increase in the critical heat flux, q_CHF, as compared to the smooth chip. The wall temperature at the CHF point was always less than the maximum allowable temperature for LSI chips (=85 °C). For a fixed value of t, q_CHF increased monotonically with increasing h. The increase was more significant for larger t. The q_CHF increased almost linearly with increasing ΔT_sub. The maximum value of allowable heat flux (=84.5 W/cm²), 4.2 times as large as that for the smooth chip, was obtained by the chip with h=270 μm and t=50 μm at ΔT_sub=45 K.     

An exact heat transfer analysis of spherical products subjected to forced-air cooling

The thermal analysis of forced-air cooling processes being of primary concern, an experimental and analytical study program was undertaken to investigate the heat transfer during the cooling of figs as spherical food products. The process conditions were analysed according to a mathematical model to gain a better understanding of the product's behaviour. The heat transfer between the product and air was influenced by conduction inside the product, convection outside the product, radiation, respiratory heat rate (internal heat generation), and moisture evaporation at the surface of the product. These situations were considered as three cases, such as h = h_c, h = h_c + h_c, and h = h_c, + h_r + h_e. The four various air velocities of 1.1, 1.5, 1.75, and 2.5 m/s were applied in the experimental study. The results obtained by the mathematical model in the estimation of the heat transfer rates from the products were compared with the experimental data, and the best agreement was found for the third case (h = h_c + h_r + h_e). The fastest cooling was accomplished with the highest airflow velocity.     

Unsteady forced convection heat transfer on a flat plate embedded in the fluid-saturated porous medium with inertia effect and thermal dispersion

For an unsteady forced convection on a flat plate embedded in the fluid-saturated porous medium with inertia effect and thermal dispersion, this paper presents a precise and rigorous method to obtain the entire solutions from one-dimensional transient conduction (ξ=0) to steady forced convection in porous medium (ξ=1) under conditions of uniform wall temperature and uniform heat flux, respectively. It is worth noted that the rate of unsteady heat transfer can be accelerated by the thermal dispersion, which may be regarded as the effect of mixing or agitating, to enhance the heat transfer in porous medium. Additionally, it is found that the time response, from the transient heat conduction to a steady forced convection in Darcy's flow, is τ=1, and is independent of wall heating condition and thermal dispersion strength (φ).     

An experimental study on convection heat transfer from an array of discrete heat sources

Convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally for air. The lower surface of the channel was equipped with 8×4 flush-mounted heat sources subjected to uniform heat flux; the sidewalls and the upper wall were insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR=2, Reynolds numbers 864≤Re_Dh≤7955, and modified Grashof numbers Gr*=1.72×10⁸ to 2.76×10⁹. From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit.     

Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure

Laminar conjugate conduction-natural convection heat transfer in a 3-D inclined cubic enclosure comprised of finite thickness conductive walls and central cavity is numerically investigated. The dimensionless governing equations describing the convective flow and wall heat conduction are solved by the high accuracy multidomain pseudospectral method. Computations are performed for different Rayleigh numbers (10³ ≤ Ra* ≤ 10⁶), thermal conductivity ratios (1 ≤ k ≤ 100), dimensionless wall thickness (0 ≤ s ≤ 0.25), and enclosure inclinations (?30° ≤ α ₁ ≤ 30°, 0° ≤ α ₂ ≤ 45°). The effects of the above controlling parameters on the heat transfer performances of the enclosure system are investigated in detail, with emphases on the variations of wall conduction and fluid convection heat transfer, and the interactive heat transfer conditions between solid walls and fluid in the central cavity. Numerical results reveal that the existence of enclosure walls reduces the temperature gradient across the cavity and alters the temperature distribution within the solid walls; thus, the fluid convection is complexly determined by the combined effects of k and s, and is greatly affected by enclosure inclinations at high Rayleigh numbers. Moreover, the temperature distributions and solid-fluid interactive heat transfer conditions are provided for further interpretation and demonstration of the effects of the solid walls.     

Buoyancy-induced flow and heat transfer in a porous annulus between concentric horizontal circular and square cylinders

ABSTRACT

This paper reports on natural convection heat transfer in a porous annulus between concentric horizontal circular and square cylinders. The heated inner circular cylinder is maintained at the uniform hot temperature T_h, whereas the cooled outer square duct is held at the uniform cold temperature T_c. A pressure-based collocated finite-volume method is used to numerically investigate the effects on the total heat transfer of Rayleigh number (Ra), Prandtl number (Pr), Darcy number (Da), porosity (?), and annulus aspect ratio (R/L). Results demonstrate that at low Ra values, conduction is the dominant heat transfer mode. Convection contribution to total heat transfer becomes more important beyond a critical Ra value, which decreases with an increase in Da and/or ?. Furthermore, an increase in the enclosure aspect ratio (R/L) leads to an increase in total heat transfer. A similar behavior is obtained with Prandtl number, where predictions indicate higher heat transfer rates at higher Pr values with its effect increasing as Ra increases. Streamlines and isotherms reveal flow separation for some of the reported cases. Limited computations are also performed for natural convection in a porous annulus between two horizontal concentric circular cylinders having the same inner and outer perimeters as the investigated enclosure. Comparison of the predicted average Nusselt number estimates with similar ones obtained in the original enclosure reveals a large percentage difference in values, demonstrating the strong influence of geometry on natural convection in enclosures.     

Experimental estimation of the transient free convection heat transfer coefficient on a vertical flat plate in air

Transient heat convection on a vertical plate has been interpreted both theoretically and experimentally, in terms of a variable heat transfer coefficient, by several authors. Few results concern the case were air is the fluid. Joule heating of a very thin vertical graphite foil has been tested experimentally here. Two different methods of inversion have been studied for estimating the local or global transfer coefficient, starting from infrared camera measurements. The second method has been able to provide the convective contribution to the measured global transfer coefficient. Experimental results with different levels of heating show that the early transfer coefficient decrease proportionally (in time t) to t⁻¹, and not to t^−1/2 as the early times conduction theory would anticipate. Other effects than those already presented in the literature remain to be investigated, in order to explain the discrepancy of this theory for air.Relaxation experiments show that enhancement of the wall/air exchange by a mastering of the transient heating of the whole wall seems to be quite difficult to obtain     

Combined mixed convection and radiation heat transfer in rectangular ducts rotating about a parallel axis

The study of combined heat transfer of convection and radiation in rectangular ducts rotating in a parallel mode was investigated numerically in detail. The coupled momentum and energy equations are solved by the DuFort–Frankel numerical scheme to examine the interactions of convection with radiation. The integro-differential radiative transfer equation is solved by the discrete ordinates method. Results are presented over a wide range of the governing parameters. The present results reveal that the rotational effect in a square duct is more significant than that in a rectangular one. The predictions also demonstrate that the radiation presents significant effects on the axial distributions of the total Nusselt number, Nu_t, and tends to reduce the centrifugal-buoyancy effects. The effect of rotation on the Nu_t is restricted in the entrance region, however, the radiation affects the heat transfer through out the channel. Additionally, the Nu_t increases with the decrease in the conduction-to-radiation parameter N_C.