The development of laminar natural-convective flow in a vertical uniform heat flux duct

An account of a theoretical and experimental study of laminar natural-convective flow in heated vertical ducts is presented. The ducts are open-ended and circular in cross-section and their internal surfaces dissipate heat uniformly.

Temperature and velocity fields and the relationship between Nusselt and Rayleigh numbers were obtained by solving the governing equations by a step-by-step numerical technique. Two Rayleigh numbers are introduced, one expressed in terms of the uniform heat flux and the other in terms of the mean wall temperature. The influence that the Prandtl number has on the relationship between the Nusselt and Rayleigh numbers is discussed. Three inlet conditions were examined; they all gave the same Nusselt relationship at small Rayleigh numbers and the differences between the Nusselt relationships obtained at large Rayleigh numbers were only small.

Experimentally determined Nusselt numbers, with air as the convected fluid, agreed satisfactorily with the theoretical relationship.     

On oscillatory Marangoni convection in a rotating fluid layer subject to a uniform heat flux from below

Linear stability theory is applied to the problem of Marangoni convection in a rotating horizontal fluid layer subject to a uniform heat flux from below. The fluid layer is bounded from below by a rigid boundary and above by a deformable free surface. We show how the P_r–T_a parameter space is divided into regions in which steady or oscillatory convection is preferred.     

Combined forced and free convection for laminar flow in horizontal tubes with uniform heat flux

This study considers the effects of free convection on laminar flow of water in horizontal circular tubes having essentially constant heat flux at the tube wall. A visual and quantitative study was performed utilizing electrically heated glass tubing. These data were combined with other data and correlations to obtain a general picture of the influence of free convection on the Nusselt number. The final correlation curves given in Fig. 11 are provisionally recommended for obtaining heat-transfer coefficients in practical situations. With reasonable heating rates, the heat-transfer coefficients can be three to four times the values predicted by traditional constant property solutions.     

Unconfined laminar nanofluid flow and heat transfer around a square cylinder

The momentum and forced convection heat transfer for a laminar and steady free stream flow of nanofluids past an isolated square cylinder have been studied numerically. Different nanofluids consisting of Al₂O₃ and CuO with base fluids of water and a 60:40 (by mass) ethylene glycol and water mixture were selected to evaluate their superiority over conventional fluids. Recent correlations for the thermal conductivity and viscosity of nanofluids, which are functions of particle volumetric concentration as well as temperature, have been employed in this paper. The simulations have been conducted for Pe = 25, 50, 100 and 200, with nanoparticle diameters of 30 and 100 nm and particle volumetric concentrations ranging from 0% to 4%. The results of heat transfer characteristics of nanofluid flow over a square cylinder showed marked improvement comparing with the base fluids. This improvement is more evident in flows with higher Peclet numbers and higher particle volume concentration, while the particle diameter imposes an adverse effect on the heat transfer characteristics. In addition, it was shown that for any given particle diameter there is an optimum value of particle concentration that results in the highest heat transfer coefficient.     

Local non-similarity solution of coupled heat—Mass transfer of a flat plate with uniform heat flux in a laminar parallel flow

The coupled heat and mass transfer problem of gas flow over a UHF flat plate with its wall coated with sublimable substance has been solved by local non-similarity method. Considerations have been given also to the effect of non-saturation of the sublimable substance in the oncoming flow and the normal injection velocity at the surface. Analytical results are given for local Nusselt and Sherwood numbers at the various locations.     

Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder

A numerical investigation was conducted to analyze the unsteady flow field and heat transfer characteristics in a horizontal channel with a built-in heated square cylinder. Hydrodynamic behavior and heat transfer results are obtained by the solution of the complete Navier–Stokes and energy equations using a control volume finite element method (CVFEM) adapted to the staggered grid. The Computation was made for two channel blockage ratios (β=1/4 and 1/8), different Reynolds and Richardson numbers ranging from 62 to 200 and from 0 to 0.1 respectively at Pr=0.71. The flow is found to be unstable when the Richardson number crosses the critical value of 0.13. The results are presented to show the effects of the blockage ratio, the Reynolds and the Richardson numbers on the flow pattern and the heat transfer from the square cylinder. Heat transfer correlation are obtained through forced and mixed convection.     

Analytical Solution of Coupled Laminar Heat-Mass Transfer in a Tube with Uniform Heat Flux

Analytical solution is obtained of coupled laminar heat-mass transfer in a tube with uniform heat flux. This corresponds to the case when a layer of sublimable material is coated on the inner surface of a tube with its outer surface heated by uniform heat flux and this coated material will sublime as gas flows throught the tube.     

Flow and heat transfer across a confined square cylinder in the steady flow regime: Effect of Peclet number

The flow and heat transfer characteristics of an isolated square cylinder in crossflow placed symmetrically in a planar slit have been investigated for the range of conditions as 1 ⩽ Re ⩽ 45, 0.7 ⩽ Pr ⩽ 4000 (Pe ⩽ 4000) and β = 1/8, 1/6 and 1/4. Heat transfer correlations have been obtained in the steady flow regime for the constant temperature and constant heat flux boundary conditions on the solid square cylinder in crossflow. In addition, variation of the local Nusselt number on each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number and blockage ratio on drag coefficient and heat transfer.     

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.     

Heat transfer characteristics of microencapsulated phase change material slurry in laminar flow under constant heat flux

Due to its large apparent specific heat during the phase change period, microencapsulated phase change material slurry (MPCMS) has been suggested as a medium for heat transfer. In this paper, the convective heat transfer characteristics of MPCMS flowing in a circular tube were experimentally and numerically investigated. The enhanced convective heat transfer mechanism of MPCMS, especially in the thermal fully developed range, was analyzed by using the enthalpy model. Three kinds of fluid–pure water, micro-particle slurry and MPCMS were numerically investigated. The results show that in the phase change heat transfer region the Ste number and the Mr number are the most important parameters influencing the Nusselt number fluctuation profile and the dimensionless wall temperature. Re_b, d_p and c also influence the Nusselt number profile and the dimensionless wall temperature, but they are independent of phase change process.     

Heat transfer characteristics of fluid flow in an annulus with an inner rotating cylinder having a labyrinth structure

The convective heat transfer coefficient was experimentally investigated in an annulus with an inner rotating cylinder to estimate the thermal fatigue of the inner and outer cylinders on the rotating machine. The following three conclusions were obtained: (1) Within the range of the experimental conditions, the heat transfer coefficient did not depend on the axial flow rate; rather, it showed a larger dependence on the inner cylinder rotating speed. (2) The heat transfer coefficient at the top of the labyrinth was about three times as large as that at the bottom. (3) An empirical correlation equation considering the gap between the inner and outer cylinders is proposed, which predicts the heat transfer coefficient on the rotating machine within ±30 percent. © 1997 Scripta Technica. Inc. Heat Trans Jpn Res. 25 (2): 103–119, 1996     

Effect of channel-confinement and aiding/opposing buoyancy on the two-dimensional laminar flow and heat transfer across a square cylinder

The effect of channel-confinement of various degree (blockage ratio of 10%, 30% and 50%) on the upward flow and heat transfer characteristics around a heated/cooled square cylinder is studied by considering the effect of aiding/opposing buoyancy at −1 Ri 1, for Re = 100 and Pr = 0.7. With increasing blockage ratio, the minimum heating (critical Ri) required for the suppression of vortex shedding decreases up to a certain blockage ratio (=30%), but thereafter increases. The influence of buoyancy and channel-confinement on the recirculation length, drag and lift coefficient, pumping power, Strouhal number and heat transfer from the cylinder, is also investigated.     

Convective heat transfer for laminar flows in a multi-passage circular pipe subjected to an external uniform heat flux

Convective heat transfer properties of an hydrodynamically and thermally fully-developed flow in a multi-passage circular tube subjected to an external uniform heat flux are analyzed. The significant dimensionless parameters affecting the problem have been determined. The expressions of Nusselt numbers on the inner and the outer wall are obtained. The limiting cases are correlated with the existing values. The representative curves illustrating the variation of Nusselt numbers with the pertinent parameters are plotted.     

Temperature field in flow over a stretching sheet with uniform heat flux

An analysis is made of the temperature distribution in the flow of a viscous incompressible fluid caused by the stretching of a sheet which issues from a slit into the fluid. The velocity of the sheet is proportional to the distance from the slit and the sheet is subject to uniform heat flux. It is shown that temperature at a point decreases with increase in the Prandtl number P. For a given surface heat flux, the temperature of the stretching sheet is also determined for several values of P.     

Non-Newtonian laminar pulsating heat and fluid flow in plane duct

In the present study, laminar pulsating power-law momentum and heat transfer in a uniformly heated plane duct is studied analytically. Assuming that fully developed conditions exist both hydrodynamically and thermally, a perturbation series method is utilized to derive analytical solutions for the momentum and energy balance equations, and the amplitude is prescribed as the perturbation parameter. For varying values of the power-law index ( $n$), representing pseudoplastic, Newtonian, and dilatant fluids, effects of dimensionless amplitude ( $ϵ$) and frequency ( $F$) on periodic and period-averaged friction factor and Nusselt number are obtained. The results obtained for Newtonian fluid are shown to be in good harmony with the corresponding findings in the open literature.     

On oscillatory Marangoni convection in rotating fluid layer with flat free surface subject to uniform heat flux from below

The effect of uniform rotation on the onset of steady and oscillatory surface-tension-driven (Marangoni) convection in a horizontal fluid layer with a flat free upper surface and heated from below with a uniform heat flux is considered theoretically using linear stability theory. The Ta–Pr parameter space, divided into domains in which either steady or oscillatory convection is preferred, is presented.     

Convective heat transfer inside a rotating cylinder with an axial air flow

This article presents an experimental identification technique for the convective heat transfer coefficient inside a rotating cylinder with an axial airflow. The method consists in heating the outer face of the cylinder using infrared lamps, and acquiring the evolution of the external surface temperature versus time using an infrared camera. Heat transfer coefficients are identified via three methods. The first one is based on an inverse model, the second one assumes the wall of the cylinder as a thermally thin wall and the third one is based on an analytical method permitting to obtain the temperature field within the whole cylinder. The experiments were carried out for a rotational speed ranging from 4 to 880 rpm corresponding to rotational Reynolds numbers varying from 1.6×10³ to 4.7×10⁵ and an air flow rate varying from 0 to which corresponds to an axial Reynolds numbers ranging from 0 to 3×10⁴. Correlations connecting the Nusselt number to the axial and rotational Reynolds numbers are also proposed.     

Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is $\overline{\text{Nu}}={\left[\frac{6.25(1+r)}{{\text{Ra}}^{″}\sin ?}+\frac{1.64}{({\text{Ra}}^{″}\sin ?{)}^{2/5}}\right]}^{-1/2}$, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of $30°\le ?\le 90°$, this correlation predicts the available data base for $10\le {\text{Ra}}^{″}\le {10}^5$ and agrees with the analytical solution for $1\le {\text{Ra}}^{″}\le {10}^2$.