Analytical study of heat transfer from circular cylinder in liquid metals

In this study the influence of a thin hydrodynamic boundary layer on the heat transfer from a single circular cylinder in liquid metals having low Prandtl number (0.004–0.03) is investigated under isothermal and isoflux boundary conditions. Two separate analytical heat transfer models, viscous and inviscid, are developed to clarify the discrepancy between previous results. For both models, integral approach of the boundary layer analysis is employed to derive closed form expressions for the calculation of the average heat transfer coefficients. For an inviscid model, the energy equation is solved using potential flow velocity only whereas for a viscous model, a fourth-order velocity profile is used in the hydrodynamic boundary layer and potential flow velocity is used outside the boundary layer. The third-order temperature profile is used inside the thermal boundary layer for both models. It is shown that the inviscid model gives higher heat transfer coefficients whereas viscous flow model gives heat transfer results in a fairly good agreement with the previous experimental/numerical results.     

Experimental study of transient forced convection heat transfer from simulated electronic chips

Experiments are performed to study the single-phase transient forced convection heat transfer on an array of four in-line, flush-mounted simulated electronic chips in a vertical rectangular channel. Water is the coolant media and the flow covers the wide range of laminar flow regime with Reynolds number, based on heat source length, from 800 to 2,625. The heat flux ranges from 1 W/cm² to 7 W/cm². The heat transfer characteristics are studied and correlations are presented. The transient correlation for overall data recommended is Nu= 0.945(Pe ^1/3) Fo^–1/2.     

A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

Natural convection heat transfer from a horizontal ice cylinder

Heat transfer characteristics passing through the maximum density point around a horizontal ice cylinder immersed in water was studied both theoretically and experimentally. For the sake of a precise comparison, the stagnation point Nusselt number was measured and results then compared with those of the numerical computations that were obtained by solving the full Navier-Stokes equations. A fairly good agreement was seen between the theory and the experiment.At about 6°C of water temperature where the stagnation Nusselt number takes its minimum value, the instability of the flow was observed. It was found that two different computer solutions exist, which shows unstable aspects corresponding to the experimental result.     

Transient free convection from an isothermal horizontal circular cylinder

A numerical solution of the unsteady free convection on an isothermal horizontal circular cylinder whose temperature is suddenly increased is presented at large Grashof number. Solutions for simultaneous development of the momentum and thermal boundary-layers are obtained by using the local non-similarity solutions method, together with the difference-differential procedure. The transient approach of velocity and thermal fields to the ultimate steady state and the variations in time of wall shear and heat transfer coefficients were found. The results at the lower stagnation point of the cylinder for Prandtl number Pr=1.0 are seen to improve the previous study of Hermann [1].     

Forced convection heat transfer from an equilateral triangular cylinder at low Reynolds numbers

An unsteady two-dimensional numerical simulation is performed to investigate the forced convection heat transfer for flow past a long heated equilateral triangular cylinder in an unconfined medium for the low Reynolds number laminar regime. The Reynolds number considered in this study ranges from 50 to 250 with three different values of Prandtl number (Pr?=?0.71, 7 and 100). Fictitious confining boundaries are chosen on the lateral sides of the computational domain that makes the blockage ratio β?=?5?% in order to make the problem computationally feasible. An unstructured triangular mesh is used for the computational domain discretization and the simulation is carried out with the commercial CFD solver Fluent. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag coefficient and Nusselt numbers are presented and discussed. The results obtained are in good agreement with the available results in the literature.     

Conjugate forced convection and heat conduction in circular microchannels

The effects of axial heat conduction in the solid walls of microchannels of circular cross-sections are analyzed here. A systematic approach is adopted, with the aim of pointing out the influence of geometrical parameters and of solid wall thermal conductivity on microchannel heat transfer. The reliability of a commonly adopted criterium, based on the so-called axial conduction number, to assess the relevance of axial heat conduction is also discussed. Numerical simulations concern the simultaneously developing laminar flow of a constant property fluid in microchannels of different length, wall thickness and wall material, heated with a uniform heat flux at the outer surface, for different values of the Reynolds number. Moreover, since often in experimental tests the two end sections of the microchannel wall are not perfectly insulated, the effects of heat losses through these sections are also considered. A hybrid finite element procedure, which implies the step-by-step solution of the parabolized momentum equations in the fluid domain, followed by the solution of the energy equation in the entire domain, corresponding to both the solid and the fluid parts, is used for the numerical simulations.     

Analysis of laminar flow forced convection heat transfer in the entrance region of a circular pipe

A numerical solution, for incompressible, steady-state, laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux and constant wall temperature. The development of velocity profile is obtained from Sparrow's entrance region solution. This velocity distribution is used in solving the energy equation numerically to obtain temperature profiles. Variation of the heat transfer coefficient for these two different boundary conditions for the early stages of boundary layer formation on the pipe wall is obtained. Local Nusselt numbers are calculated and the results are compared with those given byUlrichson andSchmitz. The effect of the thermal boundary conditions is studied by comparing the uniform wall heat flux results with uniform wall temperature.     

Turbulent forced convection heat transfer of non-Newtonian nanofluids

Forced convection heat transfer of non-Newtonian nanofluids in a circular tube with constant wall temperature under turbulent flow conditions was investigated experimentally. Three types of nanofluids were prepared by dispersing homogeneously γ-Al₂O₃, TiO₂ and CuO nanoparticles into the base fluid. An aqueous solution of carboxymethyl cellulose (CMC) was used as the base fluid. Nanofluids as well as the base fluid show shear-thinning (pseudoplastic) rheological behavior. Results indicate that the convective heat transfer coefficient of nanofluids is higher than that of the base fluid. The enhancement of the convective heat transfer coefficient increases with an increase in the Peclet number and the nanoparticle concentration. The increase in the convective heat transfer coefficient of nanofluids is greater than the increase that would be observed considering strictly the increase in the effective thermal conductivity of nanofluids. Experimental data were compared to heat transfer coefficients predicted using available correlations for purely viscous non-Newtonian fluids. Results show poor agreement between experimental and predicted values. New correlation was proposed to predict successfully Nusselt numbers of non-Newtonian nanofluids as a function of Reynolds and Prandtl numbers.     

Experimental correlation of forced convection heat transfer from a NACA airfoil

The results of an experimental investigation of the heat transfer coefficients for forced convection from a NACA-63421 airfoil are presented. Wind tunnel measurements of convection coefficients are obtained for air flow temperatures from −30 to 20 °C. The experimental data is correlated with respect to the Nusselt and Reynolds numbers. Conduction within the airfoil balances heat transfer by convection from the airfoil surface in steady-state conditions. Both average and spatial variations of the heat transfer coefficients are non-dimensionalized through modifications of a classical Hilpert correlation for cylinders in crossflow. It is shown that the functional form of the Hilpert correlation can effectively accommodate measured data for the NACA airfoil over a range of Reynolds numbers. An uncertainty analysis is performed to yield a 7.34% measurement uncertainty for experimental data correlated with the Nusselt number.     

Transient forced convection heat transfer in a channel

A numerical analysis is made of incompressible transient turbulent flow heat transfer between two parallel plates when there is a step jump in space along the channel in wall heat flux or wall temperature. The variation of the fluid velocity and effective diffusivity over the channel cross section are accounted for. The fluid is assumed to have a fully-developed turbulent velocity profile throughout the length of the channel. The thermal responses of the system are obtained by solving energy equation for air by a digital computer. The results are presented in graphical forms. The stability of the finite difference solution is studied and condition for the stability of the difference solution is derived. A method is given to obtain velocity distributions from the distribution of turbulent eddy diffusivity of momentum. Variations of Nusselt numbers are obtained as a function of time and space. Steady-state values are also given and compared with the published results.     

Experimental study of steady and transient natural convection heat transfer of mercury

An experimental investigation of transient and steady-state natural convection in a narrow vertical rectangular channel following a step-change in uniform wall-heat-flux is presented. The construction and instrumentation for two test sections are described. These test sections formed a rectangular channel 15.2×2.54×25.4 cm and consisted of: 1) both 15.2×25.4 cm faces heated uniformly by constant radiant heat flux with mercury as the fluid, and 2) the same boundary conditions as 1 but lead was used to thermally model the mercury. Initially the fluid was stagnant and at a uniform temperature. The transient was initiated by suddenly increasing the wall-heat-flux from zero to some constant, preselected value using radiant heating. Temperature-time histories were measured during the transient and steady-state regimes at several locations on the wall and in the fluid. Transient and steady-state heat transfer results are reported. The results show that when the wall-heat-flux on both faces is sufficiently large, the primary mechanism for energy transport in the fluid is molecular conduction. For lower values of imposed heat flux, natural convection, as well as conduction, contributed to the energy transfer.     

Unsteady forced convection heat/mass transfer from a flat plate

Numerical methods are used to investigate the transient, forced convection heat/mass transfer from a finite flat plate to a steady stream of viscous, incompressible fluid. The temperature/concentration inside the plate is considered uniform. The heat/mass balance equations were solved in elliptic cylindrical coordinates by a finite difference implicit ADI method. These solutions span the parameter ranges 10 Re 400 and 0.1 Pr 10. The computations were focused on the influence of the product (aspect ratio) × (volume heat capacity ratio/Henry number) on the heat/mass transfer rate. The occurrence on the plates surface of heat/mass wake phenomena was also studied.     

Analytical and numerical study of natural convection heat transfer in an inclined composite enclosure

Laminar natural convection heat transfer in inclined fluid layers divided by a partition with finite thickness and conductivity is studied analytically and numerically. The governing equations for the fluid layers are solved analytically in the limit of a thin layered system with constant flux boundary conditions. The study covers of the range of Ra from 10³ to 10⁷, from 0° to 180° and the thermal conductivity ratio of partition to fluid ratioK from 10^–2 to 10⁶. The Prandtl number was 0.72 (for air). Results are obtained in terms of an overall Nusselt number as a function of Rayleigh number, angle of inclination of the system, mid layer thickness, and mid layer thermal conductivity. The critical Rayleigh number for the onset of convection in a bottom-heated horizontal system is predicted. The results are compared with the numerical results obtained by solving the complete system of governing equations, using SIMPLER method, as well as with the limiting cases in the literature.     

A numerical and experimental study of natural convective heat transfer from an inclined isothermal square cylinder with an exposed top surface

Natural convective heat transfer from an isothermal inclined cylinder with a square cross-section which have an exposed top surface and is, in general, inclined at an angle to the vertical has been numerically and experimentally studied. The cylinder is mounted on a flat adiabatic base plate, the cylinder being normal to the base plate. The numerical solution has been obtained by solving the dimensionless governing equations subject to the boundary conditions using the commercial cfd solver, FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. Results have only been obtained for Prandtl number of 0.7. Values of inclination angle between 0° and 180° and a wide range of Rayleigh number and the dimensionless cylinder width, W = w/h, have been considered. The effects of Dimensionless widths, Rayleigh numbers, and inclination angles on the mean Nusselt number for the entire cylinder and for the mean Nusselt numbers for the various surfaces that make up the cylinder have been examined. Empirical equations for the heat transfer rates from the entire cylinder have been derived.     

A steady conjugate heat transfer problem with conduction and free convection

Summary A steady conjugate heat transfer problem dealing with conduction in a heat-generating slab and free convection in the surrounding fluid is studied analytically. Free convection is analyzed by a Görtler-type series solution to the boundary-layer equations for non-uniform surface-temperature variations, while conduction is treated by the standard technique of Fourier transforms. Interfacial temperature and heat flux variations from both solutions in series forms are then formally matched to yield algebraic relations for the coefficients in the series. These coefficients can then be simply evaluated in a given problem in terms of three physical parameters. A numerical example is shown.     

Survey of heat transfer correlations in forced convection boiling

A critical survey was conducted of the most relevant correlations of boiling heat transfer for water in forced convection flow. Most of the investigations carried out on partial nucleate boiling and fully developed nucleate boiling have led to the formulation of correlations which cannot cover a wide range of operating conditions, due to the empirical approach considered. A comparative analysis is therefore required in order to define the accuracy of the proposed correlations, on the basis of the experimental data presently available. The survey allows the accuracy of the different calculating procedures to be evaluated. The results obtained also indicate the most reliable heat transfer correlations for the different operating conditions investigated. This survey was developed considering five pressure ranges (up to 180 bar) for both saturation and subcooled boiling conditions.     

Momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel

Unsteady momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel is numerically investigated using FLUENT for the ranges of Reynolds numbers as 10≤Re≤500, of the blockage ratio as 0.1≤β≤0.4, and of the gap ratio as 0.125≤γ≤1 for a constant value of the Prandtl number of 0.744. The transition of the flow from steady to unsteady (characterized by critical Re) is determined as a function of γ and β. The effect of γ on the mean drag and lift coefficients, Strouhal number (St), and Nusselt number (Nu _w ) is studied. Critical Re was found to increase with decreasing γ for all values of β. and St were found to increase with decreasing values of γ for fixed β and Re. The effect of decrease in γ on was found to be negligible for all blockage ratios investigated.