Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Experimental and numerical study of the natural convection from a heated horizontal cylinder wrapped with a layer of textile material

Natural convection heat transfer enhancement from a horizontal cylinder with a textile coating is studied experimentally and numerically. The coating layer may be used for two purposes. According to the thickness of the coating it may be used as an insulating material or for surface augmentation. In the experimental study, two cylinders having different diameters of 4.8 mm and 9.45 mm are used. The bare cylinders having a radius smaller than a certain critical size were wrapped with a textile material. Wrapped cylinder diameters were increased to 9 and 12.8 mm respectively after coating and constant heat flux was applied to all bare and wrapped cylinders. Experimental study was carried out at different ambient temperatures in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The ambient and cylinder surface temperatures (T_∞ and T_w) varied between 10 °C – 40 °C and 20 °C – 60 °C respectively. Heat transfer rates from bare and wrapped horizontal cylinders were compared and heat transfer enhancement was observed. On the basis of the experimental data average Nusselt numbers were calculated and compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is seen that the results are in good agreement. The problem is also investigated numerically. Experimental and the numerical results fall in ± 30% band.     

Natural convection heat transfer from a horizontal cylinder using holographic interferometry

The natural convection heat transfer from a horizontal cylinder with a uniform wall temperature in an infinite space was experimentally investigated. Infinite fringe interferograms of the cylinder heated from 295.15 to 355.15 K were recorded using the holographic interferometry technique. The temperature field around the cylinder was reconstructed based on phase difference recovery using a MATLAB code. The distributions of the local and average Nusselt numbers over the cylinder were then obtained. A correlation of the average Nusselt number was proposed for a Rayleigh number range of 2.7–6.0 × 10⁴. The experimental results are in good agreement with previous correlations, with a deviation of ±10%. The holographic interferometry technique was found to be satisfactory and reliable for heat transfer analyses.     

Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below

Natural convection in air-filled 2D square enclosure heated with a constant source from below and cooled from above is studied numerically for a variety of thermal boundary conditions at the top and sidewalls. Simulations are performed for two kinds of lengths of the heated source, i.e., a small and a large source corresponding to 20% and 80% of the total length of the bottom wall, respectively. The Rayleigh number varied from 10³ to 10⁷. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface. Comparisons among the different thermal configurations considered are reported.     

Experimental and numerical study of the natural convection from a heated horizontal cylinder

Natural convection heat transfer from a horizontal cylinder is studied experimentally and numerically. Experimental study had taken place in different environmental temperature in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The environmental and cylinder surface temperatures varied between 10 °C–40 °C and 20 °C–60 °C respectively. In the experimental study, two cylinders having different diameters of 4.8 mm–9.45 mm are used and constant heat flux was applied. On the basis of the experimental data, a correlation for the average Nusselt number over the cylinder is proposed in the range of 7.4 10¹ < Ra < 3.4 10³. The proposed correlation is compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is shown that the results are in satisfactory agreement. The problem is also investigated numerically. The experimental data and the numerical results fall in ± 20% band. The numerical results obtained in this study are also compared with the results of Merkin. The characteristics of trend lines are similar.     

Application of artificial neural networks for prediction of natural convection from a heated horizontal cylinder

A generalized neural network analysis for natural convection heat transfer from a horizontal cylinder is developed in this paper. Cylinder diameter, cylinder surface temperature and ambient temperature are selected as the input parameters, while the Nusselt number as the output. A three-layer network is used for predicting the Nusselt number. The number of the neurons in the hidden layer was determined by a trial and error process together with cross-validation of the experimental data evaluating the performance of the network and standard sensitivity analysis. The trained network gives the best values over the correlations with less than 2.5% mean relative error. The experimental data of the average Nusselt number over the horizontal cylinders having different diameters of 4.8 mm–9.45 mm are from Atay?lmaz and Teke [1]. The results from the trained network were compared with the proposed correlation for the average Nusselt number over the cylinder and it is shown that the results are in satisfactory agreement. The Nusselt numbers obtained from the experimental study were seen to be consistent by ± 20% with the well known correlations for natural convection heat transfer from horizontal cylinder developed by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4]. Moreover it is seen that that results from the trained network show absolute agreement with the experimental data in ± 5% deviation band better than the correlations given by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4].     

Correlations for natural convection heat transfer in two-layer fluids with internal heat generation

Two simple semiempirical correlations for an estimate of heat transfer in horizontal layers of superposed immiscible fluids with internal heat sources are suggested. Different boundary conditions are considered. The predicted results are compared with the known experimental correlations. The results are of interest to post-accident heat removal in fast and light water reactors.     

Transient natural convection heat transfer of liquid D-mannitol on a horizontal cylinder

Transient and steady state natural convection heat transfer for D-mannitol on a horizontal cylinder was investigated experimentally at various liquid temperatures and heat input conditions. To clarify the natural convection phenomena of D-mannitol, transient and steady heat transfer coefficients were measured under various liquid temperatures of D-mannitol and periods of heat generation rates from a horizontal platinum cylinder. The platinum cylinder with a diameter of 1 mm and a length of 43.5 mm was used as the test heater in this experiment. Experimental results indicated that the steady heat transfer coefficient of D-mannitol was affected by the liquid temperature. As the liquid temperature increased, it was understood that the effect of liquid temperature weakened. When the period of the heat generation rate was changed, the heat transfer process was divided into natural convection heat transfer and conductive heat transfer. It was considered that the conductive heat transfer was more dominant as the period of the heat generation rate decreased. The empirical correlations of steady and transient heat transfer coefficients for D-mannitol were obtained.     

Free convection heat transfer of non Newtonian nanofluids under constant heat flux condition

Two different kinds of non-Newtonian nanofluids were prepared by dispersion of Al₂O₃ and TiO₂ nanoparticles in a 0.5 wt.% aqueous solution of carboxymethyl cellulose (CMC). Natural convection heat transfer of non-Newtonian nanofluids in a vertical cylinder uniformly heated from below and cooled from top was investigated experimentally. Results show that the heat transfer performance of nanofluids is significantly enhanced at low particle concentrations. Increasing nanoparticle concentration has a contrary effect on the heat transfer of nanofluids, so at concentrations greater than 1 vol.% of nanoparticles the heat transfer coefficient of nanofluids is less than that of the base fluid. Indeed it seems that for both nanofluids there exists an optimum nanoparticle concentration that heat transfer coefficient passes through a maximum. The optimum concentrations of Al₂O₃ and TiO₂ nanofluids are about 0.2 and 0.1 vol.%, respectively. It is also observed that the heat transfer enhancement of TiO₂ nanofluids is higher than that of the Al₂O₃ nanofluids. The effect of enclosure aspect ratio was also investigated. As expected, the heat transfer coefficient of nanofluids as well as the base fluid increases by increasing the aspect ratio.     

Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids

Heat transfer enhancement in horizontal annuli using nanofluids is investigated. Water-based nanofluid containing various volume fractions of Cu, Ag, Al₂O₃ and TiO₂ nanoparticles is used. The addition of the different types and different volume fractions of nanoparticles were found to have adverse effects on heat transfer characteristics. For high values of Rayleigh number and high L/D ratio, nanoparticles with high thermal conductivity cause significant enhancement of heat transfer characteristics. On the other hand, for intermediate values of Rayleigh number, nanoparticles with low thermal conductivity cause a reduction in heat transfer. For Ra = 10³ and Ra = 10⁵ the addition of Al₂O₃ nanoparticles improves heat transfer. However, for Ra = 10⁴, the addition of nanoparticles has a very minor effect on heat transfer characteristics.     

Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration

This work examines the natural convection heat and mass transfer near a sphere with constant wall temperature and concentration in a micropolar fluid. A coordinate transformation is used to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. For micropolar fluids, higher viscosity tends to retard the flow and thus decreases the natural convection heat and mass transfer rates from the sphere with constant wall temperature and concentration. Moreover, the natural convection heat and mass transfer rates from a sphere in Newtonian fluids are higher than those in micropolar fluids.     

Natural convection from narrow horizontal plates at moderate Rayleigh numbers

The present work deals with the natural convection flow and heat transfer from a horizontal plate cooled from above. Experiments are carried out for rectangular plates having aspect ratios between φ=0.036 and 0.43 and Rayleigh numbers in the range 290?Ra_w?3.3×10⁵. These values of Ra_w and φ have been selected below those commonly considered in previous research in view of a future application to the design of printed circuit boards. The plates are made of two different metals, copper and steel. The choice of a metal is relevant to the present problem because the plates are heated by means of an electric current. Important variations of the surface temperature are observed along the transverse direction for the steel plates. The surface of the copper plates is almost isothermal because of the high thermal conductivity of the metal.Calculations for a semi-infinite plate are carried out to predict the transverse profiles of the surface temperature and heat flux and to visualize the structure of the flow. Three-dimensional calculations are also used at a qualitative level to observe the changes in the flow structure due to the finite length of the plate. Present results are compared with both previous experimental work and analyses that are based on boundary layer theory. It is shown that analyses for an infinite boundary layer are not completely applicable to the present problem because of its different physics. The most relevant feature of the natural convection flow, which is not predicted by boundary layer analyses, is a thermal plume rising near the center of the plate.Present heat transfer results differ from previous experimental work because of the lower Rayleigh numbers and aspect ratios investigated here. The Nusselt number is found to depend on Ra_wⁿ, with the exponent n=0.17 being lower than most of the values reported in the literature. This comparatively low value is related to the transverse conduction of heat through the air, which becomes increasingly significant as Ra_w approaches zero. It is shown that such a low-Ra_w effect can be accounted for in a physically consistent manner by adding a constant term to the heat transfer correlation. On the other hand, it is found that the Nusselt number does not significantly depend on the aspect ratio in the range of φ investigated contrary to what has been previously reported for wider plates.     

Exergy transfer characteristics of forced convective heat transfer through a duct with constant wall heat flux

The examination of exergy transfer characteristics caused by forced convective heat transfer through a duct with constant wall heat flux for thermally and hydrodynamic fully developed laminar and turbulent flows has been presented. The exergy transfer Nusselt number is put forward and the dependence relationships of the exergy transfer Nusselt number on the heat transfer Nusselt number, Reynolds number and Prandtl number are obtained. Expressions involving relevant variables for the local and mean convective exergy transfer coefficient, non-dimensional exergy flux and exergy transfer rate, etc. have been derived. By reference to a smooth duct, the numerical results of exergy transfer characteristics for fluids with different Prandtl number are obtained and the effect of the Reynolds number and non-dimensional cross-sectional position on exergy transfer characteristics is analyzed. In addition, the results corresponding to the exergy transfer and energy transfer are compared.     

Experimental and numerical studies of natural convection from horizontal concrete cylinder heated with a cylindrical heat source

Natural convection heat transfer from horizontal concrete cylinder heated with cylindrical heat source was investigated experimentally and numerically. Bare cylinder having a diameter of 9.45 mm was buried in a cylindrical concrete cylinder and thermocouples located outside the copper tube and inside and outside of the concrete cylinder in axial, radial and angular directions. Experiments are conducted at 20 °C and 30 °C ambient temperatures in a conditioned room. Copper cylinder surface temperatures varied between 30–50 °C and 40–50 °C for 20 °C and 30 °C ambient temperatures respectively. In a numerical study, the measured temperatures in the experimental study were used for boundary conditions. Experimental and numerical results were compared and heat transfer enhancement was seen for concrete cylinder. Also the effect of the decrease in the temperature of the copper tube surface was investigated on an ideal Carnot refrigerator. It is found that the enhancement in the coefficient of performance of a Carnot refrigerator is about 35%.     

Bounds on natural convective heat transfer in a porous layer with fixed heat flux

Using the background field variational method, bounds on natural convective heat transfer in a porous layer heated from below with fixed heat flux are derived from the primitive equations. The enhancement of heat transfer beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the non-dimensional forcing scale set by the ‘effective’ Rayleigh number (Rˆ) according to Nu ≤ 0.354Rˆ^1/2 and in terms of the conventional Rayleigh number (Ra) defined by the temperature drop across the layer according to Nu ≤ 0.125Ra. It is presented that fixing the heat flux at the boundaries does not change the linear dependence between Nusselt number and Rayleigh number at high Rayleigh number region.     

Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature

This work studies the natural convection boundary layer flow of a micropolar fluid near a vertical permeable cone with variable wall temperature. The transformed boundary layer governing equations are solved by the cubic spline collocation method. The local Nusselt numbers are presented as functions of suction variables for different values of vortex viscosity parameter, surface temperature exponent, and Prandtl number. Results show that the heat transfer rates of the permeable cones with higher suction variables are higher than those with lower suction variables. Moreover, the heat transfer rate from a vertical permeable cone in Newtonian fluids is higher than that in micropolar fluids.     

Free convection in a non-Newtonian fluid along a horizontal plate embedded in porous media with internal heat generation

Similarity solutions for the problem of free convection flow over a non-isothermal horizontal plate embedded in porous media are investigated in the presence of internal heat generation. The porous medium is saturated with non-Newtonian power law fluid. Numerical results are obtained for the effect of power law temperature profile and fluid index on the heat transfer characteristics.     

Mixed convection boundary layer flow past an isothermal horizontal circular cylinder with temperature-dependent viscosity

The problem of steady laminar mixed convection boundary layer flow past an isothermal horizontal circular cylinder placed in a viscous and incompressible fluid of temperature-dependent viscosity is theoretically considered in this paper. The partial differential equations governing the flow and heat transfer are shown to be non-similar. Full numerical solutions of these governing equations are obtained using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for various values of the Prandtl number Pr, the mixed convection parameter λ and the viscosity/temperature parameter θ_r. The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters.     

Effect of radiation on natural convection flow on a sphere in presence of heat generation

Effect of radiation on natural convection flow around a sphere in presence of heat generation has been investigated. The governing equations are transformed into dimensionless non-similar equations by using a set of suitable transformations and solved numerically by the finite difference method along with Newton's linearization approximation. We have focused our attention on the evaluation of velocity profiles, temperature profiles, shear stress in terms of local skin friction and the rate of heat transfer in terms of local Nusselt number for different values of heat generation parameter, radiation parameter and the Prandlt number and the numerical results have been shown graphically.     

Viscous dissipation effects on parallel plates with constant heat flux boundary conditions

This paper investigates basic analytical expressions for Nusselt number with the effect of viscous dissipation on the heat transfer between infinite fixed parallel plates, where the focus is on hydro-dynamically and thermally fully developed flow of a Newtonian fluid with constant properties, neglecting the axial heat conduction. Thermal boundary conditions considered are: both the plates kept at different constant heat fluxes, both the plates kept at equal constant heat fluxes, and one plate insulated. From the analysis, new expressions for Nusselt numbers have been found, as a function of various definitions of the Brinkman number.