Heat transfer from a pulsed laminar impinging jet

A numerical investigation has been performed to study the effect of flow pulsations on time-averaged Nusselt number under a laminar impinging jet. The parameters considered are as follows: time-averaged jet Reynolds number (100 ≤ Re ≤ 1000), frequency of pulsation (1 ≤ f ≤ 20 Hz), and nozzle-to-target spacing (4 ≤ H/d ≤ 9). The combination of Re = 300, f = 5 Hz and H/d = 9 was found to give the best heat transfer performance. Interestingly, it was found that the onset of separation at the wall jet region of pulsating impinging jet is associated with the point of constant Nusselt number during the oscillation cycle. Downstream of the separation point in the wall jet region, the Nusselt number waveform fluctuates out of phase with the inlet velocity. Within one oscillation, large vortices existing during the minimum velocity state are broken into two smaller vortices when the flow is accelerated to reach the maximum velocity, after which the two vortices merge again when the flow decelerates back to the minimum velocity.     

Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses

Entropy generation due to conjugate natural convection heat transfer and fluid flow has been studied inside an enclosure with bounded by two solid massive walls from vertical sides at different thicknesses. Enclosure is differentially heated from vertical walls and horizontal walls are adiabatic. Governing equations which are written in streamfunction-vorticity form solved by finite difference technique for the governing parameters as Rayleigh number, 10³ ≤ Ra ≤ 10⁶, length ratio of solid walls as ₁ (for left vertical wall) and ₂ (for right vertical wall) and thermal conductivity ratio of solid to fluid (k), 1 ≤ k ≤ 10. Entropy generation contours due to fluid friction and heat transfer irreversibility, isotherms, streamlines, Nusselt numbers and velocity profiles were obtained. It is found that entropy generation increases with increasing of thermal conductivity ratio and thicknesses of the walls. Entropy generation due to heat transfer is more significant than that of fluid flow irreversibility for all values of thickness of the solid vertical walls.     

Turbulent natural convection in a porous square cavity computed with a macroscopic κ–ε model

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic κ–ε turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Computations covered the range 10 < Ra_m < 10⁶ and 10⁻⁷ < Da  < 10⁻¹⁰ and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m and for Ra_m less than a certain critical Rayleigh number, Ra_cr. This convergence of results as Ra_m decreases can be seen as a characterization of the laminarization phenomenon. For Ra_m values less than around 10⁴, both laminar and turbulent flow solutions merge, indicating that such critical value for Ra_m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra_m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.     

Effect of jet-jet spacing on convective heat transfer to confined, impinging arrays of axisymmetric air jets

The effects of jet-jet spacing (X_n/D), low nozzle-plate spacings (H/D = 0.25, 1.0 and 6.0) and spent air exits located between the jet orifices were studied on the magnitude and uniformity of the convective heat transfer coefficients for confined 3 × 3 square arrays of isothermal axisymmetric air jets impinging normally to a heated surface. Local and average Nusselt numbers are presented for Reynolds number range of 3500–20 400. The local Nusselt numbers illustrate the (non)uniformity of the heat transfer and aid in understanding the variations in the average Nusselt number. The jet-jet spacing affects the convective coefficient by varying the influence of the adjacent jet interference and fraction of the impingement surface covered by the wall jet. The addition of spent air exits increased the convective coefficient and influenced the location of the optimum separation distance. In addition, significant enhancement of the uniformity and the convective coefficients was observed at H/D = 0.25 and 1.0 when compared to H/D = 6.0.     

Cooling strategy by mixed convection of a discrete heater at its optimum position in a square cavity with ventilation ports

We studied cooling strategy in a square enclosure with ventilation ports and a discrete heat source at its optimum position. We searched the optimum heater position by maximizing the global conductance at different Rayleigh and Reynolds numbers and considered three different ventilation ports arrangements. We solved the conservation equations of mass, momentum and energy for mixed convection. We found that the heater position is at off center in all cases, its optimum position is insensitive to the variation of Ra and Re; it solely depends on the ventilation ports arrangement. The Nusselt number is dependent on Ri = Ra/Re²: at its low values, Nu is a decreasing function of Ri and at its high values, it is an increasing function of it.     

Heat transfer in inclined rectangular receivers for concentrated solar radiation

We study heat transfer in inclined rectangular cavities, which may be used as receivers of concentrated solar radiation. One of the active walls is subject to concentrated solar radiation and the other is kept at constant temperature. Continuity, momentum and energy equations are solved by finite difference — control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to10¹², the cavity aspect ratio, A = L/H from 0.5 to 2, the inclination angle, from 30 to 90°.We found that the Nusselt number is an increasing function of the Rayleigh number, the aspect ratio and the inclination angle. Based on the computed data a correlation is derived in the form of Nu = f(Ra, A, ).     

Heat transfer enhancement in a tube using circular cross sectional rings separated from wall

A numerical study was undertaken for investigating the heat transfer enhancement in a tube with the circular cross sectional rings. The rings were inserted near the tube wall. Five different spacings between the rings were considered as p = d/2, p = d, p = 3d/2, p = 2d and p = 3d. Uniform heat flux was applied to the external surface of the tube and air was selected as working fluid. Numerical calculations were performed with FLUENT 6.1.22 code, in the range of Reynolds number 4475–43725. The results obtained from a smooth tube were compared with those from the studies in literature in order to validate the numerical method. Consequently, the variation of Nusselt number, friction factor and overall enhancement ratios for the tube with rings were presented and the best overall enhancement of 18% was achieved for Re = 15,600 for which the spacing between the rings is 3d.     

Thermal performance analysis and optimum design parameters of heat exchanger having perforated pin fins

This paper reports the heat transfer enhancement and corresponding pressure drop over a flat surface equipped with circular cross section perforated pin fins in a rectangular channel. The channel had a cross section area of 100–250 mm². The experiments covered the following ranges: Reynolds number 13500–42,000, clearance ratio (C/H) 0, 0.33 and 1 and interfin spacing ratio (S_y/D) 1.208, 1.524, 1.944 and 3.417. Correlation equations were developed for the heat transfer, friction factor and enhancement efficiency. The experimental results showed that the use of circular cross section pin fins may lead to heat transfer enhancement. Enhancement efficiencies varied between 1.4 and 2.6 depending on clearance ratio and interfin spacing ratio. Using a Taguchi experimental design method, optimum design parameters and their levels were investigated. Nusselt number and friction factor were considered as performance parameters. An L₉(3³) orthogonal array was selected as an experimental plan. First of all, each goal was optimized separately. Then, all the goals were optimized together, considering the priority of the goals, and the optimum results were found to be Reynolds number of 42,000, fin height of 50 mm and streamwise distance between fins of 51 mm.     

Chimney effect in a “T” form cavity with heated isothermal blocks: The blocks height effect

In this paper, a numerical study of natural convection from a two dimensional “T” form cavity with rectangular heated blocks is conducted. The blocks are identical, and the domain presents a symmetry with respect to a vertical axis passing through the middle of the opening. The governing equations are solved using a control volume method, and the SIMPLER algorithm for the velocity–pressure coupling is employed. Special emphasis is given to detail the effect of Rayleigh number and block height on the heat transfer and the flow rate generated by the chimney effect. The results are given for the parameters of control as, 10⁴Ra3×10⁶, Pr=0.71, opening diameter (C=l^′/H^′=0.15), blocks gap (D=d^′/H^′=0.5) and blocks height (1/8B=h^′/H^′1/2). These results show that the heat transfer variation with Ra is in the same manner as those met in the case of the vertical smooth or ribbed channels.     

Laminar heat transfer to temperature-dependent Bingham fluids in tubes

This paper presents a theoretical treatment of laminar flow heat transfer in circular tubes for a temperature-dependent non-Newtonian fluid for which the relationship between the shear stress, τ, and the shear rate, ġg, can be described by an equation of the form τ=τ_y + K(T)ġgⁿ where τ_y is a yield stress, n is a constant and K(T) is a function of temperature. This model can therefore cater for both power-law and Bingham plastic behaviour. The two boundary conditions of constant wall temperature and constant wall heat flux are considered for both heating and cooling situations. The computed results are presented by plotting a Nusselt number as a function of the Graetz number with dimensionless groups specifying the temperature dependence effect, the rheological properties and the wall conditions as parameters. This method of presentation is convenient for engineering design purposes. Temperature profiles, velocity profiles and the pressure drop can also be determined.     

Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements

Experimental investigation of heat transfer and friction factor characteristics in a double pipe heat exchanger fitted with regularly spaced twisted tape elements, were studied. The inner and outer diameters of the inner tube are 50.6 and 25.8 mm, respectively and cold and hot water were used as working fluids in shell side and tube side. The twisted tapes were made of the stainless steel strip with thickness of 1 mm and the length of 1500 mm. They were inserted in the test tube section in two different cases: (1) full-length typical twisted tape at different twisted ratios (y = 6.0 and 8.0), and (2) twisted tape with various free space ratios (S = 1.0, 2.0, and 3.0). The results, obtained from the tube with twisted tape insert, were compared with those without twisted tape. The results show that the heat transfer coefficient increased with twist ratio (y). Whereas the increase in the free space ratio (S) would improve both the heat transfer coefficient and friction factor. The results from each case were correlated for Nusselt number and friction factor. Subsequently, the predicted Nusselt number and friction factor from the correlations were plotted to compare with the experimental data. It was found that Nusselt number was within ± 15% and ± 10% for friction factor.     

Apparent thermal conductivity of evacuated SiO2-aerogel tiles under variation of radiative boundary conditions

The apparent thermal conductivity λ of evacuated SiO₂-aerogel tiles was measured with our small guarded hot plate vacuum system LOLA II. In order to study the influence of the boundary emissivity on λ the plates (20 × 20 cm²) were either used with their plasma-sprayed surfaces ( ≈ 0.5) or with low-emissivity aluminum ( ≈ 0.05) foils as covers. The difference in the apparent conductivity already showed at room temperature and rose to about 50% for radiative temperatures T_r = 570 K. An important consequence is that superinsulating SiO₂-aerogel systems should always be provided with low-emissivity boundaries around the aerogel. The calorimetric results for λ are compared with radiative conductivity values derived from spectral i.r. transmission measurements.     

Conjugate natural convection in a fluid-saturated porous enclosure with two solid vertical partitions

Conjugate natural convection in a fluid-saturated square porous enclosure with two solid vertical partitions of finite and equal thickness equispaced from center of enclosure is investigated in this paper. The primary objective is to attenuate the Nusselt number (Nu) and hence the heat transfer rate across a differentially heated enclosure. Darcy's model is considered. Numerical computation is performed using successive accelerated replacement and explicit scheme. Partition ratio, partition length, thermal conductivity ratio, and modified Rayleigh number are the parameters under study. Fluid flow is analyzed by observing transient changes of streamlines and isotherms for partition length 0.3-1, thermal conductivity ratio 0.5-2, partition ratio 0.1-0.3 and modified Rayleigh number 100 and 1000 where partition ratio is the ratio of distance between center of enclosure and either of the partition center to the total length of the enclosure; while Nusselt number is calculated to estimate the heat transfer rate for each configuration. It is found that, employing a solid partition within the enclosure most definitely reduces the Nusselt number. The drop in Nusselt number is more for partition length 0-0.6 after which it does show a drop in Nu but only very subtle. Further, Nu is the least for partition ratio 0.2. Also, Nusselt number is proportional to thermal conductivity ratio which is the ratio of thermal conductivity of solid to porous medium.     

MHD free convection flow along a vertical wavy surface with heat generation or absorption effect

We formulate the problem of free convection from a vertical wavy surface embedded in a uniform porous medium in the presence of an external magnetic field and internal heat generation or absorption effects. Using the appropriate transformations, the boundary layer equations are reduced to non-linear partial differential equations. The transformed boundary layer equations are solved numerically using Runge–Kutta integration scheme with the shooting technique. We have focused our attention on the evaluation of the local Nusselt number Nu_x, dimensionless velocity, f′, and temperature, θ. The governing parameters are the amplitude of the waviness of the surface, a, ranging from 0.0 (flat plate) to 0.3, and the heat generation absorption parameter Q ranging from − 0.25 to 0.25, and magnetic parameter Mn, ranging from 0.0 to 2.0. The effect of all these parameters are discussed and plotted.     

Aspect ratio effect on natural convection in a square enclosure with a sinusoidal active thermal wall using a thermal non-equilibrium model

ABSTRACT

A numerical investigation of the aspect ratio effect on natural convection in a square enclosure is carried out by adopting the local thermal non-equilibrium model. The top and bottom walls of the enclosure are adiabatic, the left vertical wall is partially heated and cooled by the sinusoidal thermal boundary condition, and the right vertical wall is maintained at uniform thermal boundary condition. The results show the value of periodicity parameter increasing. The streamlines vary in different patterns, rotating clockwise and counterclockwise simultaneously when N > 1, and the number of clockwise and counterclockwise rotating cells increases with the increase of N and equals the value of N. The sinusoidal local Nusselt number profiles are observed and the wave amplitude of local Nusselt number decreases with the increase of aspect ratio, and the absolute values of average Nusselt number at left wall of porous cavity reach maximum when Ar = 1. The absolute value of solid-to-fluid temperature differences decreases as the inter-phase heat transfer coefficient (H) increases and it increases as the value of aspect ratio increases. The total heat transfer of porous cavity can be enhanced by increasing the aspect ratio and the thermal conductivity ratio.     

Intensification of turbulent free heat transport in various configurations with adequate binary gas mixtures

The present paper investigates a promising avenue for the intensification of turbulent free convection in various configurations using adequate binary gas mixtures in which helium (He) is the primary gas component and carbon dioxide (CO₂), methane (CH₄), nitrogen (N₂), oxygen (O₂) and xenon (Xe) are the secondary gas components. In the context of binary gas mixtures, the thermo-physical properties: viscosity, thermal conductivity, density and isobaric heat capacity depend on three quantities: temperature, pressure and molar gas composition. Within the platform of turbulent free convection using the five binary gas mixtures for Ra > 10⁹, results are presented for the allied convective coefficient h_mix/B varying with the molar gas composition w in the w-domain [0, 1]. Values of the maximum allied convective coefficients h_mix,max/B attained at the correlative optimal molar gas compositions w_opt are easily extracted from suitable design charts.     

MIXED CONVECTION IN A RECTANGULAR ENCLOSURE WITH DISCRETE HEAT SOURCES

A numerical study is carried out on mixed convective heat transfer in an enclosure. The discrete heat sources are embedded on a vertical board, which is situated on the bottom wall of an enclosure. An external airflow enters the enclosure through an opening in one vertical wall and exits from another opening in the opposite wall. This study simulates a practical system, such as air-cooled electronic devices with heated elements. Emphasis is placed on the influence of the governing parameters, such as Reynolds number, Re, buoyancy parameter, Gr/Re², location of the heat sources, and the conductivity ratio, rk, on the thermal phenomenon in the enclosure. The coupled equations of the simulated model are solved numerically using the cubic spline collocation method. The computational results indicate that both the thermal field and the average Nusselt number (Nu) depend strongly on the governing parameters, position of the heat sources, as well as the property of the heat-source-embedded board.     

Heat-transfer correlations for an immersed finned heat-exchanger coil transferring heat from a hot-water store

Natural-convection heat transfers, to a finned-tube heat-exchanger coil immersed in a hot-water store, have been investigated. Cold water was passed through the pipe of the heat-exchanger in order to extract heat rapidly from the hot water in the store. Natural convection currents in the stored water were created by buoyancy forces, which were induced by the temperature gradients that developed as a result of the heat-extraction process. A heat-transfer correlation in terms of Nusselt and Rayleigh numbers has been deduced in order to predict the natural convection heat-transfer coefficient on the outside surface of the heat exchanger. This correlation, which is valid for heat entering the fins, to within an accuracy of better than 4%, is: Nu=0·280 Ra^0·293 for 100 < Ra < 1500     

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.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.