Miniature heat-pipe thermal performance prediction tool – software development

The software for flat miniature heat-pipe parameters (Q_max, R_hp, temperature field along the pipe surface, heat transfer coefficients in the evaporator and condenser zones h_e, h_c, etc.) prediction and numerical modeling was developed. The experimental data received for the flat miniature heat pipe (2.5–4 mm thickness, 50–250 mm length, 8–11 mm width) with a copper sintered powder wick saturated with water were compared with the data of numerical analysis and results showed that experimental verification testifies the validity of the software application.     

Mass transfer effects on MHD flow and heat transfer past a vertical porous plate through a porous medium under oscillatory suction and heat source

This paper considers the effect of mass transfer on free convective flow and heat transfer of a viscous incompressible electrically conducting fluid past a vertical porous plate through a porous medium with time dependant permeability and oscillatory suction in presence of a transverse magnetic field and heat source. The solutions for velocity field, temperature field and concentration distribution are obtained using perturbation technique. The effects of the flow parameters such as magnetic parameter M, Grashof number for heat and mass transfer G_r,G_c, porosity parameter K_p, Prandtl number P_r, Schmidt number S_c, frequency parameter ω and heat source parameter S on the velocity, temperature and concentration distribution of the flow field and the skin friction, heat flux and the rate of mass transfer are studied analytically and presented with the aid of figures and tables. It is observed that the magnetic parameter and the Schmidt number retard the velocity of the flow field while the Grashof number for heat and mass transfer, the porosity parameter and the heat source parameter have accelerating effect on the velocity of the flow field at all points. Further, the Prandtl number reduces the temperature and the Schmidt number diminishes the concentration distribution of the flow field at all points. The skin friction coefficients τ₀ and τ increase due to increase in G_r,G_c and K_p while decrease due to increase in S_c, M, ω and P_r. Further, the rate of mass transfer S_h increases due to increase in S_c while an increase in ω results a decrease in S_h.     

Investigation of thermal performance of solar air heater having roughness elements as a combination of inclined and transverse ribs on the absorber plate

An experimental investigation has been carried out to study the heat transfer and friction characteristics by using a combination of inclined as well as transverse ribs on the absorber plate of a solar air heater. The experimental investigation encompassed the Reynolds number (Re) ranges from 2000 to 14 000, relative roughness pitch (p/e) 3–8 and relative roughness height (e/D_h) 0.030. The effect of these parameters on the heat transfer coefficient and friction factor has been discussed in the present paper and correlations for Nusselt number and friction factor has been developed within the reasonable limits. A procedure to compute the thermal efficiency based on heat transfer processes in the system is also given and the effect of these parameters on thermal efficiency has been discussed.     

Heat transfer and friction characteristics of an equilateral triangular solar air heater duct using inclined continuous ribs as roughness element on the absorber plate

An experimental study has been carried out to determine the effect on the heat transfer and friction characteristics of an equilateral triangular solar air heater duct using inclined continuous ribs as roughness element on the absorber plate. The experimental study encompasses the range of Reynolds numbers from 5600 to 28,000, relative roughness height (e/D_h) 0.021–0.043, relative roughness pitch (p/e) 8–16 and angle of attack (α ) 30–60°. The duct has an aspect ratio (W/H) of 1.15. The effect of flow parameters and roughness parameters on heat transfer and friction factor is discussed. The thermohydraulic performance parameter has been determined for the given range of flow parameters and roughness parameters.     

Heat transfer and friction behaviors in rectangular channels with varying number of ribbed walls

An experimental study of surface heat transfer and friction characteristics of a fully developed turbulent air flow in a square channel with transverse ribs on one, two, three, and four walls is reported. Tests were performed for Reynolds numbers ranging from 10,000 to 80,000. The pitch-to-rib height ratio, P/e, was kept at 8 and rib-height-to-channel hydraulic diameter ratio, e/D_h was kept at 0.0625. The channel length-to-hydraulic diameter ratio, L/D_h, was 20. The heat transfer coefficient and friction factor results were enhanced with the increase in the number of ribbed walls. The friction roughness function, R(e⁺), was almost constant over the entire range of tests performed and was within comparable limits of the previously published data. The heat transfer roughness function, G(e⁺), increased with roughness Reynolds number and compared well with previous work in this area. Both correlations could be used to predict the friction factor and heat transfer coefficient in a rectangular channel with varying number of ribbed walls. The results of this investigation could be used in various applications of turbulent internal channel flows involving different number of rib roughened walls.     

Experimental Study on R-410a Evaporation Heat Transfer Characteristics in Oblong Shell and Plate Heat Exchanger

The evaporation heat transfer experiments were conducted with an oblong shell and plate heat exchanger without oil in the refrigerant loop using R-410A, a mixture of 50 wt% R-32 and 50 wt% R-125 that exhibits azeotropic behavior. An experimental refrigerant loop has been established to measure the evaporation heat transfer coefficient h _r of R-410A in a vertical oblong shell and plate heat exchanger. Four vertical counter-flow channels were formed in the oblong shell and plate heat exchanger by four plates having a corrugated trapezoid shape of a 45° chevron angle. The upflow of the boiling R-410A in one channel receives heat from the hot downflow of water in the other channel. The effects of the refrigerant mass flux, average heat flux, refrigerant saturation temperature, and vapor quality of R-410A on the measured data were explored in detail. The results indicate that a rise in the refrigerant mass flux causes an increase in the h _r . Raising the imposed wall heat flux was found to slightly improve h _r . Finally, at a higher refrigerant saturation temperature, the h _r is found to be lower. Based on the present data, an empirical correlation of the evaporation heat transfer coefficient was proposed.     

Investigation for the optimal thermohydraulic performance of artificially roughened solar air heaters

Artificially roughened solar air heaters perform better than the plane ones under the same operating conditions. However, artificial roughness leads to even more fluid pressure thereby increasing the pumping power. Roughness and flow parameters viz. relative roughness pitch p/e, relative roughness height e/D and flow Reynolds number Re have a combined effect on the heat transfer as well as fluid pressure (friction factor). Investigation for the optimal thermohydraulic performance (i.e. maximum heat transfer for minimum friction loss) of artificially roughened solar air heaters has been carried out. An optimisation parameter known as roughness Reynolds number which combines the roughness and flow effect and is expressed as has been considered. Thermohydraulic performance has been defined by the equation η_thermo=(St_r/St_s)³/(f_r/f_s). It has been found that e⁺_opt24 gives the optimal thermohydraulic performance in such collectors and therefore the optimal thermohydraulic performance curves [3], for designing such collectors for practical applications are suitable. The value of optimal thermohydraulic performance has been found to be about 71% corresponding to e⁺_opt=24.     

Experimental study of dropwise condensation on plasma-ion implanted stainless steel tubes

Plasma-ion implantation was used to achieve stable dropwise condensation of saturated steam on stainless steel tubes. For the investigation of the efficiency of plasma-ion implantation regarding the condensation process a condenser was constructed in order to measure the heat flux density and the heat transfer coefficient h_c for the condensation of steam on the outside surface of a single horizontal tube. For tubes implanted with a nitrogen ion dose of 10¹⁶ cm⁻², the heat transfer coefficient h_c was found to be larger, by a factor of 3.2, in comparison to values theoretically calculated by the corrected Nusselt film theory. The heat flux density and the heat transfer coefficient h_c were found to increase with increasing ion dose and steam pressure. The heat transfer coefficient decreases with increasing surface subcooling as it has been found in former work for dropwise condensation on ion implanted vertical plates.     

Heat transfer augmentation for air jet impinged on a rough surface

An experimental investigation of heat transfer from a round air jet impinging normally from below onto a heated square plate was performed. The objective of the investigation was to study the effect of roughness on both the heat transfer and the fluid flow characteristics. Smooth and rough plates were, therefore, used in the course of the experiments. The heat transfer data were collected for four jet Reynolds numbers, ranging from 6500 to 19 000. The Reynolds numbers are based on the jet-exit velocity (U_e) and the nozzle-exit diameter (D), Re_e=U_eD/ν. The nozzle-to-plate distance ranged from 0.05 to 15 nozzle-exit diameter to cover both the potential core and the far regions of the jet flow. The roughness was composed of cubes of 1 mm dimension distributed uniformly along the plate. The local and average Nusselt number values for the rough plate showed an increase ranging from 8.9% to 28% over those for the smooth plate. Roughness was found to have a strong effect on the flow characteristics; it affected the mean velocity as well as the turbulence intensity of the flow. The mean velocity profiles for the smooth case at radial distances of r/D=1 and r/D=2.5 showed steeper near-wall velocity gradients compared with the profiles of the rough case, where r is the radial distance measured from the plate center along the plate centerline. In addition, roughness caused an increase in the turbulence intensity of the flow.     

An Experimental Study of Flow Condensation Heat Transfer Inside Circular and Rectangular Mini-Channels

Abstract

By using unique experimental techniques and the careful construction of an experimental apparatus, the characteristics of the local heat transfer were investigated using the condensing R134a two-phase flow in horizontal single mini-channels. The circular channels (D _h = 0.493, 0.691, and 1.067 mm) and rectangular channels (Aspect Ratio = 1.0; D _h = 0.494, 0.658, and 0.972 mm) were tested and compared. Tests were performed for a mass flux of 100, 200, 400, and 600 kg/m²s, a heat flux of 5 to 20 kW/m², and a saturation temperature of 40°C. In this study, the effect of heat flux, mass flux, vapor qualities, hydraulic diameter, and channel geometry on flow condensation were investigated, and the experimental local condensation heat transfer coefficients are shown. The experimental data of condensation Nusselt number are compared with existing correlations.     

Multiple and unsteady solutions for buoyancy driven flows in spherical annuli

Results from the analysis of buoyancy driven flows and heat transfer in concentric spherical annuli heated by the inner surface are presented. Crescent eddy flows obtained at low Grashof numbers, Gr, are consistent with published results. Multicellular flows, ranging from steady bicellular to oscillating five-cell flows, are calculated for Gr_c < Gr < Gr_r, the specific nature of the flows depending on γ and Gr. For Gr > Gr_r, the solution reverts to steady unicellular flows for the radial aspect ratios γ = 0.2 and 0.25, but with hysteresis for γ = 0.25. Heat transfer results, given in terms of the local and global Nusselt numbers, illustrate the effect of the flow structures on the heat transfer.     

Modeling of heat transfer and energy analysis of potato slices and cylinders during solar drying

In the present work, a method based on energy balance considering the effects of heat capacity of the food product, radiative heat transfer from food product to the drying chamber and solar radiation absorbed in the product during drying is proposed for determination of convective heat transfer coefficient, h_c. A natural convection mixed-mode solar dryer is used for performing the experiments on potato cylinders and slices of same thickness of 0.01 m with respective length and diameter of 0.05 m. The present investigation indicates that the cylindrical samples exhibit higher values of h_c and faster drying rate compared to those of slices, as expected. The h_c values for each sample shape are correlated by an equation of the form Nu = C(Ra)ⁿ. Laplace transform is applied to solve the proposed heat transfer diffusion model considering the effect of moisture transfer rate to predict the transient sample temperature. The model is validated through a close agreement between calculated and experimental results of transient sample temperature. Results of energy analysis reveal that for both the sample geometries, decreasing product moisture content during drying resulted in significant reduction in specific energy consumption. For almost similar drying conditions, a considerable amount of reduction in specific energy consumption is achieved for cylinders, as expected.     

Thermal analysis of natural convective air drying of shrinking bodies

In the present paper, a method for determination of external mass transfer coefficient h_m, during drying of shrinking bodies is described under simulated natural convective air drying conditions. The effects of sample shrinkage and air temperature on h_m during drying of cylindrical potato samples of diameter 0.01 m and length 0.05 m were experimentally investigated at air temperatures 40, 50 and 60°C. The mass transfer coefficient considering shrinkage was found to be independent of sample moisture content during drying process with mean values varying from 1.06 × 10^?7 to 2.60 × 10^?7 m s^?1 for temperature range 40–60°C. However, calculated values of h_m, with no shrinkage effect taken into account, were found to be overestimated. The experimental error in terms of percent uncertainty in mass transfer coefficient measurements was computed and found to be in the range of 0.4–2.0%. It was demonstrated that higher drying air temperature caused increased values of h_m and the variation followed Kelvin's law type relation. A mathematical model to predict the drying process of cylindrical bodies with convective mass transfer boundary condition at air–solid interface is proposed. The low range of various errors between the results of moisture content ratio predicted by the model and those obtained experimentally indicates that the present methodology is capable of simulation of drying kinetics of potato cylinders. Copyright © 2006 John Wiley & Sons, Ltd.     

Natural convective heat transfer in trapezoidal enclosure of box-type solar cooker

This paper presents simple thermal analysis to evaluate the natural convective heat transfer coefficient, h_c12 for a trapezoidal absorber plate-inner glass cover enclosure of a double-glazed box-type solar cooker. Several indoor simulation experiments in steady state conditions have been performed to measure the temperatures of absorber plate, inner and outer glass covers, ambient air, electrical input supply and wind speed. The experimental data has been correlated by an equation of the form, Nu = CRaⁿ. The values of the constants C and n, obtained by linear regression analysis are used to calculate the convective heat transfer coefficient. The heat transfer analysis predicts that h_c12 varies from 4.84 to 6.23 W m^{−2 o}C⁻¹ for the absorber plate temperature from 54 to 141 ^oC. The results of h_c12 are compared with those of rectangular enclosure for the same absorber-inner glass cover temperatures and gap spacing. The study reveals that the values of convective heat transfer coefficient and top heat loss coefficient for rectangular enclosure are lower by 31–35% and 7% respectively.     

An approach to the design of solar coil collector

A design procedure using the concept of heat exchanger “effectiveness and transfer unit” has been developed and applied to a Solar Coil Collector fabricated and tested earlier. For laminar flow the coil wall temperature T_c is obtained from the modified expression ). Where T_b = bulk liquid temperature; Q = wall heat flux; h_t = heat transfer coefficient in straight tubes; D_t = tube diameter; D_c = coil diameter; and p = a number. The calculated results are checked with the actual dimensions of the collector and are found in agreement.     

Temperatures of Coal Particle During Devolatilization in Fluidized Bed Combustion Reactor

The purpose of this study was to investigate the thermal behavior of coal during devolatilization in fluidized bed. Temperatures in the center of single coal particle were measured by thermocouple. Two coals were tested (brown coal Bogovina and lignite Kosovo), using dry coal particle, shaped into spherical form of diameters 7 and 10 mm, in temperature range from 300 to 850°C. Unsteady behavior of coal particle during heating and devolatilization in fluidized bed was described by a model that takes into account heat transfer between bed and particle surface, heat transfer through particle and an endothermic chemical reaction of first-order. Based on the mathematical model analysis and compared with experimental results, values of heat conductivity (λ _c ) and heat capacity (C _p ) of coal were determined. The best agreement was obtained for constant thermal properties, for brown coal λ _c = 0.20 W/mK and C _p = 1200 J/kgK and for lignite λ _c = 0.17 W/mK and C _p = 1100 J/kgK.     

Theoretical and experimental investigation of a heat pipe heat exchanger for energy recovery of exhaust air

Heat pipes and two-phase thermosyphon systems are passive heat transfer systems that employ a two-phase cycle of a working fluid within a completely sealed system. Consequently, heat exchangers based on heat pipes have low thermal resistance and high effective thermal conductivity, which can reach up to the order of (10⁵ W/(m K)). In energy recovery systems where the two streams should be unmixed, such as air-conditioning systems of biological laboratories and operating rooms in hospitals, heat pipe heat exchangers (HPHEs) are recommended. In this study, an experimental and theoretical study was carried out on the thermal performance of an air-to-air HPHE filled with two refrigerants as working fluids, R22 and R407c. The heat pipe heat exchanger used was composed of two rows of copper heat pipes in a staggered manner, with 11 pipes per row. Tests were conducted at different airflow rates of 0.14, 0.18, and 0.22 m³/h, evaporator inlet-air temperatures of 40, 44, and 50°C, filling ratios of 45%, 70%, and 100%, and ratios of heat capacity rate of the evaporator to condenser sections (C_e/C_c) of 1 and 1.5. For HPHE's steady-state operation, a mathematical model for heat-transfer performance was set and solved using MATLAB. Results illustrated that the heat transfer rate was in direct proportion with the evaporator inlet-air temperature and flow rate. The highest HPHE's effectiveness was obtained at a 100% filling ratio and (C_e/C_c) of 1.5. The predicted and experimental values of condenser outlet-air temperature were in good agreement, with a maximum difference of 3%. HPHE's effectiveness was found to increase with the increase in evaporator inlet-air temperature and number of transfer units (NTU) and with the decrease in airflow rate, up to 33% and 20% for refrigerants R22 and R407c, respectively. Refrigerant R22 was the superior of the two refrigerants investigated.     

Experimental investigations on overall cooling effect of ribbed channel with air bleeds

An experimental investigation on overall heat transfer performance of a rectangular channel, in which one wall has periodically placed oblique ribs to enhance heat exchange and cylindrical film holes to bleed cooling air, has been carried out in a hot wind tunnel at different mainstream temperatures, hot mainstream Reynolds numbers, coolant Reynolds numbers and blowing ratios. To describe the cooling effect of combined external coolant film with the internal heat convection enhanced by the ribs, the overall cooling effectiveness at the surface exposed in the mainstream with high temperature was calculated by the surface temperatures measured with an infrared thermal imaging system. The total mass flow rate of cooling air through the coolant channel was regulated by a digital mass flow rate controller, and the blowing ratio passing through the total film holes was calculated based on the measurements of another digital-type mass flow meter. The detailed distributions of overall cooling effectiveness show distinctive peaks in heat transfer levels near the film holes, remarkable inner convective heat transfer effect over entire channel surface, and visible conductive heat transfer effect through the channel wall; but only when the coolant Reynolds number is large enough, the oblique rib effect can be detected from the overall cooling effectiveness; and the oblique bleeding hole effect shows the more obvious trend with increasing blowing ratios. Based on the experimental data, the overall cooling effectiveness is correlated as the functions of Re_m (Reynolds number of hot mainstream) and Re_c (Reynolds number of internal coolant flow at entrance) for the parametric conditions examined.     

The Second Law of Thermodynamics for a Two-Temperature Model of Heat Transport in Metal Films

ABSTRACT

The second law of thermodynamics asserts that heat will always flow “downhill”, i.e., from an object having a higher temperature to one having a lower temperature. For a parabolic rigid heat conductor with a single temperature T and a single heat-flux q this amounts to the statement that the inner product of q and ?T must be non-positive for every point x of the conductor and for every non-negative time t. For a homogeneous and isotropic body in which classical Fourier law with a heat conductivity coefficient k is postulated, the second law is satisfied if k is a positive parameter. For ultra-fast pulse-laser heating on metal films, a parabolic two-temperature model coupling an electron temperature T_e with a metal lattice temperature T_l has been proposed by several authors. For such a model, at a given point of space x and a given time t there are two different temperatures T_e and T_l as well as two different heat-fluxes q _e and q _l related to the gradients of T_e and T_l, respectively, through classical Fourier law. As a result, for a homogeneous and isotropic model the positive definiteness of the heat conductivity coefficients k_e and k_l corresponding to T_e and T_l, respectively, implies that the second law of thermodynamics is satisfied for each of the pairs (T_e, q _e) and (T_l, q _l), separately. Also, the positive definiteness of k_e and k_l, and of the corresponding heat capacities c_e and c_l as well as of a coupling factor G imply that a temperature initial-boundary value problem for the two-temperature model has unique solution. In the present paper, an alternative form of the second law of thermodynamics for the two-temperature model with k_l = 0 and q _l =  0 is obtained from which it follows that in a one-dimensional case the electron heat-flux q_e(x, t) has direction that is opposite not only to that of ?T_e(x, t)/?x but also to that of ?T_l(x, t + τ_T)/?x, where τ_T is an intrinsic small time of the model. Also, for a general two-temperature rigid heat conductor in which k_e, k_l, c_e, c_l, and G are positive, an inequality of the second law of thermodynamics type involving a pair (T_e ? T_l, q _e ?  q _l) is postulated to prove that a two-heat-flux initial-boundary value problem of the two-temperature model has a unique solution. For a one-dimensional case, the semi-infinite sectors of the plane ( q _l, q _e) over which uniqueness does not hold true are also revealed.     

Second law optimization of a solar air heater having chamfered rib–groove roughness on absorber plate

Artificially roughened solar air heaters perform better than the plane ones under the same operating conditions. However, artificial roughness leads to even more fluid pressure thereby increasing the pumping power. The entropy generation in the duct of solar air heater having repeated transverse chamfered rib–groove roughness on one broad wall is studied numerically. Roughness parameters, viz., relative roughness pitch P/e, relative roughness height e/D_h relative groove position g/P, chamfer angle φ and flow Reynolds number Re have a combined effect on the heat transfer as well as fluid friction. The entropy generation is minimized and reasonably optimized designs of roughness are found.