Numerical studies of simultaneously developing laminar flow and heat transfer in microtubes with thick wall and constant outside wall temperature

The effects of wall axial heat conduction in a conjugate heat transfer problem in simultaneously developing laminar flow and heat transfer in straight thick wall of circular tube with constant outside wall temperature are numerically investigated. The results show that the heat transfer process is most sensitive to wall-to-fluid conductivity ratio k_sf, and when k_sf ? 25 the increasing tube thickness and the decreasing k_sf could make the inner wall surface approaching the uniform heat flux condition. It turns out that the basic function of the wall axial heat conduction for the cases studied is to unify the inner wall surface heat flux.     

Experimental study of R-134a evaporation heat transfer in a narrow annular duct

An experiment is carried out here to investigate the evaporation heat transfer and associated evaporating flow pattern for refrigerant R-134a flowing in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm. In the experiment, the effects of the duct gap, refrigerant vapor quality, mass flux and saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient h_r are examined in detail. For the duct gap of 2.0 mm, the refrigerant mass flux G is varied from 300 to 500 kg/m² s, imposed heat flux q from 5 to 15 kW/m², vapor quality x_m from 0.05 to 0.95, and refrigerant saturation temperature T_sat from 5 to 15 °C. While for the gap of 1.0 mm, G is varied from 500 to 700 kg/m² s with the other parameters varied in the same ranges as that for δ = 2.0 mm. The experimental data clearly show that the evaporation heat transfer coefficient increases almost linearly with the vapor quality of the refrigerant and the increase is more significant at a higher G. Besides, the evaporation heat transfer coefficient also rises substantially at increasing q. Moreover, a significant increase in the evaporation heat transfer coefficient results for a rise in T_sat, but the effects are less pronounced in the narrower duct at a low imposed heat flux and a high refrigerant mass flux. Furthermore, the evaporation heat transfer coefficient increases substantially with the refrigerant mass flux except at low vapor quality. We also note that reducing the duct gap causes a significant increase in h_r. In addition to the heat transfer data, photos of R-134a evaporating flow taken from the duct side show the change of the dominant two-phase flow pattern in the duct with the experimental parameters. Finally, an empirical correlation for the present measured heat transfer coefficient for the R-134a evaporation in the narrow annular ducts is proposed.     

Heat loss of a trapezoidal cavity absorber for a linear Fresnel reflecting solar concentrator

The present paper studies the heat loss of a linear absorber with a trapezoidal cavity and a set of pipes used for a linear Fresnel reflecting solar concentrator. The study includes the measurements on a 1.4 m long prototype installed in a laboratory, and its thermal simulation in steady-state using EnergyPlus software. Results of the measured vertical temperature variation inside the cavity, the surface interior and exterior wall and window temperatures, the global heat loss at steady-state and the heat loss coefficients, are presented for six different temperatures of the pipes. Measurements revealed a stable thermal gradient in the upper portion of the cavity and a convective zone below it. Around 91% of the heat transferred to outdoors occurs at the bottom transparent window, for a pipe temperature of 200 °C. The heat loss coefficient per area of absorbing pipes ranged from 3.39 W/m²K to 6.35 W/m²K (for 110 °C < T_pipe < 285 °C), and it increased with the increase of T_pipe. Simpler and less time-consuming available free software originally designed for heat transfer in buildings was tested to be a possible replacement of the highly complex CFD software commonly used to simulate the steady-state heat loss of the absorber. The experimental and predicted data sets were found to be in good agreement.     

An experimental study of axial conduction through a thermosyphon pipe wall

The effect of the axial conduction through the pipe wall on the performance of a thermosyphon was experimentally investigated in this study. Two 2-phase closed thermosyphons were tested; each had the same dimensions, materials and partially filled with R134a. The only difference between them was that one had a thermal break within the adiabatic section that resisted axial conduction between the evaporator and the condenser sections. The thermosyphons were heated by a constant-temperature hot bath and cooled by water via a concentric heat exchanger. The experiments were performed for different bath temperatures and different fill ratios. It was found that the axial conduction through the pipe wall caused an increase in the overall heat transfer coefficient, evaporation heat transfer coefficient and condensation heat transfer coefficient of the thermosyphon. However, the fraction of heat transfer associated with axial conduction decreased as the heat flux increased. For small heat flux (T_b = 30 °C), the increment of the evaporation and condensation heat transfer coefficient contributed by axial conduction reached 100% and 25%, respectively. For high heat flux (T_b = 60 °C), the increment was negligible (less than 1%).     

Heat transfer and pressure drop during HFC refrigerant saturated vapour condensation inside a brazed plate heat exchanger

This paper presents the heat transfer coefficients and the pressure drop measured during HFC refrigerants 236fa, 134a and 410A saturated vapour condensation inside a brazed plate heat exchanger: the effects of saturation temperature (pressure), refrigerant mass flux and fluid properties are investigated. The heat transfer coefficients show weak sensitivity to saturation temperature (pressure) and great sensitivity to refrigerant mass flux and fluid properties. A transition point between gravity controlled and forced convection condensation has been found for a refrigerant mass flux around 20 kg/m²s that corresponds to an equivalent Reynolds number around 1600–1700. At low refrigerant mass flux (G_r < 20 kg/m²s) the heat transfer coefficients are not dependent on mass flux and are well predicted by the Nusselt [20] analysis for vertical surface: the condensation process is gravity controlled. For higher refrigerant mass flux (G_r > 20 kg/m²s) the heat transfer coefficients depend on mass flux and are well predicted by Akers et al. [21] equation: forced convection condensation occurs. In the forced convection condensation region the heat transfer coefficients show a 25–30% increase for a doubling of the refrigerant mass flux.The frictional pressure drop shows a linear dependence on the kinetic energy per unit volume of the refrigerant flow and therefore a quadratic dependence on mass flux.HFC-410A shows heat transfer coefficients similar to HFC-134a and 10% higher than HFC-236fa together with frictional pressure drops 40-50% lower than HFC-134a and 50–60% lower than HFC-236fa.     

Natural convection in a partially open square cavity with internal heat source: An analysis of the opening mass flow

A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra_e = 10³–10⁵, while the influence of the heat source was evaluated through the relation R = Ra_i/Ra_e, investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra_e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra_e whereas these features are absent at higher Ra_e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Conjugate heat transfer of mixed convection for viscoelastic fluid past a horizontal flat-plate fin

A conjugate mixed convection heat transfer problem of a second-grade viscoelastic fluid past a horizontal flat-plate fin has been studied. Governing equations include heat conduction equation of the fin, and continuity equation, momentum equation and energy equation of the fluid, have been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat-plate flow (β = 0) on the fin surface were obtained by a generalized Falkner–Skan flow derivation. These solutions have been used to iterate with the heat conduction equation of the fin to obtain distributions of the local convective heat transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number (Pr), the elastic number (E), the free convection parameter (G) and the conduction–convection coefficient (N_cc) are from 0.1 to 100, 0.001 to 0.01, 0 to 1.5 and 0.05 to 2.0, respectively. The elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a horizontal flat-plate fin. In addition, same as results from Newtonian fluid flow and conduction analysis of a horizontal flat-plate fin, a better heat transfer has been obtained with a larger N_cc, G and Pr.     

Heatlines based natural convection analysis in tilted isosceles triangular enclosures with linearly heated inclined walls: effect of various orientations

Natural convection in isosceles triangular enclosures with various configurations (case 1 — inverted, case 2 — straight and case 3 — tilted) is studied via heatline analysis for linear heating of inclined walls. Detailed analysis and comparison for various base angles (φ = 45°, 60°) of triangular enclosures have been carried out for a range of fluids (Pr = 0.015 − 1000) within Ra = 10³ − 10⁵ using Galerkin finite element method. The heat flow distributions indicate conduction dominant heat transfer at low Ra (Ra = 10³) for case 1 and case 2 whereas in case 3, convective heat flow is observed due to high buoyancy force. As Ra increases, enhanced thermal mixing is observed at the core of the cavity. Wall to wall heat transfer occurs at walls AB and AC due to linear heating boundary condition in all the cases. Although the distributions of fluid flow and heat flow are qualitatively similar for φ = 45° and 60°, the intensity of fluid flow and heat flow decreases as φ increases. Strength of fluid flow and heat flow circulation cells is found to be higher in case 3 for identical parameters. Results show that upper side wall (AC) for case 3 exhibits higher heat transfer rates whereas heat transfer rates for walls AB and AC are the same for case 1 and case 2. Also Nu_AB is higher for case 2 followed by case 1 and case 3 at the middle portion of wall AB. Thus to achieve high heat transfer from fluid to wall at the central region, case 2 and case 3 configurations may be recommended at high Ra (Ra = 10⁵) and Pr, irrespective of φ.     

The use of phase-change coatings for estimating the heat transfer characteristics in a rotating disc system

Phase-change coatings have been applied to the axial-clearance rotor-stator cavity for the estimation of the transient heat transfer characteristics of the surface of the rotating disc. The tests were conducted for an air mass flow coefficient C_w = 1220, a gap ratio G = 0.1, an axial-clearance ratio G_ca = 0.05 and for rotational Reynolds numbers of Re? = 1 × 10⁵ and 2 × 10⁵. The phase-change coating used had a melting point of 38°C. From a video recording of the transient movement of the melt-line on the rotor (coated with the phase-change material) blown with heated air, it was possible to compute the heat transfer coefficients. The data reduction was made using the ‘semi-infinite slab’ approximation to the governing one-dimensional transient heat conduction equation.     

Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium

A numerical investigation of the steady magnetohydrodynamics free convection in a rectangular cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field, inclined at an angle γ with respect to the horizontal plane, is externally imposed. The values of the governing parameters are the inclined angle γ = 0, π/6, π/4 and π/2, Hartmann number Ha = 0, 1, 5, 10 and 50, Rayleigh number Ra = 10, 100, 10³ and 10⁵, and the aspect ratio a = 0.01, 0.2, 0.5 and 1 (square cavity). It is shown that the intensity of the core convection is considerably affected by the considered parameters. It is also found that the local Nusselt number Nu_Y decreases on the bottom wall as γ increases (magnetic field changes its direction from the horizontal to the vertical direction) and vice versa for the top wall of the cavity. The reported results are in good agreement with the available published work in the literature.     

Stability of a fluid-saturated porous medium heated from below by forced convection

A linear stability analysis determining the onset of convection in a bounded rectangular cavity containing a fluid-saturated porous medium is performed for insulated sidewalls, isothermal top wall, and bottom wall heated by forced convection. The nature of the bottom wall heating necessarily involves the Biot number, Bi. Numerical calculations of the critical Rayleigh number, R_c made over the range of Biot numbers 10⁻⁴?Bi?10⁴ for cavity aspect ratios 0?(a,b)?5 cover all effective bottom heating conditions from the constant heat flux global limit, R_c=27.096 found as Bi→0 to the isothermal global limit, R_c=4π² found as Bi→∞. Marginal stability boundaries, preferred cellular modes and disturbance temperature contours are displayed graphically.     

Natural convection effects on heat and mass transfer in a curvilinear triangular cavity

Finite element method is used in this study to analyze the effects of buoyancy ratio and Lewis number on heat and mass transfer in a triangular cavity with zig-zag shaped bottom wall. Buoyancy ratio is defined as the ratio of Grashof number of solutal and thermal. Inclined walls of the cavity have lower temperature and concentration according to zig-zag shaped bottom wall. Enclosed space consists mostly of an absorber plate and two inclined glass covers that form a cavity. Both high temperature and high concentrations are applied to bottom corrugated wall. Computations were done for different values of buoyancy ratio (?10 ? Br ? 10), Lewis number (0.1 ? Le ? 20) and thermal Rayleigh number (10⁴ ? Ra_T ? 10⁶). Streamlines, isotherms, iso-concentration, average Nusselt and Sherwood numbers are obtained. It is found that average Nusselt and Sherwood numbers increase by 89.18% and 101.91% respectively as Br increases from ?10 to 20 at Ra_T = 10⁶. Also, average Nusselt decreases by 16.22% and Sherwood numbers increases by 144.84% as Le increases from 0.1 to 20 at this Rayleigh number.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Visualization of heat flow due to natural convection within triangular cavities using Bejan’s heatline concept

Natural convection and flow circulation within a cavity has received significant attention in recent times. The wide range of applicability of flow inside a cavity (food processing industries, molten metal industries, etc.) requires thorough understanding for cost efficient processes. This paper is based on comprehensive analysis of heat flow pattern using Bejan’s heatline concept. The key parameters for our study are the Prandtl number, Rayleigh number and Nusselt number. The values of Prandtl number (0.015, 0.026, 0.7 and 1000) have been chosen based on wide range of applicability. The Rayleigh number has been varied from 10² to 10⁵. Interesting results were obtained. For low Rayleigh number, it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction. But as Ra increases, flow slowly becomes convection dominant. It is also observed that multiple secondary circulations are formed for fluids with low Pr whereas these features are absent in higher Pr fluids. Multiple circulation cells for smaller Pr also correspond multiple cells of heatlines which illustrate less thermal transport from hot wall. On the other hand, the dense heatlines at bottom wall display enhanced heat transport for larger Pr. Further, local heat transfer (Nu_l, Nu_t) are explained based on heatlines. The comprehensive analysis is concluded with the average Nusselt number plots. A correlation for average heat transfer rate and Ra has been developed and the range of Rayleigh number is also found, to depict the conduction dominant heat transfer.     

Conjugate heat transfer of magnetic mixed convection with radiative and viscous dissipation effects for second-grade viscoelastic fluid past a stretching sheet

A radiative and viscous dissipation effects conjugate heat transfer problem of a second-grade viscoelastic fluid past a stretching sheet has been studied. Governing equations for heat conduction equation of a stretching sheet, and continuity equation, momentum equation and energy equation of a second-grade fluid have been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite-difference method. These solutions are used to obtain distributions of the local convective heat transfer coefficient and the stretching sheet temperature. The ranges of these dimensionless parameters, the Prandtl number Pr, the elastic number E and the conduction–convection coefficient N_cc are from 0.001 to 10, 0.0001 to 0.01, and 0.5 to 2.0, respectively. A parameter, G, which is used to represent the strength of the buoyancy, is present in the governing equations. A parameter, M_n, which represents the strength of the magnetic filed effect, N_r shows the radiation effect are also present in governing equations. Results indicate that elastic effect in the flow may increase the local heat transfer coefficient and enhance the heat transfer of a stretching sheet. In addition, same as results from Newtonian fluid flow and conduction analysis of a stretching sheet, a better heat transfer has obtained with larger N_cc, G, E, and Pr. It shows that a non-Newtonian flow (E = 0.1, E = 0.01) have a good efficiency to reduce heat for a stretching sheet better than a nearly Newtonian flow (E = 0.001).     

Heat flow visualization for natural convection in rhombic enclosures due to isothermal and non-isothermal heating at the bottom wall

Analysis has been carried out for the energy distribution and thermal mixing in steady laminar natural convective flow through the rhombic enclosures with various inclination angles, φ for various industrial applications. Simulations are carried out for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Dimensionless streamfunctions and heatfunctions are used to visualize the flow and energy distribution, respectively. Multiple flow circulations are observed at Pr = 0.015 and 0.7 for all φs at Ra = 10⁵. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 75° at higher Pr (Pr = 7.2 and 1000) and Ra (Ra = 10⁵). Heatlines are found to be parallel circular arcs connecting the cold and hot walls for the conduction dominant heat transfer at Ra = 10³. The enhanced convective heat transfer is explained with dense heatlines and convective loop of heatlines at Ra = 10⁵. Heatlines clearly demonstrate that the left wall receives heat from the bottom wall as heatlines directly connect both the walls whereas the convective heat circulation cells play lead role to distribute the heat along the right wall, especially for smaller φs. On the other hand, the heat flow is evenly distributed to both side walls at higher φs via convection as well as direct conductive transport. Significant convective heat transfer from the bottom hot wall to the left cold wall occurs for φ = 30° cavity whereas the heat transfer to the right cold wall is maximum for φ = 75° irrespective of Pr. Average Nusselt number studies also show that φ = 30° cavity gives maximum heat transfer rate from the bottom to left wall irrespective of Pr in isothermal heating case. On the other hand, enhanced thermal mixing occurs at φ = 75° for both isothermal and non-isothermal heating strategies except at Pr = 0.015 in isothermal heating case.