Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet

The boundary layer flow and heat transfer analysis of electrically conducting viscous fluid over a nonlinearly shrinking sheet is investigated. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The system of equations is solved numerically employing an implicit finite difference scheme known as Keller-box method. It is found that dual solutions exist for this particular problem. The numerical results for the velocity, temperature, wall skin friction coefficient and local rate of heat transfer through the surface for various values of physical parameters both in case of stretching and shrinking sheet are analyzed and discussed for both the solutions. Present results in the hydrodynamic case (M = 0) are compared with existing numerical results in case of stretching flow and found in good agreement.     

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).     

Effect of optical properties on oscillatory hydromagnetic double-diffusive convection within semitransparent fluid

The effect of radiative heat transfer on the hydromagnetic double-diffusive convection in two-dimensional rectangular enclosure is studied numerically for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 10⁵, Le = 2. Uniform temperatures and concentrations are imposed along the vertical walls while the horizontal walls are assumed to be adiabatic and impermeable to mass transfer. The influences of the optical thickness and scattering albedo of the semitransparent fluid on heat and mass transfer with and without magnetic damping are depicted. When progressively varying the optical thickness, multiple solutions are obtained which are steady or oscillatory accordingly to the initial conditions. the mechanisms of the transitions between steady compositionally dominated flow and unsteady thermally dominated flow are analyzed.     

MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with non-uniform source/sink

The analysis includes a steady two-dimensional MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with the effect of non-uniform source/sink. Two types of different heating processes are considered namely (i) prescribed surface temperature (PST) and (ii) prescribed wall heat flux (PHF). The governing system of non-linear partial differential equations are transformed into ordinary differential equations using similarity transformations and which are then solved numerically using Runge Kutta Fehlberg fourth–fifth order method. Comparison of the numerical results is made with the existing literature and the results are found to be in good agreement. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that velocity distribution for clean fluid decreases where as dust fluid increases with the increase of fluid particle interaction parameter when λ > 1 and λ < 1.     

Jet impingement interaction with cross flow in horizontal porous layer under thermal non-equilibrium conditions

In the present article the jet impingement cooling of heated portion of a horizontal surface immersed in a thermally non-equilibrium porous layer is considered for investigation numerically with the presence of a cross flow. The mathematical model is derived for steady, two-dimensional laminar flow based on Darcy model and two-energy equation for fluid and solid phases. A parametric study is carried out by varying the following parameters: cross flow to jet flow velocity ratio parameter (0 ⩽ M ⩽ 1); porosity scaled thermal conductivity ratio parameter (0.1 ⩽ K_r ⩽ 1000); heat transfer coefficient parameter (0.1 ⩽ H ⩽ 1000); Péclet number (1 ⩽ Pe ⩽ 1000) and Rayleigh number (10 ⩽ Ra ⩽ 100). The total average Nusselt number is defined based on the overall thermal conductivity, which is assumed to be the arithmetic mean of the porosity scaled thermal conductivity of the fluid and solid phases. The total average Nusselt number as well as the average Nusselt number for both fluid and solid phases is presented for different governing parameters. It is found that the presence of a weak cross flow in a jet impinging jet may degrade the heat transfer. The results show that the average Nusselt number calculated from the thermal equilibrium model are the maximum possible values and these values can be reproduced by large values of H × K_r.     

The boundary layers of an unsteady stagnation-point flow in a nanofluid

The boundary layer of an unsteady two-dimensional stagnation-point flow of a nanofluid is further investigated. The similarity equations are solved numerically for three types of nanoparticles, namely copper (Cu), alumina (Al₂O₃), and titania (TiO₂) in the water based fluid with Prandtl number Pr = 6.2. The skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are presented and discussed. Effects of the solid volume fraction parameter φ on the fluid flow and heat transfer characteristics are thoroughly examined. Interesting observation is that there are dual solutions seen for negative values of the unsteadiness parameter A (decelerating flow with A < 0).     

Heat transfer on a power law stretching sheet subjected to free stream pressure gradient

The present work deals with the numerical study of temperature distribution in the laminar boundary layer driven by the stretching boundary surface subjected to pressure gradient. The similarity transformation obeying the same power law based on composite reference velocity (union of velocities of the stretching boundary and free stream) has been employed that leads to a single set of equations, irrespective of the condition whether U_w > U_∞ or U_w < U_∞, containing three parameters: β measuring the stretch rate of the moving boundary, ε is the ratio of free stream velocity to composite reference velocity and Pr is the Prandtl number of the ambient fluid. The numerical solutions of the thermal boundary layer equations are obtained for three Prandtl numbers 0.7, 1.0 and 10 for 0 ? ε ? 1 and for 0 ? β ? 2. The heat transfer coefficient show appreciable dependence on the ratio of free stream velocity to union of velocities of the stretching surface boundary and free stream.     

Three-dimensional numerical study on fin-and-oval-tube heat exchanger with longitudinal vortex generators

Three-dimensional numerical study was performed for heat transfer characteristics and fluid flow structure of fin-and-oval-tube heat exchangers with longitudinal vortex generators (LVGs). For Re (based on the hydraulic diameter) ranges from 500 to 2500, it was found that the average Nu for the three-row fin-and-oval-tube heat exchanger with longitudinal vortex generators increased by 13.6–32.9% over the baseline case and the corresponding pressure loss increased by 29.2–40.6%. The results were analyzed on the basis of the field synergy principle to provide fundamental understanding of the relation between local flow structure and heat transfer augmentation. It was confirmed that the reduction of the intersection angle θ between the velocity field and the temperature field was one of the essential factors influencing heat transfer enhancement. Three geometrical parameters – placement of LVGs (upstream and downstream), angles of attack (α = 15°, 30°, 45° and 60°) and tube-row number (n = 2, 3, 4 and 5) – were also investigated for parameter optimization. The LVGs with placement of downstream, angles of attack α = 30° and minimum tube-row number provide the best heat transfer performance. The effects of the three geometrical parameters on heat transfer enhancement were also analyzed from the view point of the field synergy principle and it was found that the results can be well explained by the field synergy principle.     

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.     

Unsteady stagnation-point flow over a plate moving along the direction of flow impingement

Unsteady plane and axisymmetric stagnation flow of an incompressible viscous fluid on the body that moves along the oncoming flow with a time-dependent velocity is studied in this work. Similarity solutions for the full Navier–Stokes equations are obtained and the results of the flow velocity, shear stress and stream lines are reported for both plane two dimensional flow and axisymmetric flow. The results show that the features of the similar boundary flow highly depends on a characteristic parameter β. There exists a critical value β_c below which no similarity solution to the flow is found. When β_c < β < 0, two solution branches exist and different flow patterns appear for each branch. Flow with monophonically growing velocity, reversed flow and flow with S-shaped velocity are obtained for various values of β. The boundary layer thickness of the plane and axisymmetric flows is tabulated, the streamlines of the flow are demonstrated, and the shear stress over the boundary layer is also discussed.     

Experimental study of evaporation heat transfer of R-134a inside a corrugated tube with different tube inclinations

Experimental heat transfer studies during evaporation of R-134a inside a corrugated tube have been carried out. The corrugated tube has been provided with different tube inclination angles of the direction of fluid flow from horizontal, α. The experiments were performed for seven different tube inclinations, α, in a range of − 90° to + 90° and four mass velocities of 46, 81, 110 and 136 kg m^− 2 s^− 1 for each tube inclination angle during evaporation of R-134a. Data analysis demonstrate that the tube inclination angle, α, affects the boiling heat transfer coefficient in a significant manner. The effect of tube inclination angle, α, on heat transfer coefficient, h, is more prominent at low vapor quality and mass velocity. In the low vapor quality region, the heat transfer coefficient, h, for the + 90° inclined tube is about 62% more than that of the − 90° inclined tube. The results also showed that at all mass velocities, the highest average heat transfer coefficient were achieved for α = + 90°. An empirical correlation has also been developed to predict the heat transfer coefficient during flow boiling inside a corrugated tube with different tube inclinations.     

Unsteady heat transfer from an elliptic cylinder

Numerical methods are used to investigate the transient heat transfer from an elliptic cylinder to a steady stream of viscous, incompressible fluid. The temperature of the cylinder is considered spatially uniform but not constant in time. The momentum and heat balance equations were solved numerically in elliptic coordinate system. The solutions span the parameter ranges 5 ? Re ? 40, 1 ? Pr ? 100 and axis ratio ε, 0.1 ? ε ? 0.75. The computations were focused on the influence of the axis ratio and volume heat capacity ratio on the heat transfer rate.     

Soret effect on the boundary layer flow regime in a vertical porous enclosure subject to horizontal heat and mass fluxes

The combined thermo- and double-diffusive convection in a vertical tall porous cavity subject to horizontal heat and mass fluxes was investigated analytically and numerically using the Darcy model with the Boussinesq approximation. The investigation focused on the effect of Soret diffusion on the boundary layer flow regime. The governing parameters were the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, N, the Soret parameter, M, which characterized the Soret effect, and the aspect ratio of the enclosure, A_r. The results demonstrated the existence of a boundary layer flow solution for which the Soret parameter had a strong effect on the heat and mass transfer characteristics. For M ≠ 1 and M ≠ −1/Le, the profiles of the vertical velocity component, v, temperature, T, and solute concentration, S, exhibited boundary layer behaviors at high Rayleigh numbers. Furthermore, as R_T increased, the temperature and solute concentration became vertically and linearly stratified in the core region of the enclosure. The thermo-diffusion effect on the boundary layer thickness, δ, was discussed for a wide range of the governing parameters. It was demonstrated analytically that the thickness of the boundary layer could either increase or decrease when the Soret parameter was varied, depending on the sign of the buoyancy ratio. The effect of R_T on the fluid flow properties and heat and mass transfer characteristics was also investigated.     

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 effective thermal properties of solid foam beds: Experimental and estimated temperature profiles

The effective radial heat conductivity of a solid foam packing and the wall heat transfer coefficient are determined under fluid flow conditions typical of catalytic reactors. A detailed 2-D heterogeneous model is phase-averaged in order to rigorously define lumped heat transfer parameters. The resulting pseudo-homogeneous model involves two fitting parameters only and it is successfully compared with experiments. First, experiments with packed extrudates validate the approach in comparison with known results. A second experiment with solid foams (polyurethane and SiC) allows correlating the radial heat conductivity to the nature of the solid, its morphology and fluid flow characteristics. The method is inspired from the correlations for particles and seems very promising. Conversely, determining the wall heat transfer coefficient yields only an average value (110 W m^?2 K^?1 ± 15%) and correlation with fluid velocity is impossible in the studied range 0.018–0.32 m s^?1.     

Unsteady heat transfer from an oblate/prolate spheroid

Numerical methods are used to investigate the transient heat transfer from an oblate/prolate spheroid to a steady stream of viscous, incompressible fluid. The temperature of the spheroid is considered spatially uniform but not constant in time. The momentum and heat balance equations were solved numerically in oblate/prolate spheroidal coordinates system. The solutions span the parameter ranges 10 ? Re ? 100 (for the oblate spheroid), 10 ? Re ? 200 (for the prolate spheroid), Pr = 1, 10 and axis ratio ε, 0.1 ? ε ? 0.9. The computations were focused on the influence of the axis ratio and volume heat capacity ratio on the heat transfer rate.     

Condensation heat transfer of R-134a inside a microfin tube with different tube inclinations

Experimental heat transfer studies during condensation of pure R-134a vapor inside a single microfin tube have been carried out. The microfin tube has been provided with different tube inclination angles of the direction of fluid flow from horizontal, α. The data are acquired for seven different tube inclinations, α, in a range of −90 to +90° and three mass velocities of 54, 81, and 107 kg/m²-s for each inclination angle during condensation of R-134a vapor. The experimental results indicate that the tube inclination angle of, α, affects the condensation heat transfer coefficient in a significant manner. The highest heat transfer coefficient is attained at inclination angle of α = +30°. The effect of inclination angle, α, on heat transfer coefficient, h, is more prominent at low vapor quality and mass velocity. A correlation has also been developed to predict the condensing side heat transfer coefficient for different vapor qualities and mass velocities.     

Effect of rotating cylinder on heat transfer in a square enclosure filled with nanofluids

Convective heat transfer in a differentially heated square enclosure with an inner rotating cylinder is studied theoretically. The free space between the cylinder and the enclosure walls is filled with water–Ag, water–Cu, water–Al₂O₃ or water–TiO₂ nanofluids. The governing equations are formulated for velocity, pressure and temperature formulation and are modeled in COMSOL, a partial differential equation (PDE) solver based on the Galerkin finite element method (GFEM). The governing parameters considered are the solid volume fraction, 0.0 ? ? ? 0.05, the cylinder radius, 0 ? R ? 0.3 and the angular rotational velocity, ?1000 ? Ω ? 1000. The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the strength of the flow circulation is much stronger for a higher nanoparticle concentration, a better thermal conductivity value and a smaller cylinder with a faster, negative rotation. The maximum heat transfer are obtained at a high nanoparticle concentration with a good conductivity value, a slow positive rotation and a moderate cylinder size located in the center of the enclosure.     

Power series solutions of momentum and energy boundary layer equations for a power-law shear driven flow over a semi-infinite flat plate

The boundary layer similarity flow past an impermeable flat plate, driven by a power law velocity profile U = γy^α, y → ∞ is considered and power series solutions of the momentum equation, valid for all the allowed range of the parameter α, are presented. The convergence radius of the proposed solutions is estimated and a comparison with numerical solutions is reported. The boundary layer energy equation is then considered for all the wall temperature profiles that admits similarity solutions and power series solutions are given for the full range of the wall temperature profile parameter n.     

Energy separation in the wake of a cylinder: Effect of Reynolds number and acoustic resonance

Energy separation is a spontaneous redistribution of total energy in a flowing fluid without external work or heat transfer. The energy separation mechanism in the vortex field behind an adiabatic circular cylinder in a cross flow of air is investigated. Time-averaged velocity and temperature measurements taken one diameter downstream of the cylinder (Re ～ 10⁵, M_∞ ～ 0.25) indicate flow reversal. The measured recovery temperature, expressed as distribution of energy separation factor indicates that energy separation is caused by the vortex flow in the wake, enhanced by acoustic excitation, and is insensitive to Reynolds number in the sub critical range studied.