Showing papers on "Film temperature published in 2023"

Individual Effect of Spatially-Periodic Vertical Surface Temperatures And Nanoparticles On Natural Convection In Water

Abstract: This paper considers the thermo-convective boundary-layer flow (BLF) of a water-copper mono-nanofluid over a flat vertical surface which is subjected to three types of periodic temperature variations described by the sinusoidal, sawtooth and triangular waveforms. The temperature of the fluid at the flat surface is greater than the surrounding ambient temperature. The governing equations describing the BLF have been reduced to a non-similar form using an appropriate stream function formulation. The Keller-Box method is used to obtain numerical solution of the boundary-value problem. The effect of the pertinent parameters on the nature of the flow and the heat transfer has been discussed using actual thermophysical data. The results about the shear-stress and heat transfer rate at the surface are presented as well. To study the nature of BLF, the velocity and thermal boundary-layers, the streamline and isotherm plots have been considered, which reveal that the nanoparticle volume-fraction, amplitude of surface temperature variations and the Grashof number play a pivotal role in enhancing/diminishing heat transfer. The final outcome reveals that the heat transfer is highest for the sinusoidal waveform, followed by that of the triangular and then, the sawtooth. An important inference is that a symmetric periodic temperature distribution at the surface enhances heat transfer more than that of a constant surface-temperature.

Analysis of Tangent Hyperbolic over a Vertical Porous Sheet of Carreau Fluid and Heat Transfer

Abstract: The purpose of this study is to investigate the boundary layer of Carreau fluid and heat transfer over an exponentially stretching plate derived in a vertical porous with variable surface thermal flux. The partial differential equations that represent the momentum equation and heat equation are commuted into nonlinear ODEs by applying similarity transformations and results found numerically. The impact of several emerging dimensionless parameters labelled the Weissenberg number (We), the power-law index ( ), Velocity slip ( ), Thermal jump ( ), and Prandtl number ( ) on the velocity profile and heat transfer on the boundary layer are showed in detail. In more detail, also the influence of physical parameters on local skin friction and Sherwood number are studied. The shooting method with the explicit technique is used to find the solution and all results are illustrated graphically and numerically. We noted that by increasing power index, radiation parameter and velocity slip, the velocity profile increases, and the temperature profile decreases. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number.

Effect of Prandtl Number and Diameter Ratio on Laminar Natural Convection from Isothermal Horizontal Cylindrical Annuli

Abstract: A numerical investigation of transient, two-dimensional natural convection in horizontal isothermal cylindrical annuli is performed to investigate the Prandtl number and diameter ratio effect on flow and heat transfer characteristics. The finite difference method is used to solve the governing equations, in which buoyancy is modeled via the Boussinesq approximation. Both vorticity and energy equations are solved using alternating direction implicit (ADI) method and stream function equation by successive over relaxation (SOR) method. Solutions for laminar case are obtained up to Grashof number of 105 as well as three different diameter ratios, namely 1.2, 1.5, and 2.0 and the Prandtl number varies from 0.7 to 10 are considered. The computed flow patterns and temperature fields are shown by means of streamlines and isotherms, respectively, and the average heat transfer coefficients are also presented. The numerical results are summarized by Nusselt number vs. Grashof number correlations with the Prandtl number and diameter ratio as a parameter. The results of the parametric study show that the diameter ratio and Grashof number have a profound influence on the temperature and flow field and they are almost independent of a low Prandtl number fluid. The average Nusselt number increases by 25% at large of diameter ratio and Prandtl number. Good agreement with earlier available data is obtained.

Magnetohydrodynamic forced convection and heat transfer of a Casson fluid flow in an anisotropic porous channel with Isoflux boundaries

Abstract: Theoretical analysis of magnetohydrodynamic fully developed forced convective flow and heat transfer characteristics of a non-Newtonian electrically conducting Casson fluid through a porous channel filled with anisotropic porous material bounded by two impermeable horizontal walls subject to constant heat flux applied to the outer walls is investigated. The extended Darcy-Brinkmann model govern the flow inside the porous channel and accounts for the presence of the inertia term, which allows for the no-slip boundary conditions at the walls. The principal axis of anisotropic permeability is oriented from to radians. The equations governing the system are solved using the inbuilt “DSolve” in Mathematica 11.1 for the velocity and temperature profiles as well as the Nusselt number (Nu), which characterizes the rate of heat transfer in the system. The effects of various parameters on the velocity, temperature and heat transfer profiles are displayed through graphs and discussed quantitatively. From the results we observed that the velocity profile reduced as the Casson parameter (ß), anisotropic ratio (Kr), orientation angle (), and Hartmann number (Ha) increased, whereas the velocity profile increased when the Darcy number (Da) and apparent viscosity () increased. Similarly, these variables also had similar effect on the temperature profile of the fluid. On the other hand, the heat transfer profile, as measured by Nusselt number, increased when the Casson parameter (ß), anisotropic ratio (Kr) and Hartmann number (Ha) increased, while increasing the orientation angle () and apparent viscosity ( ) decreased the Heat Transfer Profile. Upon further investigation, the heat transfer profile was shown to be maximum along the path of least permeability in the anisotropic porous media under investigation.

Laminar Momentum and Heat Transfer in Channels

Abstract: In this chapter, the authors consider internal laminar flow through channels. They study momentum transfer inside smooth tubes and between two infinite parallel plates to develop pertinent parameters. Duct shape and thermal boundary conditions will affect the heat transfer. The authors also study convection heat transfer in a circular pipe and between two infinite parallel plates. For fully developed heat transfer, the heat transfer coefficient is independent of axial position. It is of interest to know the variation of the convective heat transfer coefficient with distance from the entrance. Arbitrary surface temperature variation on the tube surface with the axial distance is also studied. Since the energy equation is linear in temperature, the superposition principle can be used to construct solutions to problems with variable wall temperatures from simple step function solutions. Finding the temperature distribution is an important problem when the wall surface heat flux varies arbitrarily in the axial direction.

Performance optimization of finned surfaces based on the experimental and numerical study

Abstract: This paper presents the findings of numerical and experimental investigations into the forced convection heat transfer from horizontal surfaces with straight rectangular fins at Reynolds numbers ranging from 23600 to 150000. A test set-up was constructed to measure the heat transfer rate from a horizontal surface with a constant number of fins, fin width and fin length under different flow conditions. Two-dimensional numerical analyses were performed to observe the heat transfer and flow behaviour using a computer program developed based on the OpenFOAM platform. The code developed was verified by comparing the numerical results with the experimental results. The effect of geometrical parameters on heat transfer coefficient and Nusselt number were investigated for different fin height and width ratios. Numerical results show that one way to increase heat transfer by modifying the fin structure geometrical parameters. With the help of the obtained results, a correlation for Nusselt number was developed and presented for steady-state, turbulent flows over rectangular fin arrays for Reynolds number ranging from 23600 to 150000, Prandtl number ranging from 0.705 to 5.41, for fin height ratios h/H ranging from 0.166 to 0.333, and fin thickness to fin height ratios (t/h) between of 0.066 and 0.20. The correlation developed predicts the Nusselt number with a relative RMS error of 0.36%.

Dynamics of Heat Transfer in Magneto-Micropolar Fluids Flow Past a Vertically Expanding Sheet Featuring Prescribed Wall Temperature (PWT)

Abstract: This study assesses the motion and the dynamics of heat propagation in magneto-micropolar fluid along a sheet which vertically stretches on a two-dimensional plane in a porous material. The heat distribution is developed and evaluated under the condition of the prescribed wall temperature, constant magnetic field, thermal radiation, variable heat source and viscous dissipation. The main equations are re-formulated from partial to ordinary derivatives using similarity tools and consequently solved numerically by shooting and the Runge-Kutta Fehlberg approach. The parameters of interest are presented graphically to demonstrate their reactions on the velocity profiles, thermal field and heat transfer mechanism of the problem. The outcomes of the current investigation reveal that the heat transfer appreciates in the presence of higher Prandtl number, temperature exponent term and material parameter but decreases as the magnetic field term soars.Besides, the heat boundary structure expands and heat spread occurs as the thermal radiation, magnetic field and Eckert number terms escalates but a reverse trend is encountered as the Prandtl number, material micropolar term, Grashof number and heat exponent terms grows in magnitude. Under some limiting scenarios, the obtained data strongly correspond to the published studies in the open literature.

Boundary-Layer Disruption and Heat-Transfer Enhancement in Convection Turbulence by Oscillating Deformations of Boundary.

Abstract: In this Letter, we propose a novel strategy for significantly enhancing the heat transfer in convection turbulence. By introducing a boundary deformation of the standing-wave type, flow modulation can be realized when the amplitude is comparable or larger than the boundary-layer thickness. For a fixed moderate frequency, the entire fluid layer follows the boundary motion at small wave numbers, while only the near-wall regions are affected by the boundary deformation at large wave numbers. The heat-flux enhancement happens for the latter. For a fixed wave number and gradually increasing frequency, the vortical flows inside the wave valleys exhibit nonlinear transition and alter the distribution of boundary heat flux, and the global heat flux increases significantly at large enough frequencies. The current findings suggest that oscillating deformations of boundary can efficiently break the boundary layers, which serves as the bottleneck of global heat transfer, and open a new venue for modulating the convection turbulence.

Studying the effect of the force convection boundary condition and radius magnetic field on fluid flow and heat transfer between coaxial pipes

Abstract: An investigation of the heat transfer of Newtonian fluid flow through coaxial two pipes with variable radius ratio has been conducted with the boundary conditions of forced convection on the inner pipe walls and a radius magnetic field. This paper presents an exact analytical solution to the momentum equation and a novel semi-analytic collocation method for solving the full-term energy equation that takes Joule heating into account as well as viscous dissipation. Based on the results of the numerical fourth-order Runge–Kutta method, it was found that increasing the magnetic parameter decreased the amount of friction on the surface of the pipe walls and the rate of heat transfer. As the radius ratio of the two pipes increases, so does the skin friction and heat transfer rate on the internal pipe walls. As Eckert (Ec) and Prandtl (Pr) numbers increase, the mean temperature as well as the dimensionless temperature between the two pipes increases. The increase in Biot number (Bi) has the opposite impact on the mean temperature. As Ec, Pr, and Bi increase, so does the rate of heat transfer on the inner wall of the pipe.

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

Abstract: Investigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third-grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third-grade fluids for EMHD flow and heat transfer behavior. The least-square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third-grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third-grade fluid increases.

Experimental Measurement and Theoretical Prediction of Bubble Growth and Convection Heat Transfer Coefficient in Direct Contact Heat Transfer

Abstract: The measurement of the two-phase contact area is very important to determine the heat transfer coefficient in the process of direct contact heat transfer, but the direct measurement of the two-phase contact area is a difficult problem. The experiments are carried out utilizing a cylindrical Perspex tube of 100 cm in total height and 15 cm inner diameter. The active column height throughout the experiments is taken to be equal to 50 cm. Liquid Therminol®66 with four different initial temperatures (50 °C, 60 °C, 70 °C and 80 °C) is used as a continuous phase, while liquid R245fa at a constant temperature of 23 °C is used as a dispersed phase. In this paper, the empirical correlations between bubble growth and local convection heat transfer coefficient are obtained through modeling and measurement, and its correctness is verified by experiments. The results show that the bubble diameter is positively correlated with continuous phase temperature, flow rate ratio, and height, but the local convection heat transfer coefficient is negatively correlated with continuous phase temperature, flow rate ratio, and height. At the same time, it is found that the maximum error between the actual bubble diameter and the theoretical bubble diameter is 7%, and the error between the heat flux calculated by the local convection heat transfer coefficient and the actual heat flux is within 10%. This study provides theoretical guidance for an in-depth understanding of the direct contact heat transfer process and the development of high-efficiency waste heat recovery systems.

The influence of prandtl number on heat transfer effects around a sphere placed in a turbulent boundary layer

Abstract: Direct numerical simulation (DNS) is performed to solve the governing equations for fluid flow and heat transfer around a sphere which is placed on the bottom wall of a flume. Two way coupling is used to account for the effect of the sphere on the structure of the near-wall turbulence and on the main stream. The calculation of the thermal field is done with the same grid system used for the velocity field. Water and transformer oil were used as test fluids, with the Prandtl numbers Pr = 5.4 and Pr = 55, respectively. The heat transfer calculations were carried out at the constant mean heat flux along the bottom. For both Prandtl numbers the DNS results indicate enhancement of heat transfer coefficient associated with a flow motion toward the wall. The thermal pattern around the sphere is obtained and the effect of Prandtl number is discussed.

Laminar External Boundary Layers: Momentum and Heat Transfer

Abstract: Heat transfer from a wedge surface can be obtained by solving the laminar boundary layer energy equation. The boundary layer integral equation may be used to study boundary layer flows with pressure gradient. The authors consider the classical problem of flow over an isothermal semi-infinite flat plate set at zero angle of incidence to a uniform stream of velocity. For low-Prandtl-number fluids, the velocity boundary layer is much thinner than the thermal boundary layer. Since the boundary layer energy equation is linear in temperature, the superposition principle can be used to construct solutions to problems with variable wall temperatures and heat fluxes from simple step function solutions. In some heat transfer problems, the arbitrarily varying heat flux distribution is known, and the surface temperature distribution is required. For the solution of the integral momentum equation, Pohlhausen assumed a fourth-order polynomial for the velocity profile.

Natural Convection Heat Transfer from a Plane Wall to Thermally Stratified Environment

Abstract: The effect of linear thermal stratification in stable stationary ambient fluid on free convective flow of a viscous incompressible fluid along a plane wall is numerically investigated in the present work. The governing equations of continuity, momentum and energy are solved numerically using finite difference method with Alternating Direct implicit Scheme. The velocity, temperature distributionsand the Nusselt number are discussed numerically for various values of physical parameters and presented through graphs. ANSYS program also used to solve the problem. The results show that the effect of stratification parameter is marginalized with the increase in Prandtl number, and the increase in Grashof number does not practically vary the effect of stratification parameter.

Experimental study of natural convection heat transfer on an enclosure partially filled porous medium heated from below by constant heat flux

Abstract: This study reports on natural convection heat transfer in a square enclosure of length (L=20 cm) with a saturated porous medium (solid glass beads) having same fluid (air) at lower horizontal layer and free air fill in the rest of the cavity's space. The experimental work has been performed under the effects of heating from bottom by constant heat flux q=150,300,450,600 W/m2 for four porous layers thickness Hp (2.5,5,7.5,1) cm and three heaters length δ (20,14,7) cm. The top enclosure wall was good insulated and the two side walls were symmetrically cooled at constant temperature. Four layers of porous media with small porosity, Rayleigh number range (60.354 - 241.41) and (Da) 3.025x10−8 has been investigated. The obtained data of temperature from testing rig are used to extract the temperature distribution, local Nusselt number and average Nusselt number. Moreover, a comparison between the numerical result of the same problem published recently and present experimental results has been executed and discussed. It is evinced that; the heat transfer and fluid flow are affected by thickness of porous layer and be maximum at porous layer thickness (0.25L) with larger heater length(20cm) and heat flux (q= 600 Watt/m2) which is approximately (180%) for the average Nu when compared with (Hp=0.75L). Also, the effect of the increasing in heater length (δ) on the averaged heat transfer enhancement is more pronounced for large heater size and 25% of average enhancement is achieved for (δ =20cm) compared to (δ =7cm). However, the greater temperature distribution is found at Hp=2.5cm and 5cm at bottom and first quarter of the cavity (heater surface height Y=0 cm and Y=5 cm) respectively and minimum temperature at top (insulation wall Y=20 cm). Nearly, same shape for heat transfer for different case with clearly difference at small heater (δ=7cm).

Investigation on conjugate mixed convection through a vented chamber with heat generating and conducting rotating circular cylinders

Abstract: This paper presents a comprehensive numerical solution to investigate mixed convection heat transfer inside a vented square chamber containing two heat-generating and conducting rotating cylinders. The broad range of practical and industrial applications associated with this type of heat transfer analysis make it a fascinating field of study, particularly in the context of cooling electronic chips and ventilation systems. The ventilations are accomplished by entering air from the bottom of the left sidewall and escaping from the top of both sidewalls. The chamber's upper wall is considered cold, while the other walls are insulated. Using appropriate boundary conditions, the Galerkin finite element method is employed to simulate the Navier-Stokes and heat energy equations. This study aims to determine the optimal thermo-fluid performance within the vented chamber by analyzing the impact of geometric and governing non-dimensional parameters such as the radius (R = 0.10, 0.15, 0.20) and rotational speed of the cylinders (Ω = −3, 0, 3), Grashof (103 ≤ Gr ≤ 105), Richardson (0.1 ≤ Ri ≤ 10), and Reynolds (31.63 ≤ Re ≤ 316.23) numbers. The findings of this study have been evaluated through the quantitative calculations of the average Nusselt number and average fluid temperature. It is explored that enhancement of Nusselt number becomes as high as 208.2% for varying Reynolds numbers from 31.623 to 316.23 at R = 0.10, Ω = −3, and Ri = 1. Moreover, the rotation mode is of utmost importance in studying mixed convection heat transfer to achieve optimal thermal performance. The implications of the findings from this research are poised to profoundly impact the design and operation of similar systems, fostering enhanced thermal performance and ensuring optimal safety. Additionally, this study represents a significant contribution toward developing effective and sustainable strategies for managing surplus heat in other intricate systems.

Foundations of Convective Heat Transfer

Abstract: Heat transfer is an energy transfer process because of a temperature gradient or difference. This temperature difference is called a driving force that causes heat to flow from a high-temperature region to a low-temperature region. There are basic mechanisms or modes for heat transfer: conduction, convection, and radiation. In this chapter, the authors present their fundamental equations. The continuum and thermodynamic equilibrium concepts are also discussed. In fluid mechanics, the term field describes a quantity defined as a function of both position and time for a given region. There are two approaches to describe the motion of fluid and its associated properties in fluid mechanics: Lagrangian approach and Eulerian approach. The substantial derivative represents the observed time rate of change of a quantity caused by two factors: the change in that quantity with time at each point in the flow field and the change in that quantity with time due to fluid motion.

Free Convection Heat Transfer

Abstract: In this chapter, the authors discuss forced convection heat transfer due to greater scope of its application in engineering. However, free convection is also an equally important means to transfer energy. The thermal boundary layer thickness is an important scale to estimate the heat transfer in free convection. The fluid properties are constant except the fluid density near the hot plate. Continuity, momentum, and energy equations will be solved using the similarity method. Using the similarity variables, the partial differential equations will be transformed to ordinary differential equations. The authors present some of the recommended empirical correlations for both laminar and turbulent free convection under uniform wall temperature and uniform heat flux boundary conditions. Fin arrays are used to enhance heat transfer by free convection. Fin arrays can be modeled as vertical channels formed by vertical parallel plates. The authors also present simple correlations for free convection for enclosures along with complicated empirical correlations.

Asymptotic analysis of boundary layer flow of a fluid with temperature-dependent viscosity

Abstract: In this work, we study boundary layer flows for thermo-dependent Newtonian fluids. We first show that the governing equations admit a self-similar solution. Furthermore, an asymptotic model is used to obtain correlations on heat transfer and the skin-friction coefficient. In addition, the numerical study of the complete problem enables us to specify the domain of validity of these correlations. Finally, the obtained numerical results are used to analyze the influence of the Prandtl number on the profiles of the stream function and the temperature field, and also on parameters such as the local Nusselt number and the thickness of the boundary layer.