Layer Heat Transfer Research Articles

Influence of Shape Factor and Non-Linear Stretching of the Bullet-Shaped Object on the Mixed Convection Boundary Layer Flow and Heat Transfer with Viscous Dissipation and Internal Heat Generation

The two-dimensional incompressible axisymmetric mixed convection magnetohydrodynamic fluid flow and energy transfer over a bullet-shaped object with a non-linear stretching surface have been investigated. The main goal of this problem is to discuss the effect of the shape and size of the bullet-shaped object on the fluid velocity and temperature distributions. The present analysis has been performed in about two cases ε=0.0 and 2.0. Therefore, fluid velocity and temperature distributions have been investigated in two types of flow geometries such as the thicker surface (s ≥ 2) and the thinner surface (0 < s < 2) of the bullet-shaped object. The equations for momentum and heat transfer have been converted into ODEs by using suitable local similarity transformations. These equations have been performed with a recently developed spectral quasi-linearization method (SQLM). This method helps to identify the accuracy, validity, and convergence of the present solution. The novelty of the present work has been applying the recently developed numerical method to solve these highly nonlinear differential equations. The investigation shows that in the case of a thicker bullet-shaped object (s ≥ 2) the velocity and temperature profiles do not converse the far-field boundary condition asymptotically but cross the axis with an upright angle and the boundary layer structure has no definite shape whereas in the case of a thinner bullet-shaped object (0 < s < 2) the velocity profile converge the ambient condition asymptotically and the boundary layer structure has a definite shape. The innovation of this current work lies in the unification of relevant physical parameters into the governing equations and trying to explain how the flow properties are affected by these parameters.

Numerical investigation on radiative and evaporative characteristics of a liquid droplet radiator through Monte-Carlo method

The liquid droplet radiator (LDR), a frameless heat dissipation device, is regarded as a preferred heat control solution for megawatt-scale space power systems. Accurate calculation of evaporation loss in the droplet layer is important for LDR systems since it determines the operating life of the LDR. In the present work, a novel model based on the Monte-Carlo Method (MCM) was developed to calculate the evaporation loss of the droplet layer. Compared to previous work in the literature, this model considers the evaporation loss of the droplet layer in the thickness and length directions. The radiative heat transfer characteristics of the droplet layer are also studied. The effects of optical thickness, operation temperature, and flight time on the droplet layer's heat transfer and evaporation processes were obtained and analyzed. The calculation results show that the temperature difference between the center and the edge of the droplet layer is larger than 65 K when the optical thickness is greater than 5. The heat dissipation power no longer varies significantly when the optical thickness of the droplet layer is greater than 6. The region with a negative specific evaporation loss rate accounts for 55.2 %, 58.2 %, and 0 for the whole droplet layer with optical thicknesses of 10, 5, and 0.2, respectively. The main evaporative loss comes from the beginning 5 m of the droplet layer. This paper may provide favorable reference to the design and optimization of the LDR systems.

An MHD Marangoni Boundary Layer Flow and Heat Transfer with Mass Transpiration and Radiation: An Analytical Study

This examination is carried out on the two-dimensional magnetohydrodynamic problem for a steady incompressible flow over a porous medium. The Cu−Al2O3 nanoparticles are added to the water base fluid in order to improve thermal efficiency. The transverse magnetic field with strength B0 is applied. The governing equations formed for the defined flow form a system of partial differential equations that are then converted to a system of ordinary differential equations upon applying the suitable similarity transformations. On analytically solving the obtained system, the solutions for velocity profile and temperature distribution are obtained in terms of exponential and Gamma functions, respectively. In addition, the physical parameter of interest, the local Nusselt number, is obtained. The results are analyzed through plotting graphs, and the effect of different parameters is analyzed. Furthermore, we observe that the suction/injection parameter enhances the axial velocity. The porous and radiation parameters enhance the temperature distribution, and the suction/injection parameter suppresses the temperature distribution.

Two-Dimensional Thin Layer Convective Flow and Heat Transfer of a Dusty Fluid on a Nonlinear Stretching Sheet

Two-Dimensional Thin Layer Convective Flow and Heat Transfer of a Dusty Fluid on a Nonlinear Stretching Sheet

Mixed convection MHD boundary layer flow, heat, and mass transfer past an exponential stretching sheet in porous medium with temperature-dependent fluid properties

The mixed convection MHD boundary layer flow, heat and mass transfer of a Newtonian fluid mixture across an exponentially stretched permeable sheet in porous medium with Soret and Dufour effects subject to temperature-dependent fluid properties have been investigated numerically. The distribution of temperature and concentration at the surface is supposed to grow exponentially. Temperature is considered to affect fluid viscosity and thermal conductivity. The guiding partial differential equations with appropriate boundary conditions are converted into coupled, nonlinear ordinary differential equations with variable coefficients via a similarity transformation. Matlab's built in solver bvp4c is used to find numerical solutions. Using a graphical approach, the effects of several emerging physical parameters on velocity, temperature and concentration distributions on a flow field of a chemically nonreacting fluid mixture are examined and discussed. Results are compared to earlier literature available and found to be in good agreement. Furthermore, this research demonstrates that flow, heat and mass transmission are greatly influenced by mixed convection parameters, magnetic field, Prandtl number, viscosity, conductivity, permeability, and Schmidt number. Skin friction grows for mixed convection parameter, magnetic, viscosity. Highest growths of wall temperature and wall concentration gradients are observed for Prandtl number and Schmidt number, respectively. HIGHLIGHTS Heat and mass transfer rates increase with higher values of mixed convection parameters and Darcy parameter. To reduce heat transfer rate magnetic field may be used. Fluid with lower thermal conductivity and with higher Prandtl number may be employed to boost the cooling rate in conducting flows. Higher Schmidt enhances mass transfer rates. Suction stabilizes boundary layer growth. Soret effect can be used to separate light and medium molecular weight components from a fluid mixture and hence can be used for control of air pollution.

Dynamics of Non-Newtonian Tangent Hyperbolic Liquids Conveying Tiny Particles on Objects with Variable Thickness when Lorentz Force and Thermal Radiation are Significant

The flow via needle has prominent applications in the modern world such as nano-wires, microstructure electric gadgets, microsensors, surgical instruments and biological treatments. The present investigation focuses on boundary layer heat, flow, and mass transfer of MHD tangent hyperbolic fluid (conveying tiny particles) via a thin needle under the impacts of activation energy, non-constant thermal conductivity, heat source, and nonlinear thermal radiation. In the description of the Buongiorno model, the significant features of Brownian motion and thermophoresis have been included. Adopting appropriate transformations to the given problem specified by the set of partial differential equations yields the dimensionless form of ordinary differential equations After that, these obtained ODEs are solved numerically via MATLAB bvp4c. A comparative result with previous findings is conducted. Physical parameters’ impact on flow rate, heat, and concentration is exhibited and explained in depth. The main findings of this study are that flow patterns reduce as the magnetic parameter and the Weissenberg number grow. Higher values of Brownian motion, heat source/sink, nonlinear radiation, and thermophoretic parameter improve the thermal profile. Moreover, the rate of heat transfer for the variable property case is significantly improved. Concentration profiles reduce as the thermophoresis parameter and chemical reaction parameter grow but improve as the activation energy and Brownian motion parameter rise. The percentage increase in Sherwood number is 35.07 and 5.44 when the thermophoresis takes input in the range 0 ≤ Nt ≤ 0.2 and activation energy parameters 0 ≤ E ≤ 0.2. The Weissenberg number and power-law index parameters are all designed to boost the Sherwood number.

A Conservation-Based Transitional Boundary Layer Model

Abstract A simple, flow-physics-based model of flat-plate, transitional boundary layer skin friction and heat transfer is presented. The model is based on the assumption of negligible time-, spanwise-, and streamwise-average wall-normal velocity at the top of the boundary layer. This results in a threefold increase in boundary layer thickness over the transition region. This simple velocity assumption and its boundary-layer growth implications seem to be reasonably consistent with more sophisticated (direct numerical simulation (DNS)) modeling simulations. Only two modeling parameters need to be assumed, the Reynolds numbers at the onset and at the completion of transition, for which there is guidance based on freestream turbulence intensity for smooth plates. Several experimental datasets for air are modeled. New criteria are proposed to help define the onset and completion of transition: zero net vertical (wall-normal) velocity or mass flux (integrated in time and space, spanwise and streamwise) at the top of the boundary layer, and tripling of boundary layer thickness. Also presented is a minor improvement to a previously published unheated starting length factor for flat-plate laminar boundary layers with uniform wall heat flux.

Mixed Convection Magnetic Nanofluid Flow past a Rotating Vertical Porous Cone

Magnetic nanofluids (MNFs) have been the focus of extensive research nowadays owing to their potential usefulness as a transfer medium. This study is concerned with the boundary layer flow and heat transfer of MNF past a rotating vertical cone with the embedment of the porosity regime and mixed convection. The buoyancy opposing flow on the combined free and forced convection is being emphasized in this study to evaluate the behavior of the fluid within this region and predict the point of the boundary layer transition. The initial formulation of the model is simplified appropriately by employing the suitable similarity transformation. The package of bvp4c MATLAB is employed to execute the numerical solutions. Analysis of stability is also reported. Due to the mixed convection parameter, the opposing flow contributes towards two different alternative solutions, but the second solution is not stable. A higher local Nusselt number are achieved by increasing the concentration of magnetic nanofluid up to 2% and enlarging the mixed convection parameter under the influence of the porosity regime in the vertical rotating cone. It has been established in this study that the addition of cobalt ferrite as the magnetic nanoparticles (MNPs) is proven to have the ability in enhancing the thermal performance of the fluid.

A Chebyshev Spectral Collocation Method-Based Series Approach for Boundary Layer Flow and Heat Transfer in a Micropolar Fluid past a Permeable Flat Plate

This paper demonstrates the applicability of the large parameter spectral perturbation method (LSPM) to a coupled system of partial differential equations that cannot be solved exactly. The LSPM is a numerical method that employs the Chebyshev spectral collocation method in the solution of a sequence of ordinary differential equations (ODEs) that are derived from decomposing coupled systems of nonlinear partial differential equations (PDEs) using series expansion about a large parameter. The validity of the LSPM is applied to the problem of boundary layer flow and heat transfer in a micropolar fluid past a permeable flat plate in the presence of heat generation and thermal radiation. The coupled nature of the PDEs that define the problem under investigation precludes the option of using series-based methods that seek to generate analytical solutions even in the presence of small or large parameters. The present study demonstrates that the LSPM can easily overcome this limitation while giving very accurate results in a computationally efficient manner. For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, microrotation, and temperature profiles for selected physical parameter values. The results obtained were found to correlate with the results from a published literature. For quantitative confirmation of our findings, the LSPM numerical solutions were again validated against known results from the literature and against results obtained using the multidomain bivariate spectral quasilinearisation method (MD-BSQLM), and the results were observed to be in perfect agreement. Further accuracy validation is displayed by using residual error and solution error analysis on the governing PDEs and their underlying solutions. This study’s findings indicate that the heat generation and thermal radiation parameters have related effects on the temperature profile, enhancing both the fluid temperature and the thermal boundary layer thickness.

Influence of Slip Parameter, Viscous Dissipation and Joule Heating Effect on Boundary Layer Flow and Heat Transfer Over a Power-Law Stretching Wedge-Shaped Surface with the Correlation Coefficient and Multiple Regressions

The influence of slip parameter, viscous dissipation, and Joule heating parameter on MHD boundary layer nanofluid flow over a permeable wedge-shaped surface was analysed. The PDEs and the associated boundary conditions were transformed to a set of non-similar ODEs and the obtained system of equations was solved numerically with the help of the spectral quasi-linearization method (SQLM) by applying suitable software. This method helps to identify the accuracy and convergence of the present problem. The current numerical results were compared with previously published work and are found to be similar. The fluid velocity, fluid temperature, and nanoparticle concentration within the boundary layer region for various values of the parameters such as the slip effect, magnetic strength, Prandtl number, Lewis number, stretching ratio, viscous dissipation, suction, Brownian motion, Joule heating, heat generation, and thermophoresis are studied. It is observed that the Brownian motion, Joule heating, viscous dissipation, and thermophoresis lead to decreases in the heat and mass transfer rate. The skin friction coefficient enhances with slip, magnetic, permeability, and suction parameters, but reduces with the Brownian motion, wedge angle, and stretching ratio parameters whereas there is no effect of mixed convection, thermophoresis, heat generation parameters, the Prandtl and Eckert number.

Numerical Analysis of Boundary Layer Flow and Heat Transfer over a Shrinking Cylinder

The investigation concerning the movement of the viscous fluid and heat transfer rate when the cylinder shrinks is carried out. The role of curvature parameter and effect of cylinder parameter on skin friction and heat transfer rate were studied. The existence of a dual solution is observed and subsequently identifies which solution is stable. By using the similarity transformation, the boundary layer equations are transformed into nonlinear ordinary differential equations which are then solved numerically using bvp4c in MATLAB. The results for the skin friction coefficient, temperature gradient coefficient as well as velocity and temperature profiles are presented graphically. The effects of mass suction parameter and curvature parameter on flow and heat transfer characteristics are also presented. It is found that the dual solution existed when mass suction parameter greater or equal to 2. Cylinder surface diminished the performance of skin friction coefficient and heat transfer rate. The stability analysis result is performed to verify that the upper branch solution is stable and physically meaningful.

Experimental study of steam-air mixture thermal stratification during the dropping of containment pressure

The passive containment cooling system (PCCS) as a passive technology has been applied in Generation Ⅲ nuclear power plants. Experiments were conducted in a scale model to analyze the thermal stratification in containment during the containment pressure dropping. Results indicate that the obvious thermal stratification occurs in the containment during the transient-state heat transfer process but not during the steady-state heat transfer process. For the transient-state process, the steam-air mixture temperature increases by 2 °C for each 100 mm increase in the elevation direction of the pressure tank. The nonuniform distribution of air in containment causes thermal stratification, which is more pronounced for lower air mass fraction and higher initial containment pressure. The thermal stratification effect on the condensation heat transfer process is assessed via diffusion layer heat transfer and film heat transfer to evaluate its effect. The diffusion layer heat transfer coefficient (HTC) is strongly affected by thermal stratification, whereas no effect is observed on the film HTC. This leads to the total condensation HTC at the top of the heat exchanger is approximately 3–5 times than that at the bottom in the first 100 s of the containment pressure dropping process. To improve the overall heat transfer performance of PCCS, approaches that enhance the heat transfer capacity at the bottom of the heat exchanger should be considered for prioritization, especially the methods of steam diffusion heat transfer capacity.

Unsteady Heat and Mass Transfer Slip Flow over an Exponentially Permeable Stretching Sheet

In this paper, the problem of unsteady two-dimensional boundary layer heat and mass transfer flow over an exponentially stretching sheet embedded in a porous medium in the presence of a uniform magnetic field with thermal radiation, heat generation/absorption, and suction/blowing is analyzed numerically. Instead of no-slip boundary conditions, velocity slip, thermal slip, and mass slips at the boundary are considered. Using a suitable similarity transformation, the governing partial differential equations are transformed to a system coupled with nonlinear ordinary differential equations. The reduced equations are solved numerically by using bvp4c with the MATLAB package. A detailed parametric study is performed to illustrate the physical parameters on the velocity, temperature, and concentration profile and the local skin-friction coefficient and Nusselt and Sherwood number. Then the results are exhibited in both graphical and tabular forms. It is observed that the present results have been in close agreement with the previously published studies under some special cases.

Investigations on heat and mass transfer in gas diffusion layers of PEMFC with a gas–liquid-solid coupled model

Improvement of heat and water management in gas diffusion layers (GDL) is a critical issue to high-performance proton exchange membrane fuel cells (PEMFC). In this study, we develop a gas–liquid-solid coupled solver to simultaneously model the liquid water transport, vapor condensation, conjugate heat transfer, electric conduction and their interactions. A stochastic method is employed to reconstruct the 3D structural GDL. The compression effect on the geometry during assembly is included by applying a 10% compression deformation before converting to the solid fibrous zone in the simulation. The micro-porous layer (MPL) cracks are assumed to be the intake paths of the water transport. The impacts of the liquid water distribution on the heat transfer are investigated. For the whole heat transfer process, the heat conduction is the major approach through the solid fibrous layers both in dry and wet GDL, while the water transport accompanied heat conduction and convection are also crucial in wet GDL. However, the effects of water transport on the electrical conduction can be ignored due to the significant differences of the electrical conductivities between water and solid fibrous layers. Besides, the interactions between vapor condensation and heat transfer are explored, it is shown that the temperature of the fibers under the rib is lower than that of other fibers, leading to a higher condensate water saturation and a lager droplet size at the corresponding positions. The results presented here are significantly helpful to deepen our knowledge on the interactions between heat transfer and water transport, and guide the heat and water management in the PEMFC.

Effect of viscous dissipation and thermal radiation on MHD flow and heat transfer for a power-law fluid with variable fluid properties over a permeable stretching sheet

This manuscript considers the problem of MHD boundary layer flow and heat transfer of power – law fluid with variable fluid properties over a nonlinear stretching sheet in the presence of viscous dissipation and thermal radiation subject to a non-uniform transverse magnetic field and non-uniform heat generation. The governing boundary layer equations are transformed into a system of non-linear ordinary differential equations using suitable transformation which are solved numerically using fourth order Rung-Kutta integration scheme coupled with the shooting method. The effects of various parameters on the velocity, temperature, local skin-friction and the local Nusselt number are presented and discussed. We found that is as the radiation parameter R increases the temperature of a power-law fluid and the Nusselt number increase, while the viscosity parameter increasing leads to decreasing on the velocity of the fluid and local skin-friction.

Erratum to “Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux”

We would like to acknowledge the misprinted terms in our published paper “Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux” [Chin. Phys. B 23 044702 (2014)]. Since only two misprints exist and the main results of the published paper are correct, we present the correct equations in this erratum.

Bödewadt Flow and Heat Transfer in Nanofluid over a Permeable and Radially Stretching Disk

A Bödewadt boundary layer flow and heat transfer problem in nanofluid was investigated in this study for suction/injection as well as combined effects of suction/injection and radial stretching disk. Similarity variables were introduced to transform the three-dimensional flow into a system of ordinary differential equations. Moreover, similar to the Bödewadt heat transfer problem in a viscous fluid, adequate suction is also required so that similarity solutions exist for nanofluid problems with no other boundary effects such as a partial slip or stretching disk. Both the suction and stretching disk effects can suppress the natural oscillatory behavior of flow apart from reducing the momentum and thermal boundary layer thicknesses. As expected, injection acts oppositely. However, the skin friction coefficient and heat transfer rate for Bödewadt flow increase with the increasing suction and stretching parameters. As for stagnant disk, increasing the nanoparticle volume fraction can enhance the wall shear stress, whereas nanofluid can only enhance the heat transfer when both the suction and nanoparticle volume fraction are sufficiently small. For radially stretching disk, both the local skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction increases. However, for larger suction, a smaller volume fraction of nanoparticles yielded enhanced heat transfer than the larger volume fraction of nanoparticles.

Chemical entropy generation and second-order slip condition on hydrodynamic Casson nanofluid flow embedded in a porous medium: a fast convergent method

The chemical entropy generation analysis is an approach to optimize the performance of different thermal systems by investigating the related irreversibility of the system. The influences of second-order slip with the chemical reaction on the boundary layer flow and heat transfer of a non-Newtonian nanofluid in a non-Darcian porous medium have been investigated numerically. Simultaneous solutions are presented for first and second-order velocity slips. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. The current work differs from the previous studies in the application of a new second-order slip velocity model. The Casson fluid model is applied to characterize the non-Newtonian fluid behavior. The effect of the second slip parameter on the present physical parameters was discussed through graphs and it was found that this type of slip is a very important one to predict the investigated physical model. The present study provides two fast convergent methods on the semi-infinite interval, namely Chebyshev collocation method and optimal homotopy analysis method are used to analyze the fluid flow, heat, and mass transport. Compared with available analytical and numerical solutions, current methods are effective, quickly converging, and with great accuracy. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics.

Stability Analysis of Boundary Layer Flow and Heat Transfer of Fe2O3 and Fe-Water Base Nanofluid οver a Stretching/Shrinking Sheet with Radiation Effect

In this paper, the radiation and slip effects are investigated on the boundary layer flow and heat transfer of Fe2O3 and Fe-water base nanofluids over a porous stretching/shrinking sheet. A similarity transformation is used to convert the system of governing partial differential equations into ordinary differential equations, which are then numerically solved in Maple software with the help of the shooting technique. At different ranges of the applied parameters, dual solutions are found. The effects of the different physical factors such as radiation, nanoparticle volumetric fractions, suction, and slip parameters are determined and discussed. The skin-friction coefficient and local Nusselt number are influenced significantly by the applied parameters. In the boundary layer regime, the increase in nanoparticle volume fractions and radiation parameters enhance the temperature and boundary-layer thicknesses, while increasing Prandtl number, suction, and thermal slip parameters decrease the temperature and reduce thermal boundary-layer thicknesses. The suspension of iron nanoparticles shows more enhancement in skin friction and Nusselt number than the iron oxide nanoparticles in base fluid water.

Heat Transfer Analysis of Micro Polar Fluid with AL2O3 and CuO Hybrid Nanofluid Over a Plate with and Without Out Viscous Dissipation

Abstract: This work analysis investigated with the boundary layer stream and heat transfer aspects of a micropolar nanofluid over a porous shrinking sheet with thermal radiation. The boundary layer equations governed by the partial differential equations are transformed in to a set of ordinary differential equations with the help of suitable local similarity transformations. The coupled nonlinear ordinary differential equations are solved by the commercial MATLAB code bvp4c.The solutions of dimensionless velocity ,velocity gradient and temperature profiles are analyzed by the effect of various controlling flow parameters nonlinear parameter ,material property and Eckert number. and temperature and Prandtl number. Physical quantities such as skin frication coefficient, local heat, computed. Keywords: Viscous effects .flat plate, Nanofluid, hybrid nanofluid, micro polar fluid , local Nusselt number, skin friction, micro rotation