Wall Temperature Gradient Research Articles

Soret and Dufour Effects on Viscoelastic Radiative and Heat Absorbing Nanofluid Driven by a Stretched Sheet with Inclined Magnetic Field

An investigation has been performed to analyze the impacts of Soret and Dufour on natural convective and heat absorbing flow of viscoelastic radiative nanofluid driven by a linearly stretched sheet considering inclined magnetic field. By making use of suitable linear transformations, the mathematical equations of problem are changed into the extremely non-linear coupled system of ordinary differential equations. Further, solutions of these differential equations are obtained by implementing GFEM (Galerkin finite element method). The consequence of various controlling pertinent parameters on nanofluid velocity, solutal concentration, temperature and nanofluid concentration are illustrated by means of various graphs while from engineering aspect numerical values of the shear stress, wall temperature gradient, solutal and nanoparticles concentration rate at the stretched sheet are presented in different tables. The numerical results are compared for mono and double diffusive nanofluids which yield that the aligned magnetic field, viscoelasticity, solutal and Brownian diffusivity have significant impacts on the flow field. The reliability of implemented method is authenticated by comparing our results with the previously published results under certain conditions, which signifies the correctness of the implemented method. The present investigation is applicable in several industrial processes such as coolant application, nano-drug delivery, cooling of microchip, heat exchanger technology, biological fluid movement and oceanography etc.Keywords: Magnetic field; Viscoelastic nanofluid; Thermal radiation; Heat absorption

Analytical and numerical approaches for Falkner–Skan flow of MHD Maxwell fluid using a non-Fourier heat flux model

PurposeThis paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects.Design/methodology/approachFlow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method.FindingsThe solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models.Research limitations/implicationsAn important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux.Originality/valueCurrent problem even in case of Newtonian fluid has not been attempted previously.

MODELING AND SIMULATION OF THE NANOFLUID TRANSPORT VIA ELASTIC SHEETS

The field of nanofluidics research has spanned over the past decade with a variety of promising applications. We investigate the “laminar boundary layer flow” of a Newtonian nanofluid past a moving extendable/contractable horizontal plate with surface velocity and thermal slip effects. The passively controlled nanofluid model (PCM) is considered. Such models are physically more realistic as compared to the “actively controlled models” (ACM). Using Lie symmetry group method, the governing equations are reduced by a set of highly coupled nonlinear ODE’s with thermo-solutal coupled boundary conditions. The reduced equations are solved numerically by a generalized collocation method. The influences of the emerging parameters on the local skin friction factor and the local Nusselt number are depicted numerically. The skin friction is decreased as the thermophoresis and buoyancy ratio parameters are decreased. The heat transfer rates reduce with thermophoresis and buoyancy ratio parameters. Velocity slip also leads to a rise in wall temperature gradient. This study is relevant to near-wall flows in nanofluid fuel cells, nano-materials processing, etc.

The effect of lateral thermal coupling between parallel microchannels on two-phase flow distribution

Evaporating flows in parallel channels occurring in a variety of industrial heat exchange processes can encounter non-uniform flow distribution between channels as a result of two-phase flow instabilities. Such flow maldistribution can have a negative impact on the performance, robustness and predictability of these systems. Two-phase flow modeling can assist in understanding the mechanistic behavior of this flow maldistribution, as well as determine parametric trends and identify safe operating conditions.The work described in this paper expands on prior two-phase flow distribution modeling efforts by including and assessing the effect of thermal conduction in the walls surrounding the parallel channels. This thermal conduction has a critical dampening effect on wall temperature gradients. In particular when a channel is significantly starved of flow rate and risks dryout, channel-to-channel thermal coupling can redistribute the heat load from the flow-starved channel to neighboring channels. The model is used to simulate the two-phase flow distribution in a system of two parallel channels driven by a constant flow rate pump. A comparison between thermally isolated and coupled channels indicates that thermally coupled channels are significantly less susceptible to maldistribution. Furthermore, a parametric study reveals that flow maldistribution is only possible in thermally coupled systems beyond a certain critical heat flux threshold. This threshold heat flux increases as the lateral wall conductance is increased, converging to a constant value in the limit of very high lateral conductance.

Determining solid-fluid interface temperature distribution during phase change of cryogenic propellants using transient thermal modeling

Control of boil-off of cryogenic propellants is a continuing technical challenge for long duration space missions. Predicting phase change rates of cryogenic liquids requires an accurate estimation of solid-fluid interface temperature distributions in regions where a contact line or a thin liquid film exists. This paper described a methodology to predict inner wall temperature gradients with and without evaporation using discrete temperature measurements on the outer wall of a container. Phase change experiments with liquid hydrogen and methane in cylindrical test cells of various materials and sizes were conducted at the Neutron Imaging Facility at the National Institute of Standards and Technology. Two types of tests were conducted. The first type of testing involved thermal cycling of an evacuated cell (dry) and the second involved controlled phase change with cryogenic liquids (wet). During both types of tests, temperatures were measured using Si-diode sensors mounted on the exterior surface of the test cells. Heat is transferred to the test cell by conduction through a helium exchange gas and through the cryostat sample holder. Thermal conduction through the sample holder is shown to be the dominant mode with the rate of heat transfer limited by six independent contact resistances. An iterative methodology is employed to determine contact resistances between the various components of the cryostat stick insert, test cell and lid using the dry test data. After the contact resistances are established, inner wall temperature distributions during wet tests are calculated.

Flow and heat transfer of Casson fluid over an exponentially shrinking permeable sheet in presence of exponentially moving free stream with convective boundary condition

ABSTRACTThis paper is aimed to throw a light on the steady boundary layer flow and heat transfer of a non-Newtonian Casson fluid over an exponentially permeable shrinking sheet in the presence of exponentially moving free stream with convective boundary condition. Using similarity transformations, the self-similar forms of the governing equations are obtained and then solved numerically by shooting technique. Dual solutions of the problem are also obtained. It is found that wall temperature gradient decreases with the increasing values of convective parameter. It is interesting to note that as suction and the fluid material parameter increase, wall temperature gradient decreases.

Mixed convection with entropy generation of nanofluid in a lid-driven cavity under the effects of a heat-conducting solid wall and vertical temperature gradient

Mixed convection combined with entropy generation of an alumina–water nanofluid in a lid-driven cavity with a bottom solid wall of finite thickness and conductivity has been examined numerically. Governing equations formulated in dimensionless stream function and vorticity variables on the basis of a single-phase nanofluid model under the effect of Brownian diffusion have been solved by finite difference method of the second-order accuracy. The effects of Richardson number (Ri = 0.01–10.0), thermal conductivity ratio (1.0 ≤ K ≤ 20.0), solid wall thickness (0.1 ≤ δ ≤ 0.3) and nanoparticles volume fraction (0 ≤ ϕ ≤ 0.05) on streamlines, isotherms and isentropic lines as well as average Nusselt number at solid–fluid interface and rate of fluid flow have been analyzed. It has been found that an increase in nanoparticles volume fraction leads to the heat transfer enhancement and reduction of the average Bejan number.

Flame Dynamics inside Rectangular Meso scale Channels

The present work is focused on the experimental study of flame dynamics in preheated meso-scale straight channels of various aspect ratios (2, 5, 12 and 15) and inlet dimensions.Premixed methane-air mixture were used for the reported experiments. To maintain a positive wall temperature gradient inside the channel, the lower part of the rectangular channels were heated at a constant temperature using an external electric heater. Laminar premixed flames were stabilized inside these channels. Various flame propagation modes such as concave, planar, and convex flames with respect to unburned mixture. Concave flames lead to flashback whereas convex flames lead to blowout. Increase in aspect ratio and decrease of flow velocity leads to flame flashback.

Numerical study of the influence of the convective heat transport on acoustic streaming in a standing wave.

Within this work, acoustic streaming in an air-filled cylindrical resonator with walls supporting a temperature gradient is studied by means of numerical simulations. A set of equations based on successive approximations is derived from the Navier-Stokes equations. The equations take into account the acoustic-streaming-driven convective heat transport; as time-averaged secondary-field quantities are directly calculated, the equations are much easier to integrate than the original fluid-dynamics equations. The model equations are implemented and integrated employing commercial software COMSOL Multiphysics. Numerical calculations are conducted for the case of a resonator with a wall-temperature gradient corresponding to the action of a thermoacoustic effect. It is shown that due to the convective heat transport, the streaming profile is considerably distorted even in the case of weak wall-temperature gradients. The numerical results are consistent with available experimental data.

Effects of Radiation and Viscous Dissipation on Transient Free Convection Heat Transfer Flow Past a Hot Vertical Surface in Porous Media

The radiation effects on unsteady transient free convection flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity taking viscous dissipation onto account has been carried out. Thermal radiation effects are simulated via a radiation-conduction parameter (),rK based on the Rossseland diffusion approximation. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalzed using appropriate transformations and then solved subject to physically realistic boundary conditions using the Ritz finite element method. The computed numerical results for velocity(),u temperature(),θ shear stress function()τ and wall temperature gradient function()Nu are presented through the graphs and tables for air (0.71)rP= and water (7.00).rP= It has been found that increasing thermal radiation parameter ()rKcauses a considerable increase in the flow velocity .u Temperature θ is significantly increased within the boundary layer with a rise in.rK The velocity is found to decrease with an increase in inverse permeability parameter ()pK and increases with increase in the Grashof number ()rG and Eckert number ().

Towards the minimization of thermodynamic irreversibility in an electrically actuated microflow of a viscoelastic fluid under electrical double layer phenomenon

We discuss the entropy generation minimization for electro-osmotic flow of a viscoelastic fluid through a parallel plate microchannel under the combined influences of interfacial slip and conjugate transport of heat. We use in this study the simplified Phan-Thien–Tanner model to describe the rheological behavior of the viscoelastic fluid. Using Navier’s slip law and thermal boundary conditions of the third kind, we solve the transport equations analytically and evaluate the global entropy generation rate of the system. We examine the influential role of the following parameters on the entropy generation rate of the system, viz., the viscoelastic parameter (εDe2), Debye–Hückel parameter κ¯, channel wall thickness (δ), thermal conductivity of the wall (γ), Biot number (Bi), Peclet number (Pe), and axial temperature gradient (B). This investigation finally establishes the optimum values of the abovementioned parameters, leading to the minimum entropy generation of the system. We believe that results of this analysis could be helpful in optimizing the second-law performance of microscale thermal management devices, including the micro-heat exchangers, micro-reactors, and micro-heat pipes.

Numerical assessment of solar energy aspects on 3D magneto-Carreau nanofluid: A revised proposed relation

Motivated by countless applications of nonlinear materials in the field of science and engineering, we establish a mathematical relation for 3D radiative flow of a magneto Carreau nanofluid over a bidirectional stretched surface. Additionally, the features of nanoparticles mass flux condition are occupied in this investigation. Practically, this recently recommended approach is more realistic where we assume that the nanoparticle flux is zero and nanoparticle fraction adjusts itself on the boundaries accordingly. With this convincing and revised relation, the features of Buongiorno's relation on 3D Carreau liquid can be applied in a more effective way. An appropriate transformation is vacant to alter the PDEs into ODEs and then tackled numerically by employing bvp4c scheme. The numerous consequence of scheming parameters on the Carreau nanoliquid velocity components, temperature and concentration fields are portrayed graphically and deliberated in detail. The numerical outcomes for local skin friction and the wall temperature gradient for nanoliquid are intended and vacant through tables. The outcomes conveyed here manifest that impact of Brownian motion parameter on the rate of heat transfer for nanoliquids becomes negligible for the recently recommended revised relation. It is notable that the magnetic parameter M is the diminishing function of velocity components f′(η) and g′(η) , while it enhance for temperature of Carreau liquid for both shear thinning/thickening liquids. Moreover, it is noted that the impact of the Brownian motion Nb and thermophoresis parameter Nt on the concentration of the Carreau nanofluid is quite opposite. For authentication of the present relation, the achieved results are distinguished with earlier research works in specific cases and marvelous agreement has been noted.

Analysis of hydromagnetic natural convection radiative flow of a viscoelastic nanofluid over a stretching sheet with Soret and Dufour effects

PurposeThe purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.Design/methodology/approachThe governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.FindingsNumerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.Originality/valueStudy of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.

Numerical investigation of cutting edge effect on fluid flow and heat transfer for in-phase trapezoidal air channels

This work is concerned with the numerical investigations of heat transfer and friction factor penalty inside trapezoidal in-phase corrugated-plate air channels. The influence of the flow rate represented by Reynolds number (100–1000), corrugation aspect ratio (0.2–0.5) and cutting edge ratio (0–0.6) on the flow characteristics and heat transfer was investigated. By cutting the sharp edged corners for trapezoidal channel, the large lateral vortex of the triangular channel was gradually damped resulting in lower recirculation area, lower recirculation velocities and lower velocity gradients damping the high peaks of the shear stress observed in the triangular case resulting in lower isothermal friction factor. However, the mixing effect produced by the lateral vortex decreased with its damping, which led to less uniform temperature profile resulting in lower sharper wall temperature gradients with thicker boundary layer thickness, so lower values of the Nusselt number were obtained. New correlations were developed based on the present results to evaluate Nusselt number and friction factor as a function of Reynolds number, corrugation aspect ratio, relative spacing ratio and cutting edge ratio for different corrugation shapes. The predicted results are consistent with the numerical and experimental data and lie within ±10% deviation.

Performance evaluation of compact channels with surface modifications for heat transfer enhancement: An interferometric study in developing flow regime

Performance evaluation of surface roughened compact channels for heat transfer applications has been investigated using non-intrusive, real time laser-based interferometric technique with water as the coolant medium. The lower wall of the channel has been roughened by creating hemispherical inward dimples. Projection data of the temperature field has been recorded using a Mach Zehnder interferometer. In order to facilitate direct comparison, experiments have also been conducted in smooth channel of similar dimensions. Results have been presented in the form of thermal boundary layer profiles, whole field temperature distributions and local variations of heat transfer coefficients. Direct interferometric measurements clearly reveal the disruption of thermal boundary layer due to the presence of inward dimples. Near wall temperature gradients were seen to be stronger in the case of dimpled channel in comparison with that of the smooth one resulting into a clear enhancement in heat transfer rates. At low Reynolds numbers, variation of heat transfer coefficients along the length of the dimpled channel showed the presence of local maxima. On the other hand, the corresponding profiles for the smooth channels showed a monotonic decrease with respect to the axial direction. The dynamic measurements, that are purely non-intrusive, revealed an improved thermal performance of surface roughened compact channels.

Analysis and comparison of internal and external temperature measurements of a tubular oscillating heat pipe

The current study examines the relationship between internal/fluidic and external/wall temperature measurements along the adiabatic section of an operating tubular oscillating heat pipe (T-OHP) for varying heat inputs. Temperature measurements were achieved using type-T thermocouples located either inside or along the OHP wall in the region between the evaporator and condenser. Measurements were utilized to elucidate the effects of wall thermal capacitance, external wall temperature gradient, and internal fluid advection. The internal, single-phase heat transfer coefficient was estimated, and the effective thermal conductivity of the OHP was determined. A 4-turn copper T-OHP (3.25mm ID) was charged with water (75% by volume) and tested in the bottom-heating condition. Heat input was varied in increments of 25W from 60W to 300W. Results indicate that the external thermocouples were unable to capture frequency components larger than ∼1Hz. Internal measurements indicate that average, evaporator-side fluid oscillation frequencies varied from ∼1.5Hz at 60W to ∼2.5Hz at 300W, whereas condenser-side frequencies remained fairly constant at ∼0.5Hz. The frequency transfer function corresponding to the thermal resistance network between the internal/external thermocouples was found to be constant across all tested power inputs. The low-frequency, large-amplitude changes in internal temperature associated with bulk fluid motion were not immediately measured at the external OHP tube surface. The effective thermal conductivity calculated using only external temperature measurements was found to be 4–12% lower than that calculated using internal measurements. The maximum, calculated effective thermal conductivity using internal or external temperature measurements was 15,300W/m·K and 14,000W/m·K, respectively. This difference arises from there being a smaller, length-wise temperature gradient along the fluid columns than along the tube wall due to the strong advection component of OHP heat transfer. Tube wall conduction was found to account for 2–10% of the overall heat transfer, with its significance decreasing as fluid advection increased at higher heat inputs. The heat transfer coefficient for single-phase fluid oscillation inside the OHP was estimated to be ∼1000W/m2K for power inputs larger than 100W; corresponding to Nusselt numbers between 4 and 6.

Mixed Convective Fully Developed Flow in a Vertical Channel in the Presence of Thermal Radiation and Viscous Dissipation

The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.

Dynamics of premixed methane/air mixtures in a heated microchannel with different wall temperature gradients

The unsteady flame propagation mode (FREI) is affected by the wall temperature gradient. As the temperature gradient approaches zero, the mixture ignites at its auto-ignition temperature, frequency decreases and this leads to extinction of FREI mode.

HYDROMAGNETIC NATURAL CONVECTION FLOW IN A NON-DARCY MEDIUM WITH SORET AND DUFOUR EFFECTS PAST AN INCLINED STRETCHING SHEET

The investigation of magnetohydrodynamic natural convection flow of an incompressible, electrically conducting, viscous, chemically reactive, and heat-absorbing fluid with combined heat and mass transfer past an inclined linearly stretching sheet when heat and mass fluxes are variable in nature, considering thermodiffusion and diffusion-thermo effects for the Forchheimer extended Darcy model, is carried out. To ease the analysis and process of computation, similarity transformation is used to convert the governing partial differential equations into ordinary differential equations. The Green–Swigert technique in conjunction with the Runge–Kutta fourth-order method is used to solve the transformed equations. Detailed computations for fluid velocity, fluid temperature, and species concentration as well as wall velocity gradient, wall temperature gradient, and wall concentration gradient are carried out for a range of values of pertinent flow parameters to analyze the physics of the flow. Increasing Forchheimer number (local inertia parameter) leads to a fall in fluid velocity because of a corresponding rise in Forchheimer impedance. The kind of study we have performed here has various applications in engineering and may have a bearing on problems of practical interest, namely, inclined plate clarifiers, oil–water separators, sedimentation equipment such as inclined plate settlers, fabrication of thin film, and so on.

Numerical analysis of unsteady 3D flow of Carreau nanofluid with variable thermal conductivity and heat source/sink

Inspired by modern deeds of nanotechnology and nanoscience and their abundant applications in the field of science and engineering, we establish a mathematical relation for unsteady 3D forced convective flow of Carreau nanofluid over a bidirectional stretched surface. Heat transfer phenomena of Carreau nanofluid is inspected through the variable thermal conductivity and heat generation/absorption impact. Furthermore, this research paper presents a more convincing approach for heat and mass transfer phenomenon of nanoliquid by utilizing new mass flux condition. Practically, zero mass flux condition is more adequate because in this approach we assume nanoparticle amends itself accordingly on the boundaries. Now the features of Buongiorno’s relation for Carreau nanofluid can be applied in a more efficient way. An appropriate transformation is vacant to alter the PDEs into ODEs and then tackled numerically by employing bvp4c scheme. The numerous consequence of scheming parameters on the Carreau nanoliquid velocity components, temperature and concentration fields are portrayed graphically and deliberated in detail. The numerical outcomes for local skin friction and the wall temperature gradient for nanoliquid are intended and vacant through tables. The outcomes conveyed here manifest that impact of Brownian motion parameter Nb on the rate of heat transfer for nanoliquids becomes negligible for the recently recommended revised relation. Addationally, for authentication of the present relation, the achieved results are distinguished with earlier research works in specific cases and marvelous agreement has been noted.