Thermal Stratification Parameter Research Articles

Thermal Entrainment in the Core Regions of Transitional Plane Fountains in Linearly Stratified Ambient Fluids

Thermal entrainment is an integral feature of free-shear flows involving temperature changes, including fountains (negatively buoyant jets). The understanding of thermal entrainment is essential for applications involving thermal stratification such as that in a solar water storage tank. In this study, thermal entrainment in the core regions of transitional plane fountains in linearly-stratified ambient fluids is studied numerically over a range of the Froude number, Reynolds number, and dimensionless thermal stratification parameter. The results show that thermal entrainment has a negligible effect on the inner core region, but is significant in the outer core region, particularly at the interfaces among the upflow, downflow, and ambient fluid, and the thermal entrainment parameter, which quantifies the extent of thermal entrainment, decreases with height or in a stronger stratification, but increases with increasing Froude number or Reynolds number. Several numerical relations are obtained with the numerical results for the thermal entrainment parameter.

Thermo-solutal dual stratified convective magnetized fluid flow from an exponentially stretching Riga plate sensor surface with thermophoresis

A theoretical study is presented for the coupled thermo-solutal free convection two-dimensional boundary layer flow of a of a magnetized fluid from an exponentially stretched magnetic sensor (Riga plate) surface. Heat generation/absorption, nonlinear thermal radiation and thermophoretic body force effects are included. Furthermore, thermal and solutal stratification are also featured in the boundary layer model. The derived nonlinear partial differential equation system with associated wall (sensor surface) and free stream boundary conditions is transformed to system of ordinary differential equations (ODE) via applicable similarity variables. A numerical solution is developed with the efficient Runge–Kutta–Fehlberg (RKF) technique with a shooting numerical method, in MATLAB software using the RKF-45 method. The graphical profiles were represented to examine the impacts of physically parameterics on the important physical stream features. Streamline and isotherm plots are also included for thermal buoyancy effect (Grashof number).Validation of solutions with earlier simpler models is included. A relatively well agreement is achived between model prediction and the benchmark value. Values for skin friction factor, Nusselt number and Sherwood numbers are also tabulated to quantify momentum, heat and mass (species) transfer characteristics at the sensor surface. The results indicate that the significant depletion in temperature accompanies accumulation in magnetization and thermal stratification parameters. Significant accumulation in mixed convection and Riga plate electrode width parameter enhance the concatenation profiles. Nusselt number grows substantially as thermal stratification and radiative parameter increases. Sherwood number grows substantially as solutal stratification, thermophoresis and Schmidt parameter increases. The present study generalizes previous models to include simultaneously exponential stretching, thermophoresis, thermal and solutal (mass) stratification and heat source/sink effects.

MHD flow of hybrid nanofluid past a stretching sheet: double stratification and multiple slips effects

Studies of hybrid nanofluids flowing over various physical geometries and conditions are popular among researchers to understand the behavior of these fluids. Thenceforth, the numerical solutions for hybrid Ag-CuO/H2O nanofluid flow over a stretching sheet with suction, magnetic field, double stratification, and multiple slips effects are analyzed in the present study. Governing equations and boundary conditions are introduced to describe the flow problem. Then, similarity variables are applied to transform the equations into non-linear ordinary differential equations and boundary conditions. The numerical computation for the problem is done in Matlab (bvp4c solver), and the results are presented in tables and graphs. It is found that the rise in solutal slip and stratification parameters reduces the Sherwood number. Meanwhile, the increase in thermal slip and stratification parameters lowers the Nusselt number. The skin friction coefficient is observed to increase with the augmentation of the hydrodynamic slip parameter.

Investigation of thermal stratification and nonlinear thermal radiation in Darcy-Forchheimer transport of hybrid nanofluid by rotating disk with Marangoni convection

In current frontier of fluid technology, hybrid nanofluid has sparked the curiosity of investigators due to its thermal characteristics and potential which gives an amended outcome compared to nanofluid in improving the heat transfer efficiency. Nanoparticles like (Ferro and Alumina ) and (Copper Cu and Titanium ) with water as base fluid are incorporated. Due to such properties, this article investigated the 3-D steady flow of hybrid nanofluid with the features of thermal stratification and nonlinear thermally radiative over a rotating disk with the Marangoni convection. The coupled transport equations (PDEs) are renovated into the nondimensional ODEs via suitable similarity variables after that cracked numerically through bvp4c solver via the computational software MATLAB. The physical and numerical outcomes of governing parameters such as thermal radiation parameter, thermal stratification parameter, local inertial parameter, Prandtl number, local Reynolds number and porosity parameter against governing flow equations are illustrated through graphs and tables. From the outcomes, it is observed that velocity has positive magnitude for porosity parameter, Reynolds number and variable permeability. The porosity parameter causes an increment in temperature distribution.

Non-Newtonian Cross fluid flow through a porous medium with regard to the effect of chemical reaction and thermal stratification phenomenon

A comprehensive study encompassing a general development and a presentation of results for the influence of the chemical reaction on the laminar Cross fluid flow and heat mass transfer is made here. The motion of the fluid is assumed due to the stratified stretching sheet which embedded in a porous medium. Some of important characteristics of the fluid such as the variable thermal conductivity and its dependence on the temperature field are mentioned. Accordingly, some account of the possible effects of heat generation on heat mass transfer in fluid flows is given. Numerical treatments have been introduced for the resulting coupled ordinary differential equations. Then, the results of the variation in the velocity profile, the temperature profile and the concentration profile due to porous parameter, thermal conductivity parameter, heat generation parameter, thermal stratification parameter and chemical reaction parameter are presented graphically. At the proposed physical conditions for the problem, the Sherwood number, the Nusselt number or the temperature gradient and the local skin friction coefficient were measured. It is interesting to observe that, both the solutal and the thermal stratification phenomena plays a dominant role in the mechanism of heat and mass transfer. Also, regarding the warming factors within the thermal boundary layer, both Darcy parameter and heat generation parameter have been proposed which are of special interest in heat transfer problems. Finally, the results pointed out the efficiency of the proposed numerical method, where it gives a good representation describing the mechanism of the flow, heat and mass transfer.

MHD Analysis of Couple Stress Hybrid Nanofluid Free Stream over a Spinning Darcy-Forchheimer Porous Disc under the Effect of Thermal Radiation

This article develops the semianalytical analysis of couple stress hybrid nanofluid free stream past a rotating disc by applying the magnetic flux effects and radiation of thermal energy. The analysis of such kind of mixed convective flow is most important due to numerous industrial applications such as electronic devices, atomic reactors, central solar energy equipment, and heat transferring devices. The impact of variable permeability is also considered in the study. The permeability of the disc obeys the Darcy-Forchheimer model. The hybrid nanofluid is composed of water, titanium dioxide, and aluminum oxide. The set of governing equations in the PDE form are transformed to couple ODEs by applying similarity transformations. The ODE set are solved by applying the technique of HAM. The graphs of impacts of numerous physical parameters over momentum, energy, and concentration profiles are drawn in computer-based application Mathematica 11.0.1. In the sundry physical parameters, the porosity parameter, Reynolds number, inertial parameter, Prandtl number, Schmidt number, couple stress, and quotient of rotational momentum to elongating rate are included. During the analysis, it is found that the momentum profile of the couple stress hybrid nanofluid enhances with local inertial parameter, couple stress parameter, porosity parameter, and Reynolds number but declines for the growth in Hartmann number. Heat transfer rate enhances for radiation parameter but decreases in variable for temperature, thermal stratification parameter, thermophoresis parameter, and Brownian parameter.

Comparative study of hybrid and nanofluid flows amidst two rotating disks with thermal stratification: Statistical and numerical approaches

The flow of nanofluids is of great importance because of their substantial industrial usage and alluring heat transfer capabilities. Recently, an innovative notion namely “hybrid nanofluid” has replaced the customary nanofluid flows to further enhance the heat transfer capabilities. We in this envisaged mathematical model are heading in the same direction and are intended to present a comparative analysis of the heat transfer competence of two time-dependent fluid models namely; hybrid nanofluid (Copper–Iron Oxide, Manganese- Zinc ferrite/Diathermic oil) (Cu-Fe2O4, Mn-ZnFe2O4/DO) and simple nanofluid (Mn-ZnFe2O4/DO) flows amidst two rotating disks in a porous media with Darcy-Forchheimer effect. The subject flows are assisted by the thermal stratification with nonlinear radiation effects. A blend of numerical “bvp4c” and statistical “Response Surface Method (RSM)” approaches is utilized to analyze the envisioned mathematical model. Tabulated and graphical depiction of the outcomes is given to comprehend their appraisal. It is comprehended that the radiation and thermal stratification parameters possess differing trends for the fluid temperature profile. Furthermore, it is observed that the parameter estimation and significance indicate both skin friction coefficient models are similar. The fitted model for skin friction and Nusselt number are the best fit where the normality assumption is satisfied.

Stratified heat transfer of magneto-tangent hyperbolic bio-nanofluid flow with gyrotactic microorganisms: Keller-Box solution technique

Abstract The purpose of the present investigation is to examine the heat, mass and microorganism concentration transfer rates in the magnetohydrodynamics (MHD) stratified boundary layer flow of tangent hyperbolic nanofluid past a linearly, uniform stretching surface comprising gyrotactic microorganisms as well as nanoparticles. The governing PDEs with relevant end point conditions are molded into a non-dimensional ordinary differential equation (ODE) form by means of the similarity transformation. The numerical solution of dimensionless problem is acquired within the frame of robust Keller-Box technique. The velocity, temperature, mass and motile microorganism density are investigated graphically within the context of different significant parameters. Numerical results have been inspected via plots and table (namely as the local Nusselt number, the local wall mass flux and the local microorganisms wall flux). This article proves that the energy, concentration and motile microorganism density reduce with increase in thermal, solutal and motile density stratification parameters. The asserted outcomes are beneficial to enhance the cooling and heating processes, energy generation, thermal machines, solar energy systems, industrial processes etc.

High-resolution temporal detection of cyanobacterial blooms in a deep and oligotrophic lake by high-frequency buoy data

Cyanobacterial blooms are increasing in magnitude, frequency, and duration worldwide. However, our knowledge of cyanobacterial blooms dynamics and driving mechanisms is still limited due to their high spatiotemporal variability. To determine the potential driving mechanisms of cyanobacterial blooms in oligotrophic lakes, we collected a high-frequency depth profile of chlorophyll fluorescence (ChlF) and synchronous water quality, hydrometeorological data in early spring 2016 in oligotrophic Lake Qiandaohu. The vertical distribution of ChlF exhibited two patterns, “aggregated” and “discrete”, using Morisita's index, and the aggregated ChlF presented subsurface chlorophyll maxima during the thermal stratification period. The ChlF concentration was positively correlated with water temperature and negatively correlated with turbidity. Significantly linear relationships were observed between ChlF vertical structure parameters (e.g., Morisita's index, subsurface chlorophyll maxima depth and thickness) and thermal stratification parameters (e.g., mixing layer depth and relative water column stability). After rainstorm floods, the ChlF pattern suddenly change from “aggregated” to “discrete” and a ChlF concentration <1 μg/L was observed for 7–11 days with a significant increase in the mixing depth layer and turbidity. The results suggest that cyanobacterial blooms are robustly associated with thermal stratification and rainstorm floods in the deep and oligotrophic lake. Thermal stratification boosts surface phytoplankton accumulation by increasing water temperature, enhancing light availability and restricting phytoplankton vertical distribution. Rainstorm floods interrupt the accumulation by disrupting thermal stratification and decreasing the available light. Furthermore, wind speed and air temperature both regulate the phytoplankton dynamics by affecting thermal stratification. Our research quantifies the cyanobacterial bloom dynamics and their relationship between environmental factors, improving our knowledge of the driving mechanisms of cyanobacterial bloom for the protection of drinking water safety and aquatic organism health in lakes.

Thermally stratified radiative flow of non-Newtonian fluid between two discs executing diverse type of in-plane motion

The study on heat transfer for non-Newtonian (Casson) fluid motion affected by thermal stratification and thermal radiation is carried out in the presence of vertically applied magnetic field normal to the discs. The uniqueness of the problem is that the flow is in between parallel discs which execute the diverse type of in-plane motion. The fluid flow is driven by the upper disc radially stretching/shrinking at the a rate and the lower disc rotating at the angular velocity Ω and h is the space between the discs. Using appropriate reduction parameters, the Navier-Stokes equations and heat equation are simplified to non-dimensional coupled ordinary differential equations. The impacts of the rotation parameter, Casson parameter, thermal stratification parameter, thermal radiation parameter and Reynolds number are discussed. The results obtained asymptotically and numerically. For the results' compatibility, the comparison is made with the previous study.

Triple stratification effects on bioconvective stagnation point flow pertaining carbon nanotubes due to induced magnetic field

AbstractThe bioconvective stagnation point flow involving carbon nanotubes along a lengthening sheet subject to induced magnetic field and multiple stratification effects has been considered for investigation. Relevant similarity formulas are effectuated in converting the modelled equations into a first‐order system of ODEs and are further treated in MATLAB usingODE45and Newton Raphson method. Illustrations on the consequence of effectual parameters on the physical quantities and the flow profiles are achieved with the aid of graphs. It is observed that the nanofluid temperature profile ascends with augmenting volume fraction and Eckert number. The numerical veracity of the present study is displayed through a restrictive study with prior published works and a commendable agreement is noted. Nusselt number is found to elevate with volume fraction and lower with thermal stratification parameter. Moreover, the findings of the present numerical exploration have applications in biomedical imaging, hyperthermia, targeted drug delivery, and cancer therapy.

Partially ionized hybrid nanofluid flow with thermal stratification

The flow of nanofluids is of significant prominence owing to its noteworthy industrial usage and high heat transfer capabilities. Lately, “hybrid nanofluid” is being replaced the ordinary nanofluid flows to further boosts the heat transfer competencies. This novel type of hybrid 3D nanofluid model is introduced in this investigation comprising Graphene oxide (GO), Copper (Cu), immersed into the engine Oil. The partially ionized hybrid nanofluid flow is considered on a surface that is stretched in a nonlinear manner influenced by thermal stratification and non-uniform source/sink. The governing system of partial differential equations is translated into a coupled nonlinear ordinary differential equation and addressed by using a MATLAB software function bvp4c. To witness the behavior of certain nondimensional parameters versus the velocity and temperature profiles varied graphical illustrations are plotted. Furthermore, to strengthen the physical analysis the rate of heat flux and surface drag force are given in the tabular format. The authenticity of the presented novel model is done by making a comparison with an already published research in limiting case is also an important feature of this research. The remarkable outcomes of the present study show that the rate of heat flux and the surface drag coefficient show augmentation and diminution respectively for the improved values of the thermal stratification parameter. Further, the surface drag forces in both directions are stronger for the assumed hybrid nanofluid flow while the opposing conduct is observed for the rate of heat flux.

Investigation of variable viscosity and thermal conductivity on MHD mass transfer flow problem over a moving non-isothermal vertical plate

In this paper we investigate numerically the influence of variable viscosity and thermal conductivity on MHD convective flow of heat and mass transfer problem over a moving non-isothermal vertical plate. The viscosity of the fluid and thermal conductivity are presumed to be the inverse linear functions of temperature. With the help of similarity substitution, the flow governing equations and boundary conditions are transformed into non-dimensional ordinary differential equations. The boundary value problem so obtained is then solved using MATLAB bvp4c solver. The effects of various parameters viz. magnetic parameter, viscosity parameter, thermal conductivity parameter, stratification parameter and Schmidt number on velocity, temperature and concentration are obtained numerically and presented trough graphs. Also the coefficient of skin-friction, Nusselt number and Sherwood number are computed and displayed in tabular form. The effects of the viscosity parameter and thermal conductivity parameter in particular are prominent. This study has applications in a number of technological processes such as metal and polymer extrusion.

Mathematical analysis of heat and mass transfer in a Maxwell fluid

The objective of current research is to analyze the MHD flow of a Maxwell fluid towards a stretching sheet with thermophoretic and stratification effects. The analysis of heat and mass transfer is presented in the presence of variable thermal conductivity and the Cattaneo-Christov theory. The Cattaneo-Christov theory is used instead of Fourier and Fick laws because Fourier and Fick's laws give parabolic equations, which propagate in the space with infinite speed. The under-consideration flow model is converted into a set of ordinary differential equations by using suitable transformation. The set of ODEs is numerically solved by adopting the bvp4c Matlab technique. Influences of emerging parameters on velocity profile, temperature, and concentration are discussed with graphs. It is observed that larger values of Deborah number induce a resistance, that declining the velocity of a fluid. Further, it is noticed that thermal stratification parameter and concentration stratification parameter reduce the temperature and concentration distribution.

Mathematical analysis of heat and mass transfer in a Maxwell fluid with double stratification

The objective of the present research is to study the effects of variable thermal conductivity on the three-dimensional steady flow of Maxwell nanofluid in the presence of heat generation/absorption and double stratification. The theory of Cattaneo-Christov is used instead of the law of Fourier because the law of Fourier has parabolic equations and move at infinite speed in space. By using adequate transformation, the nonlinear partial differential equations (PDEs) are transformed into a set of ordinary equations (ODEs). The set of equations are solved numerically by adopting the bvp4c Matlab technique. The effects of different evolving parameters on axial velocity, temperature, and concentration are described in graphs. It is perceived that thermal and concentration stratification parameters result in the reduction of temperature and concentration distribution. Further, the heat generation parameter enhances the temperature distribution.

Convective features of squeezing flow in nonlinear stratified fluid with inclined rheology

The current study discloses the flow of fluid through non-Darcian medium due to stretching permeable sheet under the squeezing flow phenomenon. Furthermore, inclined MHD is applied to explore the characteristics of flow. The aspects of non-linear stratification and convective conditions are employed to investigate the heat and mass process. The viscous dissipation and Ohmic heating are used to enhance the heat transfer. Homotopic technique is practiced to evaluating the non-linear reduced equations. The graphs of significant parameters have been presented to see the variation in the concerned fields. Sherwood number, skin friction and Nusselt number are elaborated graphically via numerous parameters. Outcomes pointed that concentration and temperature fields decay due to higher solutal and thermal stratification parameters. Further, concentration and temperature of fluid enhance for dominant solutal and thermal Biot numbers.

Influence of thermal stratification and thermal radiation on graphene oxide-Ag/H2O hybrid nanofluid

In this article, the behavior of MHD hybrid nanofluid passing through a stretching sheet is examined. The current consideration also flashes the thermal radiation effects on hybrid nanofluid. Hybrid nanofluid is the new class of nanofluids which is very famous nowadays. Graphene oxide and silver as nanoparticles and water as a host fluid are considered. We presume low magnetic Reynolds number, and the magnetic field is enforced in the vertical direction. Features of heat transfer are assessed first time by exploiting the graphene oxide-Ag/H2O hybrid nanofluid with thermal radiation. By utilizing suitable transformations, governing equations are incorporated for heat and flow. Corresponding ordinary differential equations are solved by the homotopic procedure. The disparity of unlike parameters on flow and heat is revealed graphically. Resistive force is incorporated mathematically. The nanoparticle volume fraction of graphene oxide enhances both the velocity and temperature of the fluid. It is noticed that the thermal stratification parameter decays the temperature field while the opposite trend is observed for the radiation parameter. The heat transfer rate is disclosed by 3D graphs. It is observed that the temperature profile diminishes for enhanced thermal stratification parameters. Also, the heat transfer rate diminishes for radiation number and stratification parameter.

Flow and heat transfer analysis of Eyring-Powell fluid over stratified sheet with mixed convection

This article presents the study of heat transfer under the influence of mixed convective flow of Eyring-Powell fluid over a stratified stretching sheet. The impact of heat generation/absorption is also discussed. The fluid is considered to be a viscous, incompressible, two dimensional, and laminar. Transformation, based on the similarity variables, is used for the alteration of modeled governing partial differential equations (PDEs) into ordinary differential equations (ODEs). The shooting approach is introduced to accomplish the mathematical solution of governing equations. Runge-Kutta method of order four is used for the integration purpose and Newton’s method helps to refine initial guesses. All the programming is done on MATLAB. The effects of emerging parameters on temperature and velocity profiles are discussed through graphs. The related physical properties of flow, i.e., the skin friction coefficient and Nusselt number are described graphically for various parameters. Numerical values for the Nusselt number and skin friction coefficient are tabulated for the various parameters. It is noted that increment in thermal stratification parameter yields fall in both velocity and temperature of fluid and a reverse relation is observed for the heat generation parameter.

Impact of double-stratification on convective flow of a non-Newtonian liquid in a Riga plate with Cattaneo-Christov double-flux and thermal radiation

The intention of the paper is to find the outcome of thermal radiation of a second grade fluid over a Riga plate with Cattaneo-Christov (CC) double flux and double stratification’s. The governing mathematical models are changed into an ordinary differential equations (ODE) using suitable transformations. These resultant models are analytically solved with homotopy analysis method. The impact of pertinent parameters on velocity distribution, temperature distribution, concentration distribution, skin friction coefficient, local Nusselt number and local Sherwood number is analyzed graphically. We found that the skin friction coefficient suppresses with enhancing the injection/suction parameter. The energy transfer gradient suppresses with rising the thermal stratification parameter. Also, we found that the mass transfer gradient decreases with increasing the solutal stratification parameter.

Darcy–Boussinesq convective flow in a trapezoidal enclosure with thermal stratification

We explore numerically the Darcy–Boussinesq convective flow of water, kerosene, and engine oil through the glass ball, aluminum foam and sandstone porous medium inside a right-angle trapezoidal enclosure taking into consideration of thermal stratification. The bottom and left walls of the enclosure are uniformly heated, whereas thermal insulation is considered for the upper wall of it. Thermal stratification is applied to the right wall. The governing nondimensional partial differential equations are simulated using the Galerkin weighted residual finite element method with the help of COMSOL Multiphysics. We explored the time evolution of solutions and investigate the effects of the Rayleigh number, thermal stratification parameter, porosity parameter, types of the solid matrix and working fluids, and on the average Nusselt numbers, streamlines and isotherms. The simulated results confirm that the heat transfer rate amplifies with the increase in Rayleigh number and diminishes with the thermal stratification, porosity and aspect ratio of the enclosure. The results further guarantee that engine oil and aluminum foam perform better for heat transfer intensification. A two-cell flow is obtained for a stronger thermal stratification.