Thermal Stratification Parameter Research Articles

Analysis of heat generation/absorption in thermally stratified Sutterby fluid flow with Cattaneo–Christov theory

In this study, heat generation (or absorption) in flow of stagnant Sutterby fluid past over a linearly shrinking sheet is analyzed. Heat transfer features are explored by implementing thermal stratification phenomenon. Cattaneo–Chrostov theory is also implemented to analyze the heat flow behavior instead of conventional law of Fourier. The constitutive flow laws are transmuted into non-linear dimensionless ordinary differential equations by the suitable variables. Homotopic procedure is adopted to solve the flow equations for the convergent iterative solutions. The behavior of fluid temperature and velocity profile are analyzed and discussed graphically for the eminent parameters involved in the governing laws. In this attempt the major found is that decreasing trend is observed in temperture distribution for thermal stratification parameter, heat generation (or absorption) paramere and thermal relaxation parameter. Morover, graphical results illustrate that behavior of velocity and temperature distributions are more dominant for $$\hbox {n}=2$$ as compared to $$\hbox {n}=1$$ .

MHD stagnation point flow of Williamson and Casson fluids past an extended cylinder: a new heat flux model

The impact of heat transfer in MHD flows along a stretching cylinder is playing a vital role for heat exchangers, fiber coating, transportation, etc. Currently, a lot of theoretical models are accessible for illustrating the thermal transfer impact of non-Newtonian liquid flows over a cylinder. Also, an external magnetic force is spot-on to deal with the physical features of the fluids to oversee the nature of thermal and momentum transfer in the system. Considering this fact, we inspect the heat transport behavior of two different non-Newtonian MHD flows due to stretching of a cylinder with heat generation, by taking the advantage of a new heat flux theory conceived by Christov–Cattaneo. The basic PDEs are converted into ODEs with the suitable similarity transformations. These ODEs are solved by fourth order Runge–Kutta based shooting system. Plots are drawn to discern the influence of sundry parameters on the flow fields (velocity and temperature). Along with them the rate of heat transfer and friction factor are bestowed in table. From the results, we notice that the influence of thermal stratification and curvature parameters have a propensity to increase both the velocity and thermal fields. Thermal relaxation parameter effectively lifts the friction factor in the flow of Williamson fluid than that of Casson fluid.

Activation energy and dual stratification effects for Walter-B fluid flow in view of Cattaneo-Christov double diffusionon

The purpose of the present article is to explore the novel aspects of activation energy in nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo-Christov double diffusion model over a permeable stretched sheet. Generalized forms of Fourier's and Fick's law are utilized through Cattaneo-Christov double diffusion. Walter-B nanomaterial model is used that describes the significant slip mechanism namely Brownian and thermophoresis diffusions. Double stratification, heat generation/absorption and chemical reaction are considered. Modified Arrhenius formula for activation energy is implemented. The acquired nonlinear system is cracked through homotopic analysis method. Effects of emanating variables are examined through graphs and tables. It is evident that temperature distribution and thermal boundary layer thickness is monotonically dwindling function of thermal stratification parameter(P1), thermal relaxation time (δ2) and upsurge for the thermophoresis parameter (Nt), heat generation/absorption parameter (B₁), Brownian motion parameter (Nb). Nanoparticle concentration is directly comparable to the activation energy of reaction and impact of thermal relaxation time is qualitatively opposite to that of thermophoretic force.

Change in viscosity of Maxwell fluid flow due to thermal and solutal stratifications

The objective of this article is to explore the computational aspects of temperature dependent dynamic viscosity of Maxwell nanofluid flow over a variable thicked surface. The dynamic viscosity of the fluid is assumed to depend on temperature and due to thermal and solutal stratifications, viscosity of the liquid also depends on thermal and concentration diffusions. Temperature dependent dynamic viscosity model causes change in thermal and solutal stratifications. The basic mathematical model (system of PDEs) is reduced into nonlinear ODEs by applying similarity variables. Computational solutions of the differential system are obtained by efficient numerical approach (fifth order Rung-Kutta Fehlberg method) along the Cash and Karp. The consequential solutions are sketched for different values of physical constraints. Parameters like the temperature dependent viscosity, the fluid relaxation parameter, the wall thickness parameter and the Hartmann number are found to control the flow field. In addition, the Prandtl number, the Brownian motion parameter, the activation energy parameter, the chemical reaction rate parameter, the thermophoresis parameter, the thermal stratification parameter, the Lewis number, and the solutal stratification parameter are found to control the concentration and temperature distributions inside the stretching surface. It can be seen that for large values of the fluid relaxation parameter, the temperature dependent viscosity and the wall thickness parameter the velocity profile declines whereas reverse behavior is noticed for Hartmann number. Moreover, for large values the Lewis number, solutal stratification parameter and activation energy parameter the concentration profile shows decrease behavior.

Novel aspects of Soret and Dufour in entropy generation minimization for Williamson fluid flow

Soret and Dufour effects on MHD flow of Williamson fluid between two rotating disks are examined. Impacts of stratification, viscous dissipation and activation energy are also considered. Bejan number and entropy generation for stratified flow is discussed. The governing PDE's are converted into ODE's by using Von Karman transformations. Convergent solution of complicated ODE's is found by homotopic procedure. The results of physical quantities are discussed through plots and numerical values. It is noted that axial and radial velocities are more for greater Weissenberg number. Temperature and concentration profiles are decreasing functions of thermal and solutal stratification parameters respectively. Entropy and Bejan number show the opposite trends for higher Weissenberg number and Brinkman number.

An investigation of thermal and solutal stratification effects on mixed convection flow and heat transfer of Williamson nanofluid

In this framework, the characteristics of Williamson fluid flow generated by an expanding/contracting inclined cylinder in the attendance of nanoparticle and magnetic field has been analyzed. The novelty of this research is to study the physical impacts of thermal and solutal stratification on mixed convection flow along with heat transfer by incorporating thermal radiation. The basic equations in dimensional form are derived for the flow and transport phenomena of Williamson nanofluids incorporating the effects of Brownian diffusion and thermophoresis. The coupled non-linear reduced expressions governing the flow fields are numerically solved with the help of Runge-Kutta integration scheme. The main view of current analysis is to explore the physical impacts of involved pertinent parameters, like, Weissenberg number, mixed convection parameter, buoyancy ratio parameter, thermal and solutal stratified parameters, Brownian motion and thermophoresis parameter and Schmidt number on dimensionless velocity, temperature and nanoparticles concentration distributions. The results highlight that, the increasing values of the Weissenberg number tends to decrease the velocity distribution. Additionally, an increment in Schmidt number reduces the concentration profiles as well as the rate of mass transfer. A significant reduction in dimensionless temperature and nanoparticles concentration distributions by uplifting the thermal stratification parameter is also observed.

Optimization of entropy generation in thermally stratified polystyrene-water/kerosene nanofluid flow with convective boundary condition

The refinements of thermodynamic features of systems greatly depend on the generation of entropy since it produces thermodynamic irreversibility more appropriately. Efficiency of energy transportation in a system can be improved by minimization of rate of entropy generation. Due to such a crucial role in thermodynamics systems, our main focus is to elaborate the features of entropy generation in polystyrenerene-water and polystyrene-kerosene nanofluids with the combined phenomena of thermal stratification and convective boundary condition. Viscous dissipation and stagnation points are implemented to analyze the flow characteristics deformed by the Riga plate. Momentum and energy equations are modeled in view of the above assumptions. Dimensionless governing equations are acquired by using similar transformations. Descriptions of numerous physical parameters are scrutinized on the temperature, entropy generation and velocity distribution. As an outcome, entropy generation can be minimized by implementing the dominant thermal stratification parameter and the further rate of decay of entropy generation is more prominent in water-polystyrene in comparison to kerosene-polystyrene nanofluid.

Mixed convection flow of Newtonian fluids over an upper horizontal thermally stratified melting surface of a paraboloid of revolution

This article presents the combined effects of melting heat transfer and linear stratification of not only the heat energy, but also stratified concentration on the motion of an electrically conducting fluid over an object with a non-uniform thickness. Owing to the melting heat transfer and stretching of fluid layers at the free stream, the case of mixed convection is considered to be more appropriate than neither free nor forced convection. Consequently, the energy and concentration equations which model the flow and satisfy the free stream conditions are presented. Suitable thermophoresis model and Boussinesq approximation for the case $$T_m(x)<T_\infty (x)$$ and $$C_m(x)<C_\infty (x)$$ were adopted. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions were solved numerically using Runge–Kutta technique along with shooting technique. Maximum variations in the local skin friction coefficients $$Re_{x}^{1/2}C_{fx}$$ with thermal stratification occur at larger values of temperature-dependent viscosity parameter. Temperature distribution, local skin friction coefficients $$Re_{x}^{1/2}C_{fx}$$ and mass transfer rate $$S_{hx}Re_{x}^{-1/2}$$ are decreasing properties of thermal stratification and thermophoresis parameter.

Influence of viscous dissipation and double stratification on MHD Oldroyd-B fluid over a stretching sheet with uniform heat source

The present report explores the discussion on 3D flow of dual stratified Oldroyd-B fluid in the direction of thermal radiation, viscous dissipation and heat source/sink. Mathematical modeling is formulated with an applied magnetic field through a stretching surface. The present flow governing system has been transformed as nonlinear ODE via suitable transformations and then concluded by using bvp4c. The graphs are described and illustrated for various non-dimensional parameters. Thermal stratification and Prandtl number parameters reduce the temperature, whereas thermal radiation and heat source parameters show reverse behavior. Numerical results are used to obtain the values of frictional drag, rate of heat and mass transfers. Finally, numerical results are compared with previous established work in a limiting case.

Interaction of thermal radiation in hydromagnetic viscoelastic nanomaterial subject to gyrotactic microorganisms

Importance of solar energy in human society cannot be ignored. Electricity, water, and heat can be achieved from solar power. Sustainable energy formation nowadays is a serious issue in the development of human society. Solar energy is deliberated as one of the greatest sources of renewable energy. This energy is 2000 times larger than the utilization of human society. Thus the intention here is to address the impact of gyrotactic microorganisms on two-dimensional (2D) stratified flow of Jeffrey nanomaterial. Applied magnetic field along with mixed convection is considered in the formulation process. Theory of microorganisms is utilized just to stabilize the suspended nanoparticles through bioconvection which has been induced by combined effects of buoyancy forces and magnetic field. Convergent series solutions for the obtained nonlinear differential systems are derived. Impacts of different emerging parameters on velocity, temperature, concentration, and motile microorganisms’ density are addressed through graphs. Numerical values for the local Nusselt, Sherwood and density number of motile microorganisms are computed and analyzed. It is observed that thermal, concentration, and motile density stratification parameters result in the reduction of temperature, concentration, and motile microorganisms’ density distributions, respectively.

Penetration of boundary-driven flows into a rotating spherical thermally stratified fluid

Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a numerical model, we explore a broad range of three key dimensionless numbers: a thermal stratification parameter (the relative size of boundary temperature gradients to imposed vertical temperature gradients), $10^{-3}\leqslant S\leqslant 10^{4}$, a buoyancy parameter (the strength of applied boundary heat-flux anomalies), $10^{-2}\leqslant B\leqslant 10^{6}$, and the Ekman number (ratio of viscous to Coriolis forces), $10^{-6}\leqslant E\leqslant 10^{-4}$. We find both steady and time-dependent solutions and delineate the regime boundaries. We focus on steady-state solutions, for which a clear transition is found between a low $S$ regime, in which buoyancy dominates the dynamics, and a high $S$ regime, in which stratification dominates. For the low-$S$ regime, we find that the characteristic flow speed scales as $B^{2/3}$, whereas for high-$S$, the radial and horizontal velocities scale respectively as $u_{r}\sim S^{-1}$, $u_{h}\sim S^{-3/4}B^{1/4}$ and are confined within a thin layer of depth $(SB)^{-1/4}$ at the outer edge of the domain. For the Earth, if lower mantle heterogeneous structure is due principally to chemical anomalies, we estimate that the core is in the high-$S$ regime and steady flows arising from strong outer boundary thermal anomalies cannot penetrate the stable layer. However, if the mantle heterogeneities are due to thermal anomalies and the heat-flux variation is large, the core will be in a low-$S$ regime in which the stable layer is likely penetrated by boundary-driven flows.

HEAT AND MASS TRANSFER ANALYSIS OF STEADY AND UNSTEADY NANOFLUID FLOW OVER A STRETCHING SHEET WITH DOUBLE STRATIFICATION

Attention is focused on heat and mass transfer by a stretched surface over a nanofluid in a steady and unsteady state in the presence of a magnetic field, thermal stratification, and solutal stratification. The proper partial differential equations governing the boundary-layer flow, heat and mass transfer are reduced to ordinary differential equations by using the similarity variable technique and solved numerically by using the Galerkin finite-element method. A parametric analysis of all pertinent parameters is carried out and a descriptive set of numerical results for the velocity, temperature, and concentration profiles as well as the skin-friction parameter, Nusselt number, and Sherwood number is demonstrated through graphs and tables. It is determined that temperature profiles deteriorate as thermal stratification parameter St increases, furthermore, the concentration profiles also decline when solutal stratification parameter Sm increases.

Behavior of stratifications and convective phenomena in mixed convection flow of 3D Carreau nanofluid with radiative heat flux

Nanoliquids, the engineered liquids with isolated effectual nanoparticles have disclosed a surprising thermo-physical effects and added functionalities and therefore have supported an extensive sort of essential applications. In particular, nanoliquids have displayed pointedly improved aptitude of heat transfer as equated to traditional functioning liquids. The notable intention of current scrutiny is to explore the features of combined convective and stratification phenomena by utilizing Brownian and thermophoresis nanoparticles on 3D mixed convection flow of magnetite Carreau fluid influenced by a bidirectional stretching surface. The heat transport phenomenon is also betrothed in the manifestation of thermal radiation and the heat sink/source. By means of suitable conversions the nonlinear PDEs transformed into nonlinear ODEs. To identify the behavior of numerous somatic parameters, numerically bvp4c tactic has been worked to elucidate the governing ODEs. The graphical depiction is delineated and tables are organized for diverse physical parameters on Carreau nanofluid. It is scrutinized that the impact of magnetic parameter on both the velocity components is analogous and diminishes both the velocities for shear thinning/thickening liquids. Moreover, the present exploration reports that the mixed convection and thermal stratification parameters decline the liquid temperature and allied thickness of the thermal boundary layer for both shear thickening/thinning liquids.

The combined influence of nonlinear thermal radiation and thermal stratification on the dynamics of micropolar fluid along a vertical surface

PurposeThe purpose of this paper is to consider the problem of thermal destratification facing engineers and scientists during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force. This paper provides an insight into the non-linear transfer of thermal radiation within the boundary layer.Design/methodology/approachSimilarity transformation and parameterization of the non-linear partial differential equation are carried out. The approximate analytical solution of the governing equation which models the free convective flow of strong and weak concentration of micro-elements in a micropolar fluid over a vertical surface is presented.FindingsIt is observed that the velocity and temperature distribution are decreasing properties of thermal stratification parameter St. Maximum local skin friction coefficients are ascertained at an epilimnion level (St=0) when the magnitude of thermal radiation is small. Thermal stratification parameter has no significant effect on the temperature distribution in the flow near a free stream.Originality/valueThe relationship between stratification of temperature and the transfer of thermal energy during the problem of thermal destratification facing engineers and scientist during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force is unravelled in this paper.

Thermal and solutal stratifications in flow of Oldroyd-B nanofluid with variable conductivity

This article reports the heat transfer enhancement on magnetohydrodynamic (MHD) flow of Oldroyd-B nanofluid influenced by stretching cylinder. The aspects of mixed convection and heat sink/source are considered. The model used for nanofluid incorporate the properties of Brownian motion and thermophoresis. The temperature-dependent thermal conductivity with the influence of thermal and mass stratifications is adopted. The nonlinear PDEs are condensed into ODEs via apposite conversions. The analytically homotopic approach has been adopted to elucidate the nonlinear ODEs. The stimulus of essential concerns on velocity, temperature, concentration, Nusselt number and Sherwood number is depicted. This analysis reported that the liquid velocity has a conflicting tendency for larger magnetic and mixed convection parameter. Furthermore, the liquid temperature decays for the higher thermal stratification parameter, whereas analogous influence is being noticed for mass stratification parameter on concentration field. For the confirmation of these outcomes an assessment table with former effort is also established.

Thermal stratification effects on mixed convective Maxwell fluid flow with variable thermal conductivity and homogeneous/heterogeneous reactions

In this article, the magnetohydrodynamic mixed convection Maxwell fluid flow over a vertical stretching sheet with variable thickness close to a stagnation point is explored numerically. The variable thermal conductivity has been assumed for the analysis of heat transfer characteristics. Furthermore, homogeneous–heterogeneous chemical reactions and thermal stratification have also been considered in the present study. Both the assisting and the opposing flows are discussed through tables and graphs. The ordinary differential equations are obtained via suitable similarity transformations. The numerical solutions of the non-dimensional velocity, temperature and concentration profiles are obtained by employing the shooting method and examined for different physical parameters such as the thermal stratification, thermal relaxation, mixed convection, thermal conductivity, stretching ratio, homogeneous reaction and heterogeneous reaction parameters. It is found that the temperature upturns for the higher values of the Maxwell and thermal conductivity parameters. Moreover, the ascending values of the thermal stratification parameter decay the temperature profile. The local Nusselt number or the heat transfer rate at the wall is higher in the assisting flow regime as compared with the opposing flow regime.

Chemically reactive flow and heat transfer of magnetite Oldroyd-B nanofluid subject to stratifications

As an emerging technology owing to countless worthy properties, nanofluids have been concerned by numerous scientists and developed a very energetic arena. Nanofluids, a colloidal assortment of nanoparticles and widespread analysis have disclosed applications of heat transfer because of their intensified aspects of thermal conductivity. The present article explores the nanofluid characteristics on MHD flow of an Oldroyd-B liquid. The convective and stratification mechanisms in the manifestation of thermal radiation and chemical reaction have been utilized for heat and mass transfer features. Additionally, the phenomenon of heat sink/source is accounted. The mathematical relation is established by means of usual boundary layer estimates. Homotopic approach has been utilized for the computation of resultant non-linear ODEs. Thermophysical properties of numerous somatic parameters on velocity, temperature and concentration are scheduled in plots as well as in tabular form. The present interruption reports that the liquid temperature declines for thermal stratification parameter, although conflicting trend is being noted for radiation parameter and thermal Biot number on temperature of Oldroyd-B fluid. The mass Biot number and chemical reaction parameter displays diminishing tendency on concentration field. Additionally, for authentication of current derived elucidations an assessment table of skin friction coefficient is prepared in restrictive cases.

Change in viscosity of Williamson nanofluid flow due to thermal and solutal stratification

Current analysis is devoted to explore the computational aspects of variable viscosity on Williamson nanofluid over a non-linear stretching sheet. Viscosity of the fluid is assumed to be depend on temperature and due to thermal stratification, viscosity of the fluid also depends upon thermal diffusion. The basic mathematical problem (system of PDEs) is converted into non-linear ODEs via applying suitable transformations. Computational solutions of the problem is achieved by efficient numerical approach (shooting method). Characteristics of controlling parameters i.e. Lewis number, thermophoresis parameter, Hartmann number, plastic dynamic viscosity parameter, Weissenberg number, Prandtl number, stretching index, Brownian motion parameter, Prandtl number, thermal and solutal stratification parameters are plotted on concentration, velocity and temperature gradients. Furthermore friction factor coefficient, heat and mass diffusion rates are presented through graphs and tables. Conclusions are made on the basis of entire investigation and it is seen that velocity profile reduces for large values of variable viscosity and thermal stratification parameters while thermal stratification parameter shows opposite behavior for temperature profile. Moreover, concentration profile reduces for enhancing values of Lewis number and increases for large values of stretching velocity parameter.

Investigation of second grade fluid through temperature dependent thermal conductivity and non-Fourier heat flux

Abstract Here we investigated stagnation point flow of second grade fluid over a stretchable cylinder. Heat transfer is characterized by non-Fourier law of heat flux and thermal stratification. Temperature dependent thermal conductivity and activation energy are also accounted. Transformations procedure is applying to transform the governing PDE’s into ODE’s. Obtained system of ODE’s are solved analytically by HAM. Influence of flow variables on velocity, temperature, concentration, skin friction and Sherwood number are analyzed. Obtained outcome shows that velocity enhanced through curvature parameter, viscoelastic parameter and velocities ratio variable. Temperature decays for larger Prandtl number, thermal stratification, thermal relaxation and curvature parameter. Sherwood number and concentration field show opposite behavior for higher estimation of activation energy, reaction rate, curvature parameter and Schmidt number.

Carreau fluid flow in a thermally stratified medium with heat generation/absorption effects

In this article theoretical attempt is carried to inspect the flow field characteristics of Carreau fluid model. The fluid flow is achieved by stretching cylindrical surface with no slip condition that is the relative velocity of Carreau fluid particles and cylindrical surface is zero. The role of both temperature stratification and heat generation/absorption are considered with the source of energy equation. The physical illustration of flow model with both temperature stratification and heat generation/absorption effects is translated in terms of partial differential equations through fundamental laws, namely law of conservation of mass, momentum and energy. The obtained partial differential equations are non-linear in nature and it seems difficult to solve them analytically. Therefore the boundary layer approximation is utilized to retain the active parts of flow narrating differential equations. Then to step down the partial differential equations in terms of ordinary differential equations a set of transformations is introduced. The reduced system is solved by shooting method and self-coded algorithm is executed in this regard. The note down observations are offered with the aid of graphs and tables. It is noticed that the Carreau fluid temperature shows decline nature towards the positive values of thermal stratification parameter and heat absorption parameter but it reflects opposite trend for the case of heat generation parameter.