Temperature Exponent Parameter Research Articles

Thermal analysis of 3D viscoelastic micropolar nanofluid with cattaneo-christov heat via exponentially stretchable sheet: Darcy-forchheimer flow exploration

This article presents a comprehensive study on the thermal behavior of a three dimensional viscoelastic micropolar nanofluid under the inspiration of Cattaneo-Christov heat conduction model. The nanofluid is subject to an exponentially stretchable sheet and the flow is characterized by Darcy-Forchheimer formulation. Similarity variables are used to convert viscoelastic nanofluids PDEs into ODEs. MATLAB platform with bvp4c command is used to solve resulting ODE. The impact of involving parameters such that velocity ratio, Schmidt number, Prandtl number, Peclet number, Forchheimer number, buoyancy ratio parameter, Brownian motion, Heat source, Magnetic parameter on velocity profiles, rotation, temperature concentration and density profiles via graphs and tables. Temperature curve is improved up for magnetic parameters, temperature exponent parameter and thermopherosis parameter while significance loss is noted for increasing value of Prandtl number Pr and relaxation time λT. This research bears significance in applications related to advanced heat exchangers, microfluidic systems, and other emerging technologies where the interplay of nanofluids, viscoelasticity, and non-local heat conduction is of paramount importance.

Statistical and entropy optimization modeling for radiative hybrid nanofluid flow with Hall effect over exponential stretching/shrinking plate

Scientists have become intrigued by the capacity of two solid components to dissolve in a conventional fluid to enhance the thermal efficiency of novel hybrid nanofluids. The Bejan number and entropy formation of three-dimensional hybrid Al2O3 − Cu/H2O nanoparticles flowing via a stretching/shrinking bidirectional exponential plate are investigated in this research while taking into account thermal radiation and the Hall Effect. In the heat equation, the Joule heating and Cattaneo-Christov heat flux model are contemplated. Through using proper similarity transformations, equations involving momentum and heat transfer are simplified into ordinary differential equations. The Homotopy analysis approach is used to solve these equations using the computer software MATHEMATICA. By resolving the flow limitations on temperature and velocity, the entropy production is computed. Using graphical demonstration, the impact of various parameters such as suction/injection parameter, Brinkman number, magnetic parameter, stretching/shrinking parameter, temperature ratio parameter on flow, thermal relaxation parameter, temperature exponent parameter, Hall effect parameter, on velocity, temperature, entropy production, and Bejan number has been thoroughly discussed. The local Nusselt number and skin friction can also be identified for practical reasons for various approximations of physical parameters. The outcomes specify that the tangential velocity and redial velocity decrease for greater values of injection and suction parameters. The temperature profile falls for larger values of the suction parameter and rises for greater values of the thermal relaxation parameter and injection parameter. Entropy production develops when the magnetic parameter is improved. Bejan number was reduced in response to rising magnetic parameter values.

Local Non-Similar Solution for Non-Isothermal Electroconductive Radiative Stretching Boundary Layer Heat Transfer with Aligned Magnetic Field

Continuous two-dimensional boundary layer heat transfer in an electroconductive Newtonian fluid from a stretching surface that is biased by a magnetic field aligned with thermal radiation is the subject of this study. The effects of magnetic induction are induced because the Reynolds number is not small. The sheet is traveling with a temperature and velocity that are inversely related to how far away from the steady edge it is from the plane in which it is traveling. We also imposed external velocity u=uex=Dxp in the boundary. The necessary major equations are made dimensionless by the local non-similarity transformation and become a system of non-linear ordinary differential equations after being transformed from non-linear partial differential equations. The subsequent numerical solution of the arisen non-dimensional boundary value problem utilizes a sixth-order Runge–Kutta integration scheme and Nachtsheim–Swigert shooting iterative technique. A good correlation is seen when the solutions are compared to previously published results from the literature. Through the use of graphical representation, the physical impacts of the fluid parameters on speed, induced magnetic field, and temperature distribution are carried out. Furthermore, the distributions for skin friction coefficient and local Nusselt number are also studied for different scenarios. The skin friction coefficient and local Nusselt number are observed to increase with greater values of the temperature exponent parameter and velocity exponent parameter. However, as heat radiation increases, the local Nusselt number decreases even though temperatures are noticeably higher. The study finds applications in magnetic polymer fabrication systems.

Entropy optimization in hybrid radiative nanofluid flow with effect of variable magnetic field over exponential stretching plate

Researchers have recently become interested in hybrid nanofluids, which are generated by dissipating two solid components in a regular fluid and can increase thermal properties. In this article, entropy optimization of three-dimensional hybrid nanoparticles flow through a bidirectional exponential stretching/shrinking plate is investigated, also MHD and thermal radiation are considered. Through appropriate similarity transformations, the conservative equation of momentum and energy are altered into nonlinear ODEs. A bvp4c method via Matlab software is utilized to solve these equations. The entropy formation is calculated using the solutions of the flow constraints on temperature and velocity. The influence of numerous constraints for instance suction/injection, stretching/shrinking, magnetic parameter, thermal radiation, Prandtl number, temperature exponent parameter, and temperature ratio parameter on flow, temperature, and entropy formation have been deliberated in detail via graphical presentation. The skin friction and local Nusselt number for altered estimations of the physical constraints are also established for practical purposes. The figures show that the stretching/shrinking and magnetic parameter raises the entropy formation while declined the Bejan number.

Investigation of three-dimensional hybrid nanofluid flow affected by nonuniform MHD over exponential stretching/shrinking plate

Abstract Hybrid nanofluids, which are formed by dispersing two solid materials in a conventional fluid, have recently attracted the attention of researchers as they are able to improve the thermal properties. The present article, therefore, conducts a numerical analysis to investigate the heat transfer in magnetohydrodynamic three-dimensional flow of magnetic nanofluid (ferrofluid) across a bidirectional exponentially stretching sheet of hybrid nanofluid. Suitable similarity transformations convert the conservative equations for mass, energy, and momentum into ordinary differential equations. To solve these equations, a fifth-order Runge–Kutta–Fehlberg method is used. The findings revealed that with the enhancement of shape factor and generation/absorption parameters, the temperature over the surface increased. But if this parameter is decreased, the temperature profiles move towards the surface. Also, when exponent parameter is decreased, the temperature profiles go near the surface and a larger temperature exponent parameter means decreased heat transfer rate closer to the surface. The findings prove that skin friction coefficient corresponds to magnetic and suction/injection parameters and local Nusselt number is decreased with larger exponent parameter and heat absorption/generation parameter.

Scrutinization of 3D flow and nonlinear radiative heat transfer of non-Newtonian nanoparticles over an exponentially sheet

PurposeThis paper aims to explore the consequence of chemical reaction on three-dimensional flow, heat and mass transfer of a Casson nano liquid over exponentially stretching surface. A numerical technique of RKF-45 method is applied to resolve the nonlinear ordinary differential equations, which are obtained by applying the similarity transformation to the nonlinear partial differential system.Design/methodology/approachRole of significant parameters on flow fields are observed graphically. Also, the strength of heat exchange (Nusselt number) and the strength of mass exchange (Sherwood number) are analyzed.FindingsThe results of numerical modeling showed that, the Prandtl number plays a key role in reducing the temperature of the system. Further, the radiation parameters manufacture a lot of heat to operating fluid and higher temperature exponent parameter and enhance the temperature of the fluid.Originality/valueThe results of numerical modeling showed that, the Prandtl number plays a key role in reducing the temperature of the system. Further, the radiation parameters manufacture a lot of heat to operating fluid and higher temperature exponent parameter and enhance the temperature of the fluid.

Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of Nanofluids Past a Bidirectional Exponential Permeable Stretching/Shrinking Sheet With Viscous Dissipation Effect

The problem of boundary layer flow and heat transfer of magnetohydrodynamic (MHD) nanofluids which consist of Fe3O4, Cu, Al2O3, and TiO2 nanoparticles and water as the base fluid past a bidirectional exponentially permeable stretching/shrinking sheet is studied numerically. The mathematical model of the nanofluid incorporates the effect of viscous dissipation in the energy equation. By employing a suitable similarity transformation, the conservative equations for mass, momentum, and energy are transformed into the ordinary differential equations. These equations are then numerically solved with the utilization of bvp4c function in matlab. The effects of the suction parameter, magnetic parameter, nanoparticle volume fraction parameter, Eckert number, Prandtl number, and temperature exponent parameter to the reduced skin friction coefficient as well as the local Nusselt number are graphically presented. Cu is found to be prominently good in the thermal conductivity. Nevertheless, higher concentration of nanoparticles leads to the deterioration of heat transfer rate. The present result negates the previous literature on thermal conductivity enhancement with the implementation of nanofluid. Stability analysis is conducted since dual solutions exist in this study, and conclusively, the first solution is found to be stable.

Three dimensional rotating flow of Maxwell nanofluid

Abstract This article investigates rotating flow of Maxwell liquid through submersion of nanoparticles. Flow created is because of an exponentially stretching sheet. Optimal homotopic scheme is implemented for the solution of governing model. The optimal values of auxiliary parameters are computed. The optimal solution expressions of temperature and concentration of nanoparticles are elaborated via plots by employing the various values of involved parameters. The physical quantities like Nusselt and Sherwood numbers are characterized by numerical values. Here we observed that temperature of liquid and its related thickness of boundary layer arise for the increasing values of local Deborah number while it retards for larger temperature exponent parameter.

Numerical study of MHD nanofluid flow and heat transfer past a bidirectional exponentially stretching sheet

Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite–Fe3O4 nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction.

Radiation effects in three-dimensional flow over a bi-directional exponentially stretching sheet

Analysis is performed to explore the characteristics of non-linear radiation heat transfer in the three-dimensional flow above an exponentially stretching sheet. The temperature is also exponentially distributed across the sheet. Local similarity solutions of the arising differential equations are computed through shooting method with fourth-fifth-order Runge–Kutta integration technique. The results corresponding to different values of temperature exponent parameter A reveal some interesting facts about the temperature distribution. The fluid's temperature is largely influenced with the variations in wall to ambient temperature ratio. The solutions are found in excellent agreement with the existing studies in the literature.

Magneto-Hydro Dynamic Flow and Heat Transfer of Nonnewtonian Power-Law Fluid Over a Non-Linear Stretching Surface with Viscous Dissipation

A fluid flow and heat transfer analysis of an electrically conducting non-Newtonian power law fluid flowing over a non-linear stretching surface in the presence of a transverse magnetic field taking into consideration viscous dissipation effects is investigated. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. By using quasi-linearization techniques first linearize the non linear momentum equation is linearized and then the coupled ordinary differential equations are solved numerically by an implicit finite difference scheme. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, Eckert number, velocity exponent parameter, temperature exponent parameter, modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed.

Dual solutions for flow and radiative heat transfer of a micropolar fluid over stretching/shrinking sheet

A boundary layer analysis is presented for the flow and radiative heat transfer of an incompressible micropolar fluid over stretching/shrinking sheet with power-law surface velocity and temperature distributions. Dual solutions are analytically obtained firstly by homotopy analysis method (HAM). It is found that dual solutions not only exist for the shrinking flow as reported in the previous literatures, but also exist for the stretching flow. The special case of the first branch (K=0, classical Newtonian fluid) is compared with the existing numerical results of stretching flow in good agreement. Our results show that both solutions are physically meaningful (two solutions are closely related to each other), unlike the results previously reported that only one solution is acceptable. Moreover, the effects of the material parameter K, the radiative Prandtl number Prn, the velocity exponent parameter m and the temperature exponent parameter λ on the flow and heat transfer characteristics are analyzed in detail.

Non-Newtonian Power-Law Fluid Flow and Heat Transfer over a Non-Linearly Stretching Surface

The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.

Homotopy analysis solution of free convection flow on a horizontal impermeable surface embedded in a saturated porous medium

In this paper, the analytic solution of the buoyancy-driven flow over a horizontal impermeable flat plate embedded in a saturated porous medium is derived using the newly developed analytic method, namely the homotopy analysis method (HAM). The HAM results show great agreement comparing with numerical results. HAM contains an auxiliary parameter ℏ that provides a simple way of controlling and adjusting the convergence region. The resultant analytic solution is valid for all acceptable values of the temperature exponent parameter λ.

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet

An analysis is made for the steady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically conducting fluid over a stretching vertical sheet in its own plane. The stretching velocity, the surface temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The transformed boundary layer equations are solved numerically for some values of the involved parameters, namely the magnetic parameter M, the velocity exponent parameter m, the temperature exponent parameter n and the buoyancy parameter λ, while the Prandtl number Pr is fixed, namely Pr = 1, using a finite difference scheme known as the Keller-box method. Similarity solutions are obtained in the presence of the buoyancy force if n = 2m−1. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M increases for fixed λ and m. For m = 0.2 (i.e. n = −0.6), although the sheet and the fluid are at different temperatures, there is no local heat transfer at the surface of the sheet except at the singular point of the origin (fixed point).

The effect of lateral mass flux on the natural convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with internal heat generation

The effect of suction or injection on the free convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with an exponential decaying heat generation is studied. Similarity solutions are obtained for the governing steady laminar boundary layer equations using Darcy and Boussinesq approximations. The plate is assumed to have a power law temperature distribution. Three distinct cases of uniform lateral mass flux, uniform surface temperature, and uniform heat flux are studied. The effects of suction/injection parameter f w and temperature exponent λ on the flow of heat transfer are studied. Some exact analytical results are obtained for λ = 1 , − 1 / 3 . Critical values of the suction/injection parameter are obtained for adiabatic surface as a function of the temperature exponent parameter λ.

Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets With Variable Viscosity and Variable Thermal Diffusivity

The paper presents a study of the laminar mixed convection adjacent to vertical continuously stretching sheets, taking into account the effects of variable viscosity and variable thermal diffusivity. The similarity solutions are reported for isothermal sheet moving with a velocity of the form uw=Bx0.5 and a continuous linearly stretching sheet with a linear surface temperature distribution. The equations of conservation of mass, momentum and energy, which govern the flow and heat transfer, are solved numerically by using the shooting method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. The numerical results show that, variable viscosity, variable thermal diffusivity, the velocity exponent parameter, the temperature exponent parameter and the buoyancy force parameter have significant influences on the velocity and temperature profiles, shear stress and Nusselt number in two cases air and water.

Laminar mixed convection adjacent to vertical, continuously stretching sheets

The analysis of laminar mixed convection in boundary layers adjacent to a vertical, continuously stretching sheet has been presented. The velocity and temperature of the sheet were assumed to vary in a power-law form, that is, u w (x)=Bx m and T w (x)−T ∞=Ax n . In the presence of buoyancy force effects, similarity solutions were reported for the following two cases: (a) n=0 and m=0.5, which corresponds to an isothermal sheet moving with a velocity of the form u w =Bx 0.5 and (b) n=1 and m=1, which corresponds to a continuous, linearly stretching sheet with a linear surface temperature distribution, i.e. T w −T ∞=Ax. Formulation of the present problem shows that the heat transfer characteristics depends on four governing parameters, namely, the velocity exponent parameter m, the temperature exponent parameter n, the buoyancy force parameter G *, and Prandtl number of the fluid. Numerical solutions were generated from a finite difference method. Results for the local Nusselt number, the local friction coefficient, and temperature profiles are presented for different governing parameters. Effects of buoyancy force and Prandtl number on the flow and heat transfer characteristics are thoroughly examined.