Temperature-dependent Heat Source Research Articles

Influence of non-uniform heat source/sink and variable viscosity on mixed convection flow of third grade nanofluid over an inclined stretched Riga plate

The present study focuses on the impact of non-uniform heat source/sink and temperature dependent viscosity modeled by Reynolds on Cattaneo-Christov heat flow of third grade nanofluid subject to an inclined stretched Riga plate. Fourth order R-K and shooting methods have been implemented to obtain the numerical solution of the transformed boundary layer equations. The achievability of the present study is that the material constants associated with third grade fluid augment the fluid motion and boils down the fluid temperature leading to ascending velocity boundary layer and descending thermal boundary layer. And viscosity parameter enhances the heat transfer rate from the plate. Furthermore, augmented space and temperature dependent heat source upsurges the fluid temperature and the related thermal boundary layer thickness.

Impact of temperature dependent heat source and non-linear radiative flow of third grade fluid with chemical aspects

This communication explores the MHD flow of third grade fluid bounded by a stretching surface with homogeneous-heterogeneous reactions. Incompressible fluid is electrically conducting in the presence of constant magnetic field. Heat transfer is performed through exponential based space internal heat source, non-linear thermal radiation and convective boundary condition. Non-linear differential systems are computed by homotopic technique. Intervals of convergence through numerical data and plots are explicitly determined. The dimensionless velocity, temperature, and concentration distributions manifesting the characteristics of various influential parameters are addressed. The skin friction coefficient and local Nusselt number are also addressed. Clearly temperature is enhanced by radiation, temperature ratio, and magnetic parameters.

Magnetic Field Effects on Chemical Reaction of Power-Law Fluid over an Axisymmetric Stretched Sheet

Numerical investigation of the effects of magnetic field strength, thermal radiation, Joule heating, and viscous heating on a forced convective flow of a non-Newtonian, incompressible power-law fluid in an axisymmetric stretching sheet with variable temperature wall is accomplished. The power-law shear-thinning viscosity-shear rate model for the anisotropic solutions and the Rosseland approximation for the thermal radiation through a highly absorbing medium is considered. The temperature-dependent heat sources, Joule heating, and viscous heating are considered to be the source terms in the energy balance. The non-dimensional boundary-layer equations are solved numerically in terms of similarity variable. A parameter study on the boundary value of chemical reaction and Nusselt number is performed as a function of thermal radiation parameter, Brinkman number, Prandtl number, Hartmann number, power-law index, heat source coefficient, Brownian parameter, thermophoresis parameter, and the chemical reaction parameter. The results show that the chemical reaction parameter has an increasing effect on the chemical reaction boundary while the magnetic, thermophoresis, and Brownian effects decrease the rate of the chemical reaction at the boundary.

Effectiveness of exponential heat source, nanoparticle shape factor and Hall current on mixed convective flow of nanoliquids subject to rotating frame

PurposeThe study of novel exponential heat source (EHS) phenomena across a flowing fluid with the suspension of nanoparticles over a rotating plate in the presence of Hall current and chemical reaction has been an open question. Therefore, the purpose of this paper is to investigate the impact of EHS in the transport of nanofluid under the influence of strong magnetic dipole (Hall effect), chemical reaction and temperature-dependent heat source (THS) effects. The Khanafer-Vafai-Lightstone model is used for nanofluid and the thermophysical properties of nanofluid are calculated from mixture theory and phenomenological laws. The simulation of the flow is also carried out using the appropriate values of the empirical shape factor for five different particle shapes (i.e. sphere, hexahedron, tetrahedron, column and lamina).Design/methodology/approachUsing Laplace transform technique, exact solutions are presented for the governing nonlinear equations. Graphical illustrations are pointed out to represent the impact of involved parameters in a comprehensive way. The numeric data of the density, thermal conductivity, dynamic viscosity, specific heat, Prandtl number and Nusselt number for 20 different nanofluids are presented.FindingsIt is established that the nanofluid enhances the heat transfer rate of the working fluids; the nanoparticles also cause an increase of viscous. The impact of EHS advances the heat transfer characteristics significantly than usual thermal-based heat source (THS).Originality/valueThe effectiveness of EHS phenomena in the dynamics of nanofluid over a rotating plate with Hall current, chemical reaction and THS effects is first time investigated.

Entropy generation and heat transport analysis of Casson fluid flow with viscous and Joule heating in an inclined porous microchannel

The combined effects of the magnetic field, suction/injection, and convective boundary condition on heat transfer and entropy generation in an electrically conducting Casson fluid flow through an inclined porous microchannel are scrutinized. The temperature-dependent heat source is also accounted. Numerical simulation for the modelled problem is presented via Runge–Kutta–Felhberg-based shooting technique. Special attention is given to analyze the impact of involved parameters on the profiles of velocity [Formula: see text], temperature [Formula: see text], entropy generation [Formula: see text], and Bejan number [Formula: see text]. It is established that entropy generation rate decreases at the walls with an increase in Hartmann number [Formula: see text], while it increases at the center region of the microchannel.

Three Dimensional Slip Flow of a Chemically Reacting Casson Fluid Flowing over a Porous Slender Sheet with a Non-Uniform Heat Source or Sink

In this paper, we propose a mathematical model to analyze the effect of a non-uniform heat source or sink on chemically reacting magnetohydrodynamic Casson fluid flowing across a slendering sheet. A chemically reacting fluid with multiple slips has various applications in controlling heating and mass transport phenomena such as biological reactants being converted to products, biomedical signal processing and image processing to establish a dynamic area of specialization in research aspects of biomedical engineering. For these reasons multiple slips (diffusion, thermal and momentum slips) are applied in modeling the heat and mass transfer process. The non-linear ordinary differential equations (ODEs) are solved using the Runge-Kutta-Fehlberg integration method. The characteristics of the velocity, temperature and concentration boundary layers are presented for different physical parameters such as space and temperature-dependent heat source or sink parameter, porosity parameter, chemical reaction parameter, velocity slip parameter, and temperature and concentration jump parameters. Moreover, the skin friction coefficient, and the local Nusselt and Sherwood numbers have been estimated for different parameters are discussed from an engineering point of view. We found a significant increase in thickness of the thermal and concentration boundary layer when the strength of the thermophoresis parameter is increased. In contrast, the thermal boundary layer increases with increasing the Brownian motion parameter while the reverse trend holds true for the concentration field.

Optimal Homotopy Analysis of MHD Natural Convection Flow of Thixotropic Fluid under Subjection of Thermal Stratification: Boundary Layer Analysis

In this article, the model of a non-Newtonian fluid (Thixotropic) flow past a vertical surface in the presence of exponential space and temperature dependent heat source in a thermally stratified medium is studied. It is assumed that free convection is induced by buoyancy and exponentially decaying internal heat source across the space. The dynamic viscosity is taken to be constant and thermal conductivity of this particular fluid model is assumed to vary linearly with temperature. Thermal stratification has been properly incorporated into the governing equation so that its effect can be revealed and properly reported. The governing partial differential equations describing the model are transformed and parameterized to a system of non-linear ordinary differential equation using similarity transformations. Approximate analytic solutions were obtained by adopting Optimal Homotopy Analysis Method (OHAM). The results show that for both cases of non-Newtonian parameters (Thixotropic) (K1=K2=0 & K1=K2=1.0), increasing stratification parameters, relate to decreasing in the heat energy entering into the fluid region and thus reducing the temperature of the Thixotropic fluid as it flows.

Comments on the paper “Impact of temperature dependent heat source and non-linear radiative flow of third grade fluid with chemical aspects”

The current discussion is presented to increase the awareness among the readers of the journal Thermal Science. Comments are presented in particular on the paper by Hayat et al. [1] where the authors investigated effect of non-linear radiative flow of third grade fluid and temperature dependent heat source with chemical aspects. The current discussion concerns some questionable results included in the aforementioned paper.

Free Convection Flow of an Electrically-Conducting Micropolar Fluid between Parallel Porous Vertical Plates Using Differential Transform

In the present study, the effect of temperature-dependent heat sources on the fully developed free convection flow of an electrically conducting micropolar fluid between two parallel porous vertical plates in the presence of a strong cross magnetic field is analyzed. The micropolar fluid fills the space inside the porous plates when the rate of suction at one boundary is equal to the rate of injection at the other boundary. The coupled nonlinear governing differential equations are solved using the differential transform method (DTM). Moreover, the Runge-Kutta shooting method (RKSM), which is a numerical method, is used for the validity of DTM method and an excellent agreement is observed between the solutions of DTM and RKSM. Trusting this validity, the effects of Hartmann number, Reynolds number, micropolar parameter, and applied electric field load parameter are discussed on the velocity, microrotation velocity, and temperature. The skin friction, the couple stress, and Nusselt numbers at the plates are shown in graphs. It is observed that the Hartmann number and the micropolar parameter decreases the skin friction and the couple stress at both plates for suction and injection.

Effects of non-Darcian and temperature dependent heat source on two-phase flow in a vertical porous space with thermal radiation

Effects of non-Darcian and temperature dependent heat source on two-phase flow in a vertical porous space with thermal radiation

Effect of radiation and Navier slip boundary of Walters’ liquid B flow over a stretching sheet in a porous media

This paper investigates the steady-state momentum and radiation heat transfer flow of a viscoelastic fluid in a porous media in the presence of a linear Navier slip boundary condition. The velocity of the fluid over the linear stretching sheet is varied linearly with the axial distance while a Walters’ liquid-B model is assumed for the viscosity. A similarity transformation reduces the Navier–Stokes equations to a set of partial differential equations that are converted into ordinary differential equations and solved analytically for the velocity. Moreover, heat is balanced between a temperature dependent heat source and radiation and leads to a differential equation with variable coefficients. The temperature equation is transformed to a confluent hypergeometric differential equation using the Rosseland approximation for the radiation and solved analytically. Results are discussed for two boundary conditions of the sheet, the prescribed surface temperature and the wall heat flux. Parameters like the Reynolds number, the viscoelastic parameter and the boundary slip parameter are found to determine the flow field. In addition, the Prandtl number, the radiation number, the wall temperature and the heat source/sink parameters are found to control the temperature distribution inside the stretching sheet.

Effect of Space and Temperature Dependent Heat Source on Heat Transfer of MHD Nanofluid Due to Non-Linear Stretching Sheet with Chemical Reaction

Effect of Space and Temperature Dependent Heat Source on Heat Transfer of MHD Nanofluid Due to Non-Linear Stretching Sheet with Chemical Reaction

Marangoni convection radiative flow of dusty nanoliquid with exponential space dependent heat source

Abstract The flow of liquids submerged with nanoparticles is of significance to industrial applications, specifically in nuclear reactors and the cooling of nuclear systems to improve energy efficiency. The application of nanofluids in water-cooled nuclear systems can result in a significant improvement of their economic performance and/or safety margins. Therefore, in this paper, Marangoni thermal convective boundary layer dusty nanoliquid flow across a flat surface in the presence of solar radiation is studied. A two phase dusty liquid model is considered. Unlike classical temperature-dependent heat source effects, an exponential space-dependent heat source aspect is considered. Stretching variables are utilized to transform the prevailing partial differential system into a nonlinear ordinary differential system, which is then solved numerically via the Runge-Kutta-Fehlberg approach coupled with a shooting technique. The roles of physical parameters are focused in momentum and heat transport distributions. Graphical illustrations are also used to consider local and average Nusselt numbers. We examined the results under both linear and quadratic variation of the surface temperature. Our simulations established that the impact of Marangoni flow is useful for an enhancement of the heat transfer rate.

Numerical Study of the Magnetic Field Effects on the Heat Transfer and Entropy Generation Aspects of a Power Law Fluid over an Axisymmetric Stretching Plate Structure

Numerical investigation of the effects of magnetic field strength, thermal radiation, Joule heating, and viscous heating on a forced convective flow of a non-Newtonian, incompressible power law fluid in an axisymmetric stretching sheet with variable temperature wall is accomplished. The power law shear thinning viscosity-shear rate model for the anisotropic solutions and the Rosseland approximation for the thermal radiation through a highly absorbing medium are considered. The temperature dependent heat sources, Joule heating, and viscous heating are considered as the source terms in the energy balance. The non-dimensional boundary layer equations are solved numerically in terms of similarity variable. A parameter study on the Nusselt number, viscous components of entropy generation, and thermal components of entropy generation in fluid is performed as a function of thermal radiation parameter (0 to 2), Brinkman number (0 to 10), Prandtl number (0 to 10), Hartmann number (0 to 1), power law index (0 to 1), and heat source coefficient (0 to 0.1).

Finite element solution of MHD power-law fluid with slip velocity effect and non-uniform heat source/sink

The laminar steady boundary layer flow of an incompressible MHD Power-law fluid past a continuously moving surface is investigated numerically. The study involves the influence of surface slip and non-uniform heat source/sink on the flow and heat transfer. The governing boundary layer flow equations are transformed into non-dimensional, non-linear coupled ordinary differential equations with the help of suitable similarity transformations. The Galerkin finite element method is implemented to crack the resulting system. The impact of different involved physical parameters is exhibited on the dimensionless velocity profile, temperature distributions and rate of heat transfer in graphical and tabular forms for pseudoplastic and dilatant fluids. The local Nusselt number is found to be the decreasing function of slip parameter, temperature and space-dependent heat sink parameter whereas it increases with increasing values of temperature and space dependent heat source parameter. The problem has important application in attaining the sustainable heat transfer rate for the cooling of fluids, especially in heat exchangers used frequently in chemical industry, in order to increase the trustworthiness of a system, as it removes high heat loads from these systems.

The effect of internal heat generation on a steady hydromagnetic poiseuille fluid flow between two parallel porous plates

This paper investigates the effects of internal heat generation on the steady flow of an incompressible and electrically conducting fluid flowing through a channel made up of two parallel porous plates with isothermal wall temperature, under the influence of a transverse magnetic field strength and temperature dependent heat source. The variable of an internal heat generation is assumed to be a linear function of temperature. The semi-analytical solutions of the equations governing the fluid flow are obtained for velocity and temperature profiles using a rapidly convergent Adomian decomposition method (ADM). Attention is focused on the influence of internal heat generation on the velocity and temperature profiles and the effects of other various physical parameters such as porous medium permeability parameter, viscous heating parameter, pressure gradient and magnetic field intensity on the fluid flow are also presented and discussed.

Unsteady MHD convective flow of Second grade fluid through a porous medium in a Rotating parallel plate channel with temperature dependent source

In this paper, we make an initial vale investigation of hydromagnetic convective flow of a viscous electrically conducting second grade fluid through a porous medium in a rotating parallel plate channel in the presence of a temperature dependent heat source. The perturbations in the flow are created by a constant pressure gradient along the plates in addition to non-torsional oscillations of the lower plate. The exact solutions of the velocity and the temperature fields consist of the steady state and the transient components using Laplace transform technique. The time required for the transient effects to decay is discussed in detail and the ultimate steady state consists of boundary layers on the plates and an interior. Attention is focused on the physical nature of the solutions, and the structure of the various kinds of boundary layers formed on the plates. The final steady state velocity and temperature fields are numerically discussed for different values of the governing parameters. The shear stresses and the Nusselt number are tabulated. Particular case when both the plates are at rest has also been computed and analyzed.

Marangoni Effects on Forced Convection of Power Law Fluids in Thin Film over an Unsteady Horizontal Stretching Surface with Heat Source

Objectives: In this paper, the effect of surface tension gradient on the transport phenomenon and temperature differences within a power-law liquid film on an unsteady horizontal stretching sheet with heat source is been investigated. Method: The flow of a fluid film and the heat transfer from the subsequent stretching surface is been found by applying similarity transformation. The numerical computation of the problem is done with aid of Maple. The system of governing non-linear partial differential equation is converted to a set of nonlinear ordinary differential equation using local similarity transformations, then solved numerically applying the Runge Kutta Felhberg-45 method. The effect of power law index n, Prandtl number Pr, the unsteadiness parameter S, Space dependent heat source parameter α 1 , temperature dependent heat source parameter β 1 , and film thickness parameter β(=η) on heat transfer and flow are studied and graphically presented. And it was found that the surface tension gradient and nonuniform heating source have tremendous impact on controlling the rate of convective heat transfer near the boundary layer region.

Unsteady Boundary Layer Flow over a Vertical Surface due to Impulsive and Buoyancy in the Presence of Thermal-Diffusion and Diffusion-Thermo using Bivariate Spectral Relaxation Method

In this article, unsteady boundary layer flow formed over a vertical surface due to impulsive motion and buoyancy is investigated. The mathematical model which properly accounts for space and temperature-dependent internal heat source in a flowing fluid is incorporated into the energy equation. This model is presented in this study as a term which accounts for two different forms of internal heat generation during the short time period and long time period. Due to the fluid flow under consideration, the influence of thermal-diffusion and diffusion-thermo are incorporated into the governing equation since it may not be realistic to assume that both effects are of smaller order of magnitude than the effects described by Fourier’s or Fick’s law. The corresponding effect of internal heat source on viscosity is considered; the viscosity is assumed to vary as a linear function of temperature. The flow model is described in terms of a highly coupled and nonlinear system of partial differential equations. The governing equations are non-dimensionalized by using suitable similarity transformation which unraveled the behavior of the fluid flow at short time and long time periods. The dimensionless system of non-linear coupled partial differential equations (PDEs) is solved using Bivariate Spectral Relaxation Method (BSRM). A parametric study of selected parameters is conducted and results of the surface shear stress, heat transfer and mass transfer at the wall are illustrated graphically and physical aspects of the problem are discussed.

Dual solutions for three-dimensional MHD flow of a nanofluid over a nonlinearly permeable stretching sheet

In this study we investigated the effect of space and temperature dependent heat generation/absorption on three-dimensional magnetohydrodynamic nanofluid flow over a nonlinearly permeable stretching sheet. After using appropriate self-similarity transformation the governing equations are solved numerically using bvp4c Matlab package. The effects of the non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed with the help of graphs. Also, coefficient of skin friction and Nusselt number is analyzed and presented through tables. It is found that present results have an excellent agreement with the existed studies under some special cases. Results indicate that an increase in space and temperature dependent heat source or sink increases the temperature and concentration profiles of the flow. Dual solutions exist only for certain range of power-law index.