Inverse Linear Function Of Temperature Research Articles

BIO-MAGNETIC FLOW OF HEAT TRANSFER OVER MOVING HORIZONTAL PLATE BY THE PRESENCE OF VARIABLE VISCOSITY AND TEMPERATURE

This work aims at the investigation of 2D, steady, laminar, viscous, incompressible boundary layer and heat transfer flow of a biomagnetic fluid over a convectively heated moving horizontal plate in the presence of a magnetic dipole. It is assumed that the fluid viscosity is the inverse linear function of temperature and the temperature at the wall varies as power law function. The governing equations involve a system of coupled PDEs (momentum and energy equations) which are converted into a system of nonlinear ODEs by utilizing similarity transformations. The transformed ODEs along with the boundary conditions are then solved numerically by adopting a finite difference algorithm. The physical effects of the governing parameters (i.e., ferrohydrodynamic interaction parameter, buoyancy force parameter, viscosity-temperature parameter, wall parameter) on the flow fields along with the skin friction and heat transfer rate are presented. Verification of this work has been done by comparing former published results and acceptable agreement is found. It has been analyzed theoretically by using suitable transformations, that the ferrohydrodynamic interaction parameter, has a great enhancement effect on biomagnetic fluid rather than that on a regular fluid. It has been discovered that the inclusion of certain intensity of magnetic field along with the consideration of the variable viscosity and temperature, has significant effects on the flow and heat transfer mechanism. These outcomes could be of interest in medical as well as bioengineering implementations, like magnetic drug delivering in blood cells, separating RBCs (Red Blood Cells), controlling the flow of blood during surgeries and treating cancer by producing magnetic hyperthermia.

The Effect of Variable Viscosity on Unsteady Free Convective Fluid Flow over a Stretching Surface in the Presence of Thermal Radiation and Viscous Dissipation

The unsteady free convective flow of an incompressible, viscous, electrically conducting fluid over a vertical stretching surface with variable viscosity and thermal radiation in the presence of viscous dissipation is considered. The fluid is assumed to be gray, absorbing emitting but non-scattering medium. Thus, the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The viscosity of the fluid is assumed to be an inverse linear function of temperature. Specifically, the study is aimed at determining the effects of variable viscosity parameter ( ), Eckert number ( ), and radiation parameter ( ) on temperature distribution profiles, while holding the Prandtl number constant that is corresponding to air. The specific energy equation governing the fluid flow is solved numerically by the finite difference method. The nonlinear partial differential equation is solved numerically by the finite difference method. MATLAB code is used to solve the Forward Time and Centered Space (FTCS) scheme. Further, stability and consistency analyses are performed on the FTCS scheme to determine the convergence of the scheme. Results for temperature distribution profiles are presented graphically for different values of variable viscosity ( ), Eckert number ( ), radiation parameter ( ). The findings are that an increase in variable viscosity and Eckert number causes an enhancement of temperature distribution profiles whereas an increase in radiation parameter leads to a decrease in temperature distribution profiles. The FTCS scheme was found to be unconditionally stable and consistent. The results obtained in this study follow expected trends and are in good agreement with some previous studies.

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.

Effect of Variable Viscosity and Thermal Conductivity on Unsteady Free Convective Flow of a Micropolar Fluid Past a Vertical Cone

A numerical investigation of the effects of variable viscosity and thermal conductivity on an unsteady free convective MHD flow of a micropolar fluid past a vertical cone with variable heat flux, viscous dissipation, and Joule dissipation is carried out. The fluid viscosity and thermal conductivity are modeled by inverse linear functions of temperature. The governing partial differential equations are reduced to nondimensional ones, which are discretized using an efficient and unconditionally stable implicit finite difference method of the Crank–Nicolson type and solved for prescribed boundary conditions by an iterative scheme based on the Gauss–Seidel method. Numerical results are presented for the velocity, temperature, and microrotation rate profiles. The values of the skin friction and Nusselt number for various combinations of parameters are given.

Effects of Variable Viscosity and Thermal Conductivity on Micropolar Fluid Flow Due to a Stretching Cylinder in Presence of Magnetic Field

In the presence of magnetic field, steady flow of a micropolar fluid due to a stretching cylinder is studied. Viscosity and thermal conductivity are assumed to be inverse linear functions of temperature. The governing partial differential equations are converted into ordinary differential equations using suitable similarity transformations and then solved by fourth order Runge-Kutta shooting method and developing Matlab programme. The graphs show the effects of different parameters and the skin friction coefficient and Nusselt numbers are shown in tabular form.

Effect of Variable Fluid Properties on MHD Mixed Convection Flow of Second-Grade Fluid Over a Linear Heated Stretching Sheet with a Convective Boundary Condition

An analysis has been carried out to study the effect of variable fluid properties on MHD mixed convection flow of second-grade fluid flowing along an infinite stretching sheet with convective boundary condition. The fluid is placed on an infinite heated elastic surface with linear stretching rate and a vertical velocity component due to suction at the sheet is considered. The combined effects of inertia, viscous, visco-elastic, and magnetic forces are analyzed. The basic equations governing the flow, heat transfer, and mass transfer are reduced to a set of nonlinear ordinary differential equations by using appropriate similarity transformations for velocity, temperature, and concentration. The fluid viscosity is assumed to vary as an inverse linear function of temperature, whereas the thermal conductivity as a linear function of temperature. These equations are solved numerically and the results for velocity, temperature, concentration, skin friction, local Nusselt number, and local Sherwood number are discussed using flow parameters. The investigation reveals that Joule heating and viscous dissipation enhance the temperature profile, and there are considerable effects in the presence of variable fluid properties. Comparison with previous studies shows good agreement as a special case of the problem.

Impact of temperature-dependant viscosity and thermal conductivity on MHD boundary layer flow of two-phase dusty fluid through permeable medium

The distribution of solid particles in a fluid leading to two-phase nature as in micro-propulsion, aerosol filtration, conveying of powdered materials, petroleum industry and lunar ash flow can be described as an open question. In this study, boundary layer flow of an electrically conducting magnetohydrodynamic dusty fluid in a porous medium is presented. Fluid viscosity and thermal conductivity are assumed to be an inverse linear function of temperature. The governing nonlinear partial differential equations and their physically realistic boundary conditions are reduced into dimensionless form by using appropriate transformations. The resultant coupled system of equations is discretized using finite difference scheme and Thomas algorithm is implemented to solve the linear algebraic equation. A representative set of numerical results are plotted to visualize the impact of existing fluid interaction parameters. Skin-friction, heat and mass transfer coefficients are tabulated and results obtained are in good agreement with the literature. From this investigation, velocity, temperature and concentration fields are observed to be an increasing function in accordance with the raise in both viscosity variation parameter (θr) and thermal conductivity variation parameter (θc). This computation illustrates that the friction factor coefficient is found to be less for low thermal expansion coefficient irrespective of all emerging parameters of the flow. Furthermore, enhancement in θr reduces the heat transfer rate and strengthens the mass transfer rate whereas the reverse trend is observed for θc.

Exact similarity solutions for forced convection flow over horizontal plate in saturated porous medium with temperature-dependent viscosity

In this paper, we revisit a mathematical model representing a two-dimensional forced convection boundary-layer flow over a horizontal impermeable plate with a variable heat flux and viscosity. It is assumed that the fluid viscosity varies as an inverse linear function of temperature, the free stream velocity varies as an inverse linear of x and the wall heat flux varies with x as $x^{\lambda}$ ; where $\lambda > -1$ and x measures the distance along the surface. Analytical local similarity solutions are presented which reveal that there are two competing effects: $\lambda$ and $\theta_{e}$ ; where $\theta_{e}$ is the variable viscosity parameter. It has been shown that for $\theta_{e} > 0$ dual solutions exist and boundary separation occurs, while a unique local similarity solution exists for any $\theta_{e} < 0$ .

Combined influence of radiation absorption and Hall current effects on MHD double-diffusive free convective flow past a stretching sheet

Abstract An analysis has been carried out on the influence of radiation absorption, variable viscosity, Hall current of a magnetohydrodynamic free-convective flow and heat and mass transfer over a stretching sheet in the presence of heat generation/absorption. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The boundary-layer equations governing the fluid flow, heat and mass transfer under consideration have been reduced to a system of nonlinear ordinary differential equations by employing a similarity transformation. Using the finite difference scheme, numerical solutions to the transform ordinary differential equations have been obtained and the results are presented graphically. The numerical results obtained are in good agreement with the existing scientific literature.

Effects of variable viscosity and thermal conductivity on magnetohydrodynamic free convection flow of a micropolar fluid past a stretching plate through porous medium with radiation, heat generation, and Joule dissipation

The effects of temperature-dependent viscosity and thermal conductivity on free convection magnetohydro- dynamic ow of an optically thin gray, viscous, and incompressible micropolar uid and heat transfer past a stretching plate through porous medium in the presence of radiation, heat generation, and Joule dissipation were studied. The uid viscosity and thermal conductivity were assumed to vary as inverse linear functions of temperature. Using similarity transformation, the governing partial differential equations of motion were reduced to ordinary ones, which were solved numerically for prescribed boundary conditions using the shooting method. Numerical results for the velocity, angular velocity, and temperature proles are shown graphically and the skin friction and Nusselt number are presented in tab- ular form for various values of the parameters, giving the ow and heat transfer characteristics. We found that viscosity enhanced microrotation, while an increase in thermal conductivity reduced the temperature.

Effects of Variable Viscosity and Thermal Conductivity on Combined Free-Forced Convection Heat and Mass Transfer MHD Flow of Micropolar Fluid past a Vertical Porous Plate in a Porous Medium

The effect of temperature dependent viscosity and thermal conductivity on combined free-forced convection heat and mass transfer MHD flow of micropolar fluid past a vertical porous plate in a porous medium is studied where the viscosity and thermal conductivity are assumed to be inverse linear functions of temperature. The partial differential equations governing the flow with heat and mass transfer of the problem are transformed into dimensionless form of ordinary differential equations by using similarity substitutions. The governing boundary value problems are then solved numerically using shooting method. The effects of various parameters viz. viscosity parameter, thermal conductivity parameter, thermal buoyancy parameter, mass buoyancy parameter, coupling constant parameter, Prandtl number and magnetic parameter on velocity, micro-rotation, temperature and species concentration fields are investigated and presented graphically. The coefficient of skin-friction, Nusselt number and Sherwood number are also computed and presented tabular form.

Dufour and soret effects on steady MHD convective flow of a fluid in a porous medium with temperature dependent viscosity: Homotopy analysis approach

This paper presents an analytical method of solution to steady two-dimensional hydromagnetic flow of a viscous incompressible, electrically conducting fluid past a semi-infinite moving permeable plate embedded in a porous medium. It is assumed that the fluid properties are constant except for the fluid viscosity which vary as an inverse linear function of temperature. The boundary layer equations are transformed in to a coupled ordinary differential equations with the help of similarity transformations. The resulting coupled ordinary differential equations were solved using the Homotopy Analysis Method (HAM). The combined effects of Dufour and Soret was investigated and presented graphically with controlling pertinent physical parameters.

Effects of Variable Viscosity and Thermal Conductivity on the Flow of Dusty Fluid over a Continuously Moving Plate

paper investigates the effects of variable viscosity and thermal conductivity of flow and heat transfer of dusty fluid over a continuously moving plate with suction or injection. The fluid viscosity and thermal conductivity are assumed to be vary as an inverse linear function of temperature. The flow governing equations are transformed into ordinary differential equations and the resulting coupled non-linear boundary value problem is solved numerically using Runge-Kutta shooting method. The results are represented graphically to illustrate influence of the various physical parameters on the velocity and temperature profiles of both fluid and dust phases. Skin friction and Nusselt number are also coupled and presented in tabular form. Keywordsmoving plate, variable viscosity and thermal conductivity, dusty fluid, fluid-particle interaction parameter, shooting method.

Effects of Variable Viscosity and Thermal Conductivity on MHD Flow of Micropolar Fluid in a Continuous Moving Flat Plate

of temperature dependent viscosity and thermal conductivity on magnetohydrodynamic flow and heat transfer over a continuous moving plate of a micropolar fluid have been studied. The fluid viscosity and thermal conductivity are assumed to be vary as inverse linear functions of temperature. Using similarity transformations the governing partial differential equations of motion are reduced to ordinary ones, which are solved numerically for prescribed boundary conditions using shooting method. Numerical results for the velocity, angular velocity, temperature profiles and magnetic field are shown graphically and the Skin friction and Nusselt number are presented in tabular form for various values of the parameters giving the flow and heat transfer characteristics.

Effects of Double Dispersion on Mixed Convection in a Power-law Fluid Saturated Porous Medium with Variable Properties Using Lie Scaling Group Transformations

The present study is to investigate the influence of the variable properties and double dispersion on mixed convection flow over a vertical plate embedded in a power-law fluid saturated porous medium. The variable viscosity is assumed to vary as a inverse linear function of temperature and thermal conductivity as a linear function of temperature. Similarity transformations of the governing partial differential equations are obtained using Lie scaling group transformations. These similarity equations are solved numer- ically by using the Shooting technique. The numerical results for the non dimensional velocity, temperature and concentration are displayed graphically for different values of variable viscosity, thermal conductivity, thermal dispersion and solutal dispersion. Local heat and mass transfer are shown in a tabular form. The present results are compared with previously published work and are found to be in good agreement.

Effect of variable viscosity on flow past a porous wedge with suction or injection: new results

An analysis is carried out to study the problem of the steady flow and heat transfer of an incompressible fluid over a static wedge in the presence of suction/injection with variable viscosity. The viscosity is assumed to vary as inverse linear function of temperature. The governing partial differential equations are first transformed into a system of non-linear ordinary differential equations using similarity transformations, and later solved numerically by using Runge–Kutta–Fehlberg method with shooting technique. The velocity and temperature profiles, the skin friction and the rate of heat transfer are computed and discussed for various values of suction/injection parameter, viscosity parameter and Hartree pressure gradient parameter for gases and liquids.

Finite Element Analysis of Radiative Mixed Convection Magneto‐Micropolar Flow in a Darcian Porous Medium with Variable Viscosity and Convective Surface Condition

A mathematical study is presented for the collective influence of the buoyancy parameter, convective boundary parameter and temperature dependent viscosity on the steady mixed convective laminar boundary flow of a radiative magneto‐micropolar fluid adjacent to a vertical porous stretching sheet embedded in a Darcian porous medium. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Using appropriate transformations, the governing equations of the problem under consideration are transformed into a system of dimensionless nonlinear ordinary differential equations, which are then solved with the well‐tested, efficient finite element method. The results obtained are depicted graphically to illustrate the effect of the various important controlling parameters on velocity, microrotation, and temperature functions. The skin friction coefficient, wall couple stress, and the rate of heat transfer have also been computed and presented in tabular form. Comparison of the present numerical results with earlier published data has been performed and the results are found to be in good agreement, thus validating the accuracy of the present numerical code. The study finds applications in conducting polymer flows in filtration systems, trickle bed magnetohydrodynamics in chemical engineering, electro‐conductive materials processing, and so on.

Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium

Abstract This work is focused on the study of unsteady magnetohydrodynamics boundary-layer flow and heat transfer for a viscous laminar incompressible electrically conducting and rotating fluid due to a stretching surface embedded in a saturated porous medium with a temperature-dependent viscosity in the presence of a magnetic field and thermal radiation effects. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. With appropriate transformations, the unsteady MHD boundary layer equations are reduced to local nonsimilarity equations. Numerical solutions of these equations are obtained by using the Runge–Kutta integration scheme as well as the local nonsimilarity method with second order truncation. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity in primary and secondary flows as well as the local skin-friction coefficients and the local Nusselt number are illustrated graphically to show interesting features of Darcy number, viscosity-variation, magnetic field, rotation of the fluid, and conduction radiation parameters.

The Combined Effect of Chemical Reaction, Radiation on Heat and Mass Transfer along a Continuously Moving Surface in Presence of Thermophoresis

The effect of chemical reaction, radiation on heat and mass transfer along a continuously moving surface in presence of thermophoresis has been discussed. The fluid viscosity is assumed as an inverse linear function of temperature. The system of non-linear partial differential equations developed in the process have finally transformed into a set of ordinary differential equations with the help of similarity transformation and then solved numerically using RungaKutta method with shooting technique. The results showing the effect of physical parameters on velocity, temperature and concentration have been computed and presented graphically to discuss them in detail. It has been observed that temperature increases with an increase in radiation parameter. Also, it is seen that the concentration decreases with the increase in chemical reaction parameter and Schmidt number.

Boundary layer flow over a yawed cylinder with variable viscosity

PurposeThe purpose of this paper is to study the effect of non‐uniform double slot suction (injection) into a steady laminar boundary layer flow over a yawed cylinder when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Non‐similar solutions have been obtained from the starting point of the streamwise co‐ordinate to the exact point of separation.Design/methodology/approachThe governing equations are tackled by the implicit finite difference scheme in combination with the quasi‐linearization technique. Quasi‐linear technique can be viewed as a generalization of the Newton‐Raphson approximation technique in functional space. An iterative sequence of linear equations is carefully constructed to approximate the nonlinear equations for achieving quadratic convergence and monotonicity. The quadratic convergence and monotonicity are unique characteristics of the quasilinear implicit finite difference scheme, which makes this scheme superior to built‐in iteration of upwind or finite amplitude techniques.FindingsThe results indicate that the separation can be delayed by non‐uniform double slot suction and also by moving the slot downstream. However, the effect of non‐uniform double slot injection is just the opposite. Yaw angle has very little affect on the location of the point of separation.Originality/valueThis analysis is useful in understanding many boundary layer problems of practical importance for undersea applications, for example, in suppressing recirculating bubbles and controlling transition and/or separation of the boundary layer over submerged bodies.