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1.
This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.  相似文献   

2.
This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.  相似文献   

3.
In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.  相似文献   

4.
Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic (MHD) flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.  相似文献   

5.
In this paper, the viscoelsatic boundary layer flow and the heat transfer near a vertical isothermal impermeable surface and in a quiescent fluid are examined. The gov-erning equations are formulated and solved numerically using MackCormak’s technique. The results show excellent agreement with previously published results by a compari-sion. Representative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers, and local skin friction coefficients are shown graphically for different values of viscoelsatic parameters. In general, it is found that the velocities increase inside the hydrodynamic boundary layers and the temperatures decrease inside the thermal boundary layers for the viscoelsatic fluid as compared with the Newtonian fluid due to favorable tensile stresses. Consequently, the coefficients of friction and heat transfer enhance for higher viscoelsatic parameters.  相似文献   

6.
The magnetohydrodynamic(MHD) flow of the third grade fluid between two permeable disks with heat transfer is investigated.The governing partial differential equations are converted into the ordinary differential equations by suitable transformations.The transformed equations are solved by the homotopy analysis method(HAM).The expressions for square residual errors are defined,and the optimal values of convergencecontrol parameters are selected.The dimensionless velocity and temperature fields are examined for various dimensionless parameters.The skin friction coefficient and the Nusselt number are tabulated to analyze the effects of dimensionless parameters.  相似文献   

7.
The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.  相似文献   

8.
The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.  相似文献   

9.
The steady, laminar, incompressible flow and heat transfer of a viscous fluid between two circular cylinders for two different types of thermal boundary conditions are investigated. The governing Navier-Stokes and thermal equations of the flow are reduced to a nonlinear system of ordinary differential equations. The equations are solved analyt- ically using the homotopy analysis method (HAM). Convergence of the HAM solutions is discussed in detail. These solutions are then compared with recently obtained numericM and perturbative solutions. Plots of the velocity and temperature profiles are provided for various values of the relevant parameters.  相似文献   

10.
In this paper, the influence of heat transfer and induced magnetic field on peristaltic flow of a Johnson-Segalman fluid is studied. The purpose of the present investigation is to study the effects of induced magnetic field on the peristaltic flow of non-Newtonian fluid. The two-dimensional equations of a Johnson-Segalman fluid are simplified by assuming a long wavelength and a low Reynolds number. The obtained equations are solved for the stream function, magnetic force function, and axial pressure gradient by using a regular perturbation method. The expressions for the pressure rise, temperature, induced magnetic field, pressure gradient, and stream function are sketched and interpreted for various embedded parameters.  相似文献   

11.
The main aim of the present work is to investigate the flow and heat transport properties of non-Newtonian Casson-Williamson fluid through an upright microchannel along with entropy generation analysis, and explore the effects of convective boundary conditions, Couette-Poiseuille flow, and nonlinear radiation. The movement of liquid is scrutinized with the Hall effect and exponential heat source. The rheological characteristics of the Casson-Williamson fluid model are also considered. By considering the desirable similarity variables, the equations of motion are reduced to nonlinear ordinary differential equations. The Runge-Kutta-Fehlberg fourth-fifth order method along with the shooting method is adopted to solve these dimensionless expressions. The detailed investigation is pictorially displayed to show the influence of effective parameters on the entropy generation and the Bejan number. One of the major tasks of the exploration is to compare the Casson fluid and the Williamson fluid. The results show that the rate of heat transfer in the Casson fluid is more remarkable than that in the Williamson fluid.  相似文献   

12.
This paper presents a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation and work due to deformation are considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case).  相似文献   

13.
The present paper deals with the analysis of boundary layer flow and heat transfer of a dusty fluid over a stretching sheet with the effect of non-uniform heat source/sink. Here we consider two types of heating processes namely (i) prescribed surface temperature and (ii) prescribed surface heat flux. The momentum and thermal boundary layer equations of motion are solved numerically using Runge Kutta Fehlberg fourth–fifth order method (RKF45 Method). The effects of fluid particle interaction parameter, Eckert number, Prandtl number, Number of dust particle and non-uniform heat generation/absorption parameter on temperature distribution are analyzed and also the effect of wall temperature gradient function and wall temperature function are tabulated and discussed.  相似文献   

14.
An analysis is performed for flow and heat transfer of a steady laminar boundary layer flow of an electrically conducting fluid of second grade in a porous medium subject to a transverse uniform magnetic field past a semi-infinite stretching sheet with power-law surface temperature or power-law surface heat flux. The effects of viscous dissipation, internal heat generation of absorption and work done due to deformation are considered in the energy equation. The variations of surface temperature gradient for the prescribed surface temperature case (PST) and surface temperature for the prescribed heat flux case (PHF) with various parameters are tabulated. The asymptotic expansions of the solutions for large Prandtl number are also given for the two heating conditions. It is shown that, when the Eckert number is large enough, the heat flow may transfer from the fluid to the wall rather than from the wall to the fluid when Eckert number is small. A physical explanation is given for this phenomenon.  相似文献   

15.
16.
An analysis is carried out to study the momentum, mass and heat transfer characteristics on the flow of visco-elastic fluid (Walter's liquid-B model) past a stretching sheet in the presence of a transverse magnetic field.In heat transfer, two cases are considered:
1.
The sheet with prescribed surface temperature (PST case); and
2.
The sheet with prescribed wall heat flux (PHF case).
The solution of equations of momentum, mass and heat transfer are obtained analytically. Emphasis has been laid to study the effects of various parameters like magnetic parameter Mn, visco-elastic parameter k1, Schmidt number Sc, and Prandtl number Pr on flow, heat and mass transfer characteristics.  相似文献   

17.
An analysis is carried out to study the flow and heat transfer characteristics in a second grade fluid over a stretching sheet with prescribed surface temperature including the effects of frictional heating, internal heat generation or absorption, and work due to deformation. In order to solve the fourth-order non-linear differential equation, associated with the flow problem, a fourth boundary condition is augmented and a proper sign for the normal stress modulus is used. It is observed that for a physical flow problem the solution is unique. The solutions for the temperature and the heat transfer characteristics are obtained numerically and presented by a table and graphs. Furthermore, it is shown that the heat flow is always from the stretching sheet to the fluid.  相似文献   

18.
Exact solutions are obtained for the heat transfer in an electrically conducting fluid past a stretching sheet subjected to the thermal boundary with either a prescribed temperature or a prescribed heat flux in the presence of a transverse magnetic field. The solutions for the heat transfer characteristics are evaluated numerically for different parameters, such as the magnetic parameterN, the Prandtl numberPr, the surface temperature indexs, and the surface heat flux indexd. It is observed that for the prescribed surface temperature case the fluid temperature increases due to the existance of the magnetic field, and decreases as the Prandtl number or the surface temperature index increases; for the prescribed surface heat flux case, the surface temperature decreases as the Prandtl number of the surface heat flux index increases, and the magnetic parameter decreases. In addition, varying the prescribed surface temperature indexs affects the mechanism of heat transfer.  相似文献   

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