Vertical Slender Hollow Cylinder Research Articles

Effect of heat radiating and generating second-grade mixed convection flow over a vertical slender cylinder with variable physical properties

The boundary-layer flow and heat transfer characteristics of an incompressible thermally radiating second-grade fluid on a linearly stretching permeable vertical slender hollow cylinder subject to viscous dissipation and convection heat exchange at the wall with the surroundings in conjunction with augmented far-field condition is studied. The free-stream or ambient velocity is considered to be linearly stretching while the prescribed surface temperature of the cylinde varies nonlinearly as the axial distance in the presence of elastic deformation and volumetric heat generation. The model incorporates the temperature dependent fluid properties as per dynamic viscosity and thermal conductivity while the viscoelastic or second-grade parameters are temperature-free. In virtue of appropriate transformation, the energy and momentum equations are reduced to nonlinear ordinary differential equations, and then solved numerically using forty-fifth order Runge-Kutta-Fehlberg (RKF45) integration scheme in tandem with shooting method. Analysis is carried out through simulated tables and codes generated graphs. This study reveals that the wall shear stress factor increases with the velocity ratio, mixed convection, curvature and suction parameters but reduces with the stretching parameter. Also the local heat transfer rate enhances with the Prandtl number, suction, curvature, velocity ratio and stretching parameters in contrast to that due to viscoelastic parameter.

Conjugate Heat and Mass Transfer on Steady MHD Mixed Convection Flow along a Vertical Slender Hollow Cylinder with Heat Generation and Chemical Reaction Effects

This paper studies the effects of heat generation and chemical reaction on the coupled conjugate heat and mass transfer by MHD laminar mixed convective flow along a vertical slender hollow cylinder. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a non similar transformation and the resulting equations are then solved by the finite difference method using Matlab@ following the code bvp4c. Numerical results of the velocity, temperature and concentration for different values of the conjugate heat transfer parameter p, the magnetic parameter M, the heat generation Q, and the chemical reaction K are studied. The local skin friction, Nusselt number and Sherwood number are also analyzed and presented graphically. In the numerical ranges of the main parameters, it is found mainly that working with strong conjugate heat transfer or/and all others parameters affects negatively the Nusselt and Sherwood numbers. The same trend is revealed for the skin friction factor.

Flow visualization using heat lines for unsteady radiative hydromagnetic micropolar convection from a vertical slender hollow cylinder

The present study aims to investigate the thermal radiation heat transfer effect on unsteady magnetohydrodynamic flow of micropolar fluid over a uniformly heated vertical hollow cylinder using Bejan's heat function concept. The normalized conservation equations emerge as a system of time-dependent non-linear coupled partial differential equations. Under appropriate wall and free stream conditions these equations are solved with an efficient unconditionally stable implicit scheme of Crank-Nicolson type. Important thermo-physical parameters featured include the magnetic body force parameter (M), Grashof (free convection) parameter (Gr), Eringen micropolar material parameter (K), Prandtl number (Pr), conjugate heat transfer parameter (P) and radiative-conductive Rosseland parameter (N), are analyzed on the flow-field with ranges 0–3, 105–106, 0–1.2, 0.7–7.0, 0–0.5 and 0–15, respectively. The time-histories of average values of momentum and heat transport coefficients, as well as the steady-state flow variables are presented for selected values of these non-dimensional parameters. With elevation in magnetic parameter or radiation parameter, the time taken for the flow-field variables to attain the time-independent state increases. The dimensionless thermal radiative heat function values are closely correlated with the overall rate of heat transfer on the outer hot cylindrical wall. Bejan's heat flow visualization implies that the thermal radiative heat function contours are compact in the neighbourhood of leading edge of the boundary layer on the outer hot cylindrical wall. Increasing radiation or magnetic parameter values result in an increase in the deviation of heat lines from the hot wall. Also, the heat lines are observed to depart slightly away from the hot wall with greater values of vortex viscosity. Furthermore, the deviations of flow variables from the hot wall for a micropolar fluid are significant compared to the Newtonian fluid (vanishing micropolar vortex viscosity).

Bejan’s Heat Flow Visualization for Unsteady Micropolar Fluid Past a Vertical Slender Hollow Cylinder with Large Grashof Number

The heat function concept has been developed for the heatline visualization to study the conjugate heat transfer effects at large Grashof number. The time-dependent natural convective micropolar fluid flow past a vertical slender hollow cylinder with the inner wall kept at a uniform temperature is the physical model. The mathematical model of this problem is given by highly time reliant non-linear coupled equations and is resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and heat transport coefficients as well as the steady-state velocity, microrotation and temperature are plotted for different values of non-dimensional parameters arising in the system across the boundary layer. As the vortex viscosity parameter increases, the time taken for the flow-field variables to attain the time-independent state decreases, while the reverse trend is noticed for the conjugate heat transfer parameter. The dimensionless heat function values are closely associated with the overall rate of heat transfer. The Bejan’s heat flow visualization implies that the heat function contours are compact in the neighborhood of leading edge of the hot cylindrical wall. It is observed that as the vortex viscosity parameter values get amplified, the deviations of heatlines from the heated wall is more. It is seen that the deviations of flow variables from the heated wall for a micropolar fluid are significant compared to the Newtonian fluid.

Heat flow visualization for unsteady Casson fluid past a vertical slender hollow cylinder

The conjugate heat transfer (CHT) effects have been studied on the heat function concept. The physical model consists of the Casson fluid flowing past a slender vertical cylinder. The inner wall of the hollow cylinder is maintained with identical temperature. The solutions of the governing equations which are coupled and non-linear are found by applying implicit scheme. The plots on the flow are depicted pictorially for all the controlling parameters. The steady-state time is extended for the Casson fluid parameter. The Bejan’s heat flow visualization implies that the heat function contours are compact in the neighbourhood of leading edge at the wall of the cylinder having more temperature. The deviations of the heatlines from the hot wall go on reducing by escalating the values of all the controlling parameters. The Casson fluid plays a significant role at the hot wall when compared to the Newtonian fluid.

The effect of the conjugate-conduction parameter and Prandtl number on the free convective couple stress fluid flow over a vertical cylinder

Numerical analysis is performed to study the conjugate heat transfer effects on the transient free convective couple stress fluid flow over a vertical slender hollow circular cylinder with the inner surface at a constant temperature. A set of non-dimensional governing equations namely, the continuity, momentum and energy equations is derived and these equations are unsteady non-linear and coupled. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretised forms of governing equations. These equations are solved using the Thomas and pentadiagonal algorithms. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. Transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is observed that the time required for the variables to reach the steady-state increases with the increasing values of conjugate-conduction parameter (P) and Prandtl number. In the vicinity of the hot wall, the velocity and temperature of the fluid decrease as P increases. It is noticed that the steady-state values of and decreases as P increases.

Heatline visualization for conjugate heat transfer of a couple stress fluid from a vertical slender hollow cylinder

The flow visualization has been made using the heat function concept for the conjugate heat transfer effects on the transient free convective couple stress fluid flow over a vertical slender hollow circular cylinder with the inner surface kept at a constant temperature. The governing non-linear equations are solved numerically by using an unconditionally stable implicit method. Numerical results show that the deviations of flow variables of couple stress fluid from those of the Newtonian fluid turn out to be considerable. Boundary layer flow visualization indicates that the streamlines exist starting from the leading edge to the far downstream, while the heatlines terminate at a finite distance from the cylinder wall. It is noticed that the steady-state values of average skin-friction and heat transfer rate decrease as the conjugate-conduction parameter increases.

Finite element modeling of conjugate mixed convection flow of Al2O3–water nanofluid from an inclined slender hollow cylinder

Steady laminar mixed convection flow and heat transfer characteristics of Al2O3–water nanofluid about a vertical slender hollow cylinder are investigated numerically, under the effect of wall conduction. The transformed, non-dimensional, nonlinear governing equations (obtained with the Boussinesq approximation) are solved, using a robust, extensively validated, Galerkin finite element method for spherical-shaped nanoparticles with volume fraction ranging up to 4%, with associated boundary conditions. Nine-node quadrilateral finite elements are employed. Experimental models for thermal conductivity and viscosity incorporating Brownian motion terms have been taken into consideration. The influence of physical parameters, namely wall conduction parameter, Richardson number (buoyancy parameter) and nanoparticle volume fraction, on velocity profile, temperature profile and on Nusselt number is shown graphically. Excellent validation of the present numerical results has been achieved with earlier published results. Both skin friction coefficient and Nusselt number are enhanced with increasing Richardson number. With increasing inclination angle there is a decrease in average Nusselt number. Furthermore, average Nusselt number and interfacial temperature are both reduced with nanoparticle diameter. The flow is accelerated with increasing Richardson number whereas the bulk temperature is found to be suppressed. The study has important applications in thermal enhancement of solar energy systems.

Transient Free Convective Conjugate Heat Transfer from a Vertical Slender Hollow Cylinder

A numerical study has been carried out for the conjugate heat transfer on unsteady natural convection boundary layer flow of a viscous incompressible fluid over a vertical slender hollow cylinder. A Crank-Nicolson type of implicit method is used to solve the governing unsteady, non-linear and coupled equations. The resulting system of equations are solved by using the Thomas algorithm. The computations are carried out for different values of Prandtl number Pr and conjugate-conduction parameter P.

Conjugate Transient Free Convective Heat Transfer from a Vertical Slender Hollow Cylinder with Heat Generation Effect

Numerical analysis is performed to study the conjugate heat transfer and heat generation effects on the tran- sient free convective boundary layer flow over a vertical slender hollow circular cylinder with the inner surface at a con- stant temperature. A set of non-dimensional governing equations namely, the continuity, momentum and energy equations is derived and these equations are unsteady non-linear and coupled. As there is no analytical or direct numerical method available to solve these equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The dis- cretized equations are solved using the tridiagonal algorithm. Numerical results for the transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is ob- served that the time required to reach the steady-state increases as the conjugate-conduction parameter or heat generation parameter increases.

MHD-Conjugate Heat Transfer Analysis for Transient Free Convective Flow Past a Vertical Slender Hollow Cylinder

In this paper the effects of magnetic field and conduction on the transient free convective boundary layer flow over a vertical slender hollow circular cylinder with the inner surface at a constant temperature are investigated. The trans- formed dimensionless governing equations for the flow and conjugate heat transfer are solved by using the implicit finite difference scheme. For the validation of the current numerical method heat transfer results for a Newtonian fluid case where the magnetic effect and conduction is zero are compared with those available in the existing literature, and an excellent agreement is obtained. Numerical results for the transient flow variables, average wall shear stress and average heat transfer rate are shown graphically. In all these profiles it is observed that the times needed to reach the steady-state and the temporal maximum increases as the magnetic parameter or conjugate heat transfer parameter increases.

Effects of buoyancy and conjugate heat transfer on non-Darcy mixed convection about a vertical slender hollow cylinder embedded in a porous medium with high porosity

This study investigates mixed convection heat transfer about a vertical slender hollow cylinder in the buoyancy and conjugate heat transfer effects in the porous medium with high porosity. The non-similar solutions using the Keller box method are obtained. The wall conduction parameter p, the porous medium parameter k 1, the Forchheimer parameter F∗ and the Richardson number are the main parameters. For various values of these parameters the local skin friction and local heat transfer parameters are determined. The validity of the methodology is checked by comparing the results with those available in the open literature and a fairly good agreement is observed. Finally, it is determined that the local skin friction and the local heat transfer coefficients increase with an increase buoyancy parameter Ri, porous medium parameter k 1, Forchheimer parameter F∗ and decrease with conjugate heat transfer parameter p.

The effect of conjugate heat transfer on MHD mixed convection about a vertical slender hollow cylinder

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical slender hollow cylinder is studied numerically, under the effect of wall conduction. A uniform magnetic field is applied perpendicular to the cylinder. The non-similar solutions using the Keller box method are obtained. The wall conduction parameter, the magnetic parameter and the Richardson number are the main parameters. For various values of these parameters the local skin friction and local heat transfer parameters are determined. The validity of the methodology is checked by comparing the results with those available in the open literature and a fairly good agreement is observed. Finally, it is determined that the local skin friction and the local heat transfer coefficients increase with an increase the magnetic parameter Mn and buoyancy parameter Ri and decrease with conjugate heat transfer parameter p.

Numerical simulation for natural convection of micropolar fluids flow along slender hollow circular cylinder with wall conduction effect

This paper presents a numerical analysis of the flow and heat transfer characteristics of natural convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with conduction effects. The nonlinear formulation governing equations and their associated boundary conditions are first cast into dimensionless forms by a local non-similar transformation. The resulting equations are then solved using the cubic spline collocation method and the finite difference scheme. This study investigates the effects of the conjugate heat transfer parameter, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The conjugate heat transfer parameter reduces the solid–liquid interfacial temperature, the skin friction factor and the local heat transfer rate. The effect of wall conduction on the local heat transfer rate, interfacial temperature and skin friction factor is found to be more pronounced in a system with a greater Prandtl number. Moreover, the current results are comparing with Newtonian fluid to obtain the important results of the heat transfer and flow characteristics on micropolar fluids. It shows that an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.

Conjugate free convection over a vertical slender hollow cylinder embedded in a porous medium

A numerical study of the steady conjugate free convection over a vertical slender, hollow circular cylinder with the inner surface at a constant temperature and embedded in a porous medium is reported. The governing boundary layer equations for the fluid-saturated porous medium over the cylinder along with the one-dimensional heat conduction equation for the cylinder are cast into dimensionless form, by using a non-similarity transformation. The resulting non-similarity equations with their corresponding boundary conditions are solved by using the Keller box method. Emphasis is placed on the effects caused by the wall conduction parameter, p, and calculations have covered a wide range of this parameter. Heat transfer results including the temperature profiles, the interface temperature profiles and the local Nusselt number are presented.

Effect of wall conduction on natural convection over a vertical slender hollow circular cylinder

An analysis is made of the laminar natural convection of incompressible fluids over a slender, hollow circular cylinder with the inner surface at a constant temperature ofTb. The temperature of the outer surface must be solved from the coupled conduction of the cylinder and the natural convection of the fluid over the cylinder. The objective of this paper is to investigate the effect of conduction on the heat transfer characteristics of the natural convection boundary layer of the fluid. A wall conduction parameter,p, is introduced which is a measure of the heat conductivities of the solid and the fluid and the thickness of the cylindrical shell. The governing differential equations, being non-similar, are solved by a finite-difference method. Numerical results are generated for a series of values ofp's and Prandtl numbers.