Conjugate Heat Transfer Parameter Research Articles

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.

Entropy generation in purely electroosmotic flows of non-Newtonian fluids in a microchannel

In this work, the entropy generation rate in a purely electroosmotic flow of a non-Newtonian fluid in a parallel flat plate microchannel is studied. The power-law model is used for the rheological constitutive equation of the fluid under consideration. The entropy generation rate is obtained as an asymptotic solution to the conjugate heat transfer problem between the fluid and the solid walls of the microchannel. The influence of the following dimensionless parameters on the entropy generation rate is predicted: the flow behavior index, n, the electrokinetic parameter, κ¯, the well-known Péclet number, Pe, the normalized power generation term, Λ, the dimensionless temperature difference, Ω, the ratio of the microchannel thickness to the microchannel length, β, the ratio of the microchannel wall thickness to the microchannel wall length, ε, and a conjugate heat transfer parameter, α¯, which relates the competition between the conductive heat in the microchannel wall and the conductive heat in the laminar flow. This set of parameters directly determines the thermal performance of the microchannel model. We predict that the entropy generation is dominated by Joule heating.

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.

VARIABLE VISCOSITY EFFECTS ON A CONJUGATE LAMINAR FILM-CONDENSATION PROCESS

In this work, we treat theoretically the conjugate film-condensation process on a vertical fin immersed in a saturated vapor, taking into account that the viscosity of the condensed film is a well-defined function of the temperature. In order to predict the thickness of the film, the momentum and energy balance equations for the condensate and the energy equation for the vertical fin are reduced to a nonlinear system of two ordinary differential equations. These governing equations contain four nondimensional parameters, the Jakob number, Ja, a conjugate heat transfer parameter, α, the aspect ratio of the fin, ϵ, and , that take into account the effect of the variable viscosity. Using the limit Ja < <1 and the boundary layer approximation for the film-condensation process, the nondimensional heat transfer and the overall mass flow rates of the condensed fluid have been obtained as functions of the involved nondimensional parameters.

Conjugate Heat Transfer Analysis of the Film Condensation on a Vertical Fin Immersed in a Porous Medium

Abstract. In the present work, we treat theoretically the conjugate film-condensation heat transfer process on a vertical fin embedded in a homogeneous porous medium. Due to the finite thermal conductivity of the fin, the simultaneous thermal interaction between the vertical fin and the film condensation is presented. In order to predict the thickness of the condensate, the momentum and energy balance equations of the condensate and the energy equation for the fin are reduced to a nonlinear system of two ordinary differential equations with three non-dimensional parameters: the Jakob number, , a conjugate heat transfer parameter Ja α and the aspect ratio of the fin e . Using the limit of and the boundary layer approximation for the film-condensation process, the nondimensional heat transfer and the overall mass flow rates of condensed fluid have been obtained as functions of the involved nondimensional parameters. 1 Ja Mecanica Computacional Vol XXV, pp. 281-296 Alberto Cardona, Norberto Nigro, Victorio Sonzogni, Mario Storti. (Eds.) Santa Fe, Argentina, Noviembre 2006

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.

Numerical simulation of micropolar fluid flow along a flat plate with wall conduction and buoyancy effects

This paper presents a numerical analysis of the flow and heat transfer characteristics of mixed convection in a micropolar fluid flowing along a vertical flat plate with conduction effects. The governing non-linear 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 examines the effects of the buoyancy parameter, the conjugate heat transfer parameter, the micropolar parameter and the Prandtl number on the flow and the thermal fields. The results show that the conjugate heat transfer parameter has a significant influence on the fluid flow and heat transfer characteristics. The buoyancy parameter reduces the solid–liquid interfacial temperature but increases 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 buoyancy effect. Finally, compared with the case of pure forced convection, a reduction in the interfacial temperature, an increase in the skin friction factor and an increase in the local heat transfer rate are obtained in the current mixed convection case.

Conjugate mixed convection laminar non-Darcy film condensation along a vertical plate in a porous medium

This study numerically investigates the coupling of the wall conduction with laminar mixed-convection film condensation along a vertical plate within a saturated vapor porous medium. The Darcy–Brinkman–Forchheimer model is utilized to treat the flow field and the effect of heat conduction across the wall is taken into account. The governing system of equations with their corresponding boundary conditions are first transformed into a dimensionless form by a non-similar transformation and the resulting equations are then solved by the cubic spline collocation method. Of interest are the effects of the conjugate heat transfer parameter A, the Jakob number Ja, the Peclet number Pe and the inertia parameter Γ on the fluid–solid interfacial temperature distribution and the local heat transfer rate. The results indicate that the effect of wall conduction has great influences on the filmwise condensation heat transfer, and is to reduce the local heat transfer rate as well as the dimensionless interfacial temperature in comparison with the isothermal plate case. It is found that the local heat transfer rate increases with a decrease in the Jakob number, the Peclet number, and the inertial parameter or an increase in the conjugate heat transfer parameter. In addition, the overall surface heat transfer rate for different values of A and Ja are also obtained.

The coupling of conduction with mixed convection of micropolar fluids past a vertical flat plate

In this paper, the thermo-fluid-dynamic field resulting from the coupling of wall conduction with laminar mixed convection heat transfer of micropolar fluids along a vertical flat plate is studied. A conjugate heat transfer is proposed to serve as a controlling index that indicates the effect of wall conduction. After a suitable coordinate transformation to reduce the complex of the governing boundary layer equations, the resulting nonlinear differential equations were solved with an implicit finite difference method. The effects of the micropolar material parameters, the buoyancy parameter, the Prandtl number and the conjugate heat transfer parameter on the flow and the thermal fields are discussed in detail.

Effect of wall conduction on natural convection flow of micropolar fluids along a flat plate

This article numerically studies the coupling of wall conduction with laminar free convective heat transfer of micropolar fluids along a vertical flat plate. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting equations are then solved by the cubic spline collocation method. The effects of the conjugate heat transfer parameter p, the micropolar material parameter Δ and the Prandtl number Pr on the flow and thermal fields are discussed in detail. The results clearly indicate that the conjugate heat transfer parameter has a significant influence on the fluid flow and heat transfer characteristics in comparison with those reported for isothermal flat plate. The interfacial temperature increases monotonically along the streamwise direction. The conjugate heat transfer parameter is to reduce the solid-liquid interfacial temperature, the skin friction factor, the wall couple stress and the local heat transfer rate. The effect of wall conduction on the local heat transfer rate is more pronounced for a system with larger Prandtl numbers or smaller micropolar material parameters. In addition, comparing it to Newtonian fluids, a reduction in the skin friction factor and the local heat transfer rate is reported.