Conjugate mixed convection-conduction heat transfer along a vertical cylindrical fin in non-newtonian fluids

By considering the interaction between conduction within the fin and convection to the fluid surrounding the fin, an analysis is presented to study the heat transfer characteristics of laminar mixed convection of a non-Newtonian fluid flow over a vertical cylindrical fin. Due to the compatibility conditions of heat flux and temperature at the surface of fin, the boundary layer equations of the fluid are coupled with the heat conduction equation of the fin and should be solved simultaneously. Of interest are the effects of transverse curvature parameter, bouyancy parameter, power-law viscosity index, generalized Prandtl number and conjugate convection-conduction parameter on the local heat transfer coefficient, local heat flux and temperature distribution of the fin. Comparison of the calculated results with available data sets in the open literature for a Newtonian fluid shows a very good performance of the present numerical procedure.     

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

The transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21012     

Conjugate heat transfer of mixed convection for viscoelastic fluid past a horizontal flat-plate fin

A conjugate mixed convection heat transfer problem of a second-grade viscoelastic fluid past a horizontal flat-plate fin has been studied. Governing equations include heat conduction equation of the fin, and continuity equation, momentum equation and energy equation of the fluid, have been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat-plate flow (β = 0) on the fin surface were obtained by a generalized Falkner–Skan flow derivation. These solutions have been used to iterate with the heat conduction equation of the fin to obtain distributions of the local convective heat transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number (Pr), the elastic number (E), the free convection parameter (G) and the conduction–convection coefficient (N_cc) are from 0.1 to 100, 0.001 to 0.01, 0 to 1.5 and 0.05 to 2.0, respectively. The elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a horizontal flat-plate fin. In addition, same as results from Newtonian fluid flow and conduction analysis of a horizontal flat-plate fin, a better heat transfer has been obtained with a larger N_cc, G and Pr.     

Convective‐radiative fins with simultaneous variation of thermal conductivity,heat transfer coefficient,and surface emissivity with temperature

This paper is a numerical study of thermal performance of a convective‐radiative fin with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. The convective heat transfer is assumed to be a power function of the local temperature between the fin and the ambient which allows simulation of different convection mechanisms such as natural convection (laminar and turbulent), boiling, etc. The thermal conductivity and the surface emissivity are treated as linear functions of the local temperature between the fin and the ambient which provide a satisfactory representation of the thermal property variations of most fin materials. The thermal performance is governed by seven parameters, namely, convection–conduction parameter Nc, radiation–conduction parameter Nr, thermal conductivity parameter A, emissivity parameter B, the exponent n associated with convective heat transfer coefficient, and the two temperature ratios, θ_a and θ_s, that characterize the temperatures of convection and radiation sinks. The effect of these parameters on the temperature distribution and fin heat transfer rate are illustrated and the results interpreted in physical terms. Compared with the constant properties model, the fin heat transfer rate can be underestimated or overestimated considerably depending on the values of the governing parameters. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20408     

Performance of a Circular Fin in a Cylindrical Porous Enclosure

The problem of natural convection heat transfer from a vertical cylindrical fin to a saturated porous medium in a cylindrical enclosure is solved numerically. A conjugate conduction-convection analysis is accomplished by solving the equation of heat conduction in the fin together with the mass, momentum and energy balance equations in the porous medium. Numerical results are obtained by using ADI method. The effects of the conduction-convection ratio parameter, aspect ratio and Darcy number on local heat transfer coefficients and fin efficiency are discussed. Comparison of the local heat transfer coefficients and fin efficiency is shown with those for non-porous medium.     

Conjugate forced convection-conduction plate fin in power law fluids

The heat transfer characteristics of laminar, forced convection flow for power law fluids from a vertical plate fin are studied analytically based on the conjugate convection and conduction theory. The resulting boundary layer equations of fluids are coupled with the one-dimensional heat conduction equation of fin through interfacial conditions. Numerical results for the local heat flux, local heat transfer coefficient, and temperature distribution along the fin surface and overall heat transfer rate under the effects of the conjugate convection-conduction parameter, generalized Prandtl number and fluid flow index are illustrated. The results obtained of the non-Newtonian power law fluid are found to have trends similar to those of the Newtonian fluids.     

Frost behavior on a fin considering the heat conduction of heat exchanger fins

A mathematical model is proposed for predicting frost behavior on a heat exchanger fin under frosting conditions, taking into account fin heat conduction. The change in the three-dimensional airside airflow caused by frost growth is reflected in this model. The numerical estimates of frost thickness are consistent with experimental data, with an error of less than 10%. Due to fin heat conduction, frost thickness decreases exponentially toward the fin tip, while considerable frost growth occurs near the fin base. When a constant fin surface temperature is assumed, the predicted frost thickness was larger by more than 200% at maximum, and the heat flux by more than 10% on average, compared to results obtained with fin heat conduction taken into account. Therefore, fin heat conduction could be an essential factor in accurately predicting frost behavior. To improve prediction accuracy under the assumption of constant fin surface temperature, the equivalent temperature (for predicting frost behavior) is defined to be the temperature at which the heat transfer rate neglecting fin heat conduction is the same as the heat transfer rate with fin heat conduction taken into consideration. Finally, a correlation for predicting the equivalent temperature is suggested.     

Heat transfer from a vertical fin array by laminar natural convection and radiation—A quasi‐3D approach

A quasi‐3D numerical model is developed to study the problem of laminar natural convection and radiation heat transfer from a vertical fin array. An enclosure is formed by two adjacent vertical fins and vertical base in the fin array. Results obtained from this enclosure are used to predict heat transfer rate from a vertical fin array. All the governing equations related to fluid in the enclosure, together with the heat conduction equation in both fins are solved by using the Alternating Direction Implicit (ADI) method for getting the temperatures along the height of the fin and the temperature of the fluid in the enclosure. Separate analysis is carried out to calculate the heat transfer rates from the end fins in the fin array. A numerical study has been carried out for the effect of fin height, fin spacing, fin array base temperature, and fin emissivity on total heat transfer rates and effectiveness of the fin array. The numerical results obtained for an eight‐fin array show good agreement with the available experimental data. Results show that the fin spacing is the most significant parameter and there exists an optimum value for the fin spacing for which the heat transfer rate from the fin array is maximum. Correlations are presented for predicting the total heat transfer rate, average Nusselt number, and effectiveness of the fin array. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20360     

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

The heat transfer and thermal distribution through porous fins have gotten a lot of attention in recent years due to their extensive applications in the manufacturing and engineering field. In porous fins, the impact of magnetic field aids in improved heat transfer enhancement. Also, the combination of an electric effect and a magnetic field considerably enhances heat transfer. In this direction, the thermal distribution through a convective–radiative longitudinal trapezoidal porous fin with the impact of an internal heat source and an electromagnetic field is discussed in the present analysis. The governing heat equation is nondimensionalized with nondimensional terms, and the transformed nonlinear ordinary differential equation is solved analytically using the DTM–Pade approximant algorithm. Furthermore, the graphical discussion is presented to explore the impact of various nondimensional parameters, such as convection-conduction parameter, fin taper ratio, thermomagnetic field, radiation–conduction parameter, internal heat generation parameter, and thermoelectrical field on the temperature gradient of the fin. The investigation's key findings disclose that as the magnitude of the convection–conduction parameter, fin taper ratio, and radiation–conduction parameter increase, the thermal distribution through the fin reduces. The thermal distribution inside the fin increases for the heat-generating parameter, thermoelectric, and thermomagnetic fields.     

Optimum design of a longitudinal fin array with convection and radiation heat transfer using a genetic algorithm

In the present work, the optimization of a longitudinal fin array is investigated. Heat is transferred by conduction along the fins and dissipated from the fin surface via natural convection to the ambient and radiation to other fin surfaces and surrounding. The aim of the optimization is to find the optimum geometry and the number of fins in such a way that the rate of heat transfer from the array is maximized. A modified genetic algorithm is used to maximize the objective function which is defined as the net heat rate from the fin surface for a given length. The fin profile is represented by B-spline curves, where the shape of fin is determined by the positions of a set of control points. The effects of the base temperature, the fin length and the height of array on the optimum geometry and on the number of fins are investigated by comparing the results obtained for several test cases. In addition, the contributions of convective heat transfer and radiative heat transfer in net heat transfer are studied for these cases. The enhancement of heat transfer due to the optimum fin geometry is examined by comparing the results obtained for the optimum fin profile with those with conventional profiles.     

MHD-conjugate heat transfer analysis for a vertical flat plate in presence of viscous dissipation and heat generation

In this paper, the effects of magnetic field, viscous dissipation and heat generation on natural convection flow of an incompressible, viscous and electrically conducting fluid along a vertical flat plate in the presence of conduction are investigated. Numerical solutions for the governing momentum and energy equations are given. A discussion is provided for the effects of magnetic parameter, viscous dissipation parameter and heat generation parameter on two-dimensional flow. Detailed analysis of the velocity profile, temperature distribution, skin friction, rate of heat transfer and the surface temperature distribution are shown graphically.     

Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity

A hybrid numerical technique which combines the differential transformation and finite difference method is utilized to investigate the annular fin with temperature-dependent thermal conductivity. The exposed surfaces of the fin dissipate heat to the surroundings by convection and radiation. The influences of the convective heat transfer coefficient, absorptivity, emissivity and thermal conductivity parameter on the temperature distribution are examined. The results show that the convective heat transfer plays a dominant role for heat dissipation under the convection–radiation condition. The optimum radii ratio of fin which maximizes the heat transfer rate and fin efficiency is also discussed.     

Laminar conjugate mixed convection in a vertical channel with heat generating components

Conjugate mixed convection arising from protruding heat generating ribs attached to substrates (printed circuit boards) forming channel walls is numerically studied. The substrates with ribs form a series of vertical parallel plate channels. Assuming identical disposition and heat generation of the ribs on each board, a channel with periodic boundary conditions in the transverse direction is considered for analysis. The governing equations are discretised using a control volume approach on a staggered mesh and a pressure correction method is employed for the pressure–velocity coupling. The solid regions are considered as fluid regions with infinite viscosity and the thermal coupling between the solid and fluid regions is taken into account by the harmonic thermal conductivity method. Parametric studies are performed by varying the heat generation based Grashof number in the range 10⁴–10⁷ and the fan velocity based Reynolds number in the range 0–1500, with air as the working medium. Results are obtained for the velocity and temperature distributions, natural convection induced mass flow rate through the channel, the maximum temperatures in the heat sources and the local Nusselt numbers. The natural convection induced mass flow rate in mixed convection is correlated in terms of the Grashof and Reynolds numbers. In pure natural convection the induced mass flow rate varies as 0.44 power of Grashof number. The maximum dimensionless temperature is correlated in terms of pure natural convection and forced convection inlet velocity asymptotes. For the parameter values considered, the heat transferred to the working fluid via substrate heat conduction is found to account for 41–47% of the heat removal from the ribs.     

Heat transfer from a horizontal fin array by natural convection and radiation—A conjugate analysis

The problem of natural convection heat transfer from a horizontal fin array is theoretically formulated by treating the adjacent internal fins as two-fin enclosures. A conjugate analysis is carried out in which the mass, momentum and energy balance equations for the fluid in the two-fin enclosure are solved together with the heat conduction equations in both the fins. The numerical solutions by using alternating direction implicit (ADI) method yield steady state temperature and velocity fields in the fluid, and temperatures along the fins. Each end fin of the array is exposed to limited enclosure on one side and to infinite fluid medium on the other side. Hence a separate analysis is carried out for the problem of end fin exposed to infinite fluid medium with appropriate boundary conditions. From the numerical results, the heat fluxes from the fins and the base of the two-fin enclosure, and the heat flux from the end fin are calculated. Making use of the heat fluxes the total heat transfer rate and average heat transfer coefficient for a fin array are estimated. Heat transfer by radiation is also considered in the analysis. The results obtained for a four-fin array are compared with the experimental data available in literature, which show good agreement. Numerical results are obtained to study the effectiveness for different values of fin heights, emissivities, number of fins in a fixed base, fin base temperature and fin spacing. The numerical results are subjected to non-linear regression and equations are obtained for heat fluxes from the two-fin enclosure and single fin as functions of Rayleigh number, aspect ratio and fin emissivity. Also regression equations are obtained to readily calculate the average Nusselt number, heat transfer rate and effectiveness for a fin array.     

Optimum geometry of fixed volume plate fin for maximizing heat transfer

A method is presented for finding the plate fin geometry for maximizing total heat transfer when cooled by forced or natural convection. The method is based on an approximate treatment of conjugated heat transfer in which analytical results are utilized. As a result of this type of approach, non-dimensional variables have been found that contain the geometrical and thermal properties of a fin and the flow. An essential fact is that there is no need to evaluate convection heat transfer coefficients. Only one variable with a fixed value is needed to determine the geometry of a fixed volume fin that gives the maximum heat transfer.     

Radiative nanofluid flow and heat transfer between parallel disks with penetrable and stretchable walls considering Cattaneo–Christov heat flux model

In this work, we explore the unsteady squeezing flow and heat transfer of nanofluid between two parallel disks in which one of the disks is penetrable and the other is stretchable/shrinkable, in the presence of thermal radiation and heat source impacts, and considering the Cattaneo–Christov heat flux model instead of the more conventional Fourier's law of heat conduction. A similarity transformation is utilized to transmute the governing momentum and energy equations into nonlinear ordinary differential equations with the proper boundary conditions. The achieved nonlinear ordinary differential equations are solved by the Duan–Rach Approach (DRA). This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of diverse active parameters, such as the suction/injection parameter, the solid volume fraction, the heat source parameter, the thermal relaxation parameter, and the radiation parameter on flow and heat transfer traits are examined. In addition, the value of the Nusselt number is calculated and portrayed through figures.     

Inverse and efficiency of heat transfer convex fin with multiple nonlinearities

In this article, we first propose the novel semi‐analytical technique—modified Adomian decomposition method (MADM)—for a closed‐form solution of the nonlinear heat transfer equation of convex profile with singularity where all thermal parameters are functions of temperature. The longitudinal convex fin is subjected to different boiling regimes, which are defined by particular values of n (power index) of heat transfer coefficient. The energy balance equation of the convex fin with several temperature‐dependent properties are solved separately using the MADM and the spectral quasi‐linearization method. Using the values obtained from the direct heat transfer method, the unknown parameters of the profile, such as thermal conductivity, surface emissivity, heat generation number, conduction‐convection parameter, and radiation‐conduction parameter are inversely predicted by an inverse heat transfer analysis using the simplex search method. The effect of the measurement error and the number of measurement points has been presented. It is found that present measurement points and reconstruction of the exact temperature distribution of the convex fin are fairly in good agreement.     

Analysis of conjugated laminar and turbulent forced convection- conduction heat transfer of a plate fin

A numerical investigation of conjugated forced convection — conduction heat transfer of a plate fin is presented. Laminar and turbulent cases are considered. A second-order finite difference technique and a two-equation turbulence model are applied. Results are presented for various values of the convection-conduction parameter and the Reynolds number. It is found that if the boundary layer flow is mainly laminar or turbulent, the conventional fin theory yields acceptable prediction of the fin efficiency although errors in the fin temperature and local heat flux distributions may occur. However, if the boundary layer has laminar and turbulent parts of about equal spacial extent, an application of the conventional theory may result in large errors even in the efficiency.     

Conjugate heat transfer analysis of a heat generating vertical plate

This paper mainly deals with conjugate heat transfer problem pertinent to rectangular fuel element of a nuclear reactor dissipating heat into an upward moving stream of liquid sodium. Introducing boundary layer approximations, the equations governing the flow and thermal fields in the fluid domain are solved simultaneously along with two-dimensional energy equation in the solid domain by satisfying the continuity of temperature and heat flux at the solid–fluid interface. The boundary layer equations are discretized using fully implicit finite difference scheme so as to adopt marching technique solution procedure, while second-order central difference scheme is employed to discretize the energy equation in the solid domain and the resulting system of finite difference equations are solved using Line-by-Line Gauss–Seidel iterative solution procedure. Numerical results are presented for a wide range of parameters such as aspect ratio, A_r, conduction–convection parameter, N_cc, heat generation parameter, Q, and flow Reynolds number, Re. It is concluded that there exist an upper or a lower limiting value of these parameters above or below which the temperature in the fuel element crosses its allowable limit. It is also found that an increase in Re results in considerable increase in overall heat dissipation rate from the fuel element.     

TRANSIENT CONJUGATE NATURAL CONVECTION HEAT TRANSFER ALONG A VERTICAL PLATE FIN IN A HIGH-POROSITY MEDIUM

The non-Darcian effects on transient conjugate natural convection-conduction heat transfer from a two-dimensional vertical plate fin embedded in a high-porosity medium are studied numerically. The coupled nonlinear partial differential equations for transient natural convection in the porous medium and transient heat conduction in the fin are solved numerically with a cubic spline collocation method. Numerical results for the heat transfer characteristics are presented for water and air at selected values of the convection-conduction parameter at different times. It is shown that the inertial effect on heat transfer characteristics is negligible at short times; its effect, however, becomes increasingly important at longer times. The time taken to reach steady state is longer for a fluid with a smaller Prandtl number and for a system with a smaller value of the convection-conduction parameter.