Application of the Haar wavelet method on a continuously moving convective‐radiative fin with variable thermal conductivity

In this paper, we numerically investigate the heat transfer in a continuously moving convective‐radiative fin with variable thermal conductivity by using Haar wavelets. Heat is dissipated to the environment simultaneously through convection and radiation. The effect of various significant parameters—in particular the thermal conductivity parameter a, convection‐sink temperature θ_a, radiation‐sink temperature θ_s, convection‐radiation parameter N_c, radiation‐conduction parameter N_r, and Peclet number Pe—on the temperature profile of the fin are discussed and interpreted physically through illustrative graphs. Computational results obtained by the present method are in good agreement with the standard numerical solutions. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21038     

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     

Thermal analysis of a moving fin using the radial basis function approximation

In this study, the heat transfer and temperature distribution in a moving fin have been analyzed. The fin velocity was considered constant, and the thermal conductivity coefficient was variable with temperature, and the fin was under the effect of convection, radiation, and conduction heat transfer. The main equation of the problem was solved by the radial basis function method and validated by the numerical 4th-order Runge–Kutta method. Several parameters such as thermal conductivity parameter from 0 to 1, sink temperature parameter from 0.2 to 0.8, and N_r, N_c, Pe number from 1 to 4, were examined. The outcomes illustrate that increasing the thermal conductivity by 51.5% raises the conduction heat transfers as well as the dimensionless temperature by 3.42%. Moreover, increasing the sink temperature leads to a slow rise in ambient temperature by 22.8% in the maximum state. By raising the N_c and N_r parameters, near 33.3%, the temperature distribution profile is declined by 4% and 10.5%, respectively. And increasing the Pe number by 100% results in a rise in the temperature distribution by about 7%.     

A dimensionless analysis of heat and mass transport in an adsorber with thin fins; uniform pressure approach

A numerical study on heat and mass transfer in an annular adsorbent bed assisted with radial fins for an isobaric adsorption process is performed. A uniform pressure approach is employed to determine the changes of temperature and adsorbate concentration profiles in the adsorbent bed. The governing equations which are heat transfer equation for the adsorbent bed, mass balance equation for the adsorbent particle, and conduction heat transfer equation for the thin fin are non-dimensionalized in order to reduce number of governing parameters. The number of governing parameters is reduced to four as Kutateladze number, thermal diffusivity ratio, dimensionless fin coefficient and dimensionless parameter of Γ which compares mass diffusion in the adsorbent particle to heat transfer through the adsorbent bed. Temperature and adsorbate concentration contours are plotted for different values of defined dimensionless parameters to discuss heat and mass transfer rate in the bed. The average dimensionless temperature and average adsorbate concentration throughout the adsorption process are also presented to compare heat and mass transfer rate of different cases. The values of dimensionless fin coefficient, Γ number and thermal diffusivity ratio are changed from 0.01 to 100, 1 to 10^− 5 and 0.01 to 100, respectively; while the values of Kutateladze number are 1 and 100. The obtained results revealed that heat transfer rate in an adsorbent bed can be enhanced by the fin when the values of thermal diffusivity ratio and fin coefficient are low (i.e., α^? = 0.01, Λ = 0.01). Furthermore, the use of fin in an adsorbent bed with low values of Γ number (i.e. Γ = 10^− 5) does not increase heat transfer rate, significantly.     

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     

Heat transfer enhancement in annular fins using functionally graded material

This study presents a new approach on the heat transfer enhancement of annular fins with constant thickness using functionally graded materials. The thermal conductivity of the annular fin is assumed to be graded along the fin radius as a power‐law function. The resulting fin equation is solved by an approximate analytical method using the mean value theorem. The variable coefficients of second and third terms in the second‐order differential equation of the fin are replaced with their mean values along the fin radius. Several different graphs regarding the computed temperature profile, fin tip temperature, and fin efficiency are plotted with respect to the radii ratio thermo‐geometric parameter, and inhomogeneity parameter. It is demonstrated that the inhomogeneity parameter plays an important role on the heat transfer enhancement of the annular fin. However, for large radii ratios the effect of the inhomogeneity parameter decreases. Finally, it is stated that application of the functionally graded material in the annular fins, enhances the heat transfer rate between the fin and surrounding fluid resulting from the higher fin efficiency in comparison to the homogeneous annular fin. It is hoped that the results obtained from this study arouse interest among thermal designers and heat exchanger industries. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 603–617, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21053     

Natural convection heat transfer from a thermal heat source located in a vertical plate fin

A steady state conjugate conduction–convection investigation is performed on vertical plate fin in which a small heat source is located. Heat from the fin surface is transferred to the surroundings by laminar natural convection. The governing equations for the problem are the heat conduction equation for the fin and the boundary layer equations, which are continuity, momentum and energy equations, for the fluid. A computer program is written by using the finite difference method in order to solve the governing equations which are nonlinear and coupled. The best location of the heat source in the fin for maximum heat transfer rate depends on two parameters which are the conduction–convection parameter and the Prandtl number. The obtained results have shown that for the fin with large conduction–convection parameter, a heat source location for maximum heat transfer rate exists.     

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.     

Analytical Solution and Numerical Simulation for One‐Dimensional Steady Nonlinear Heat Conduction in a Longitudinal Radial Fin with Various Profiles

In this article we consider a model describing the temperature profile in a longitudinal fin with rectangular, concave, triangular, and convex parabolic profiles. Both thermal conductivity and the heat transfer coefficient are assumed to be temperature‐dependent, and given by a linear function and by power laws, respectively. In addition, the effects of the thermal conductivity gradient have been investigated. Optimal homotopy analysis method (OHAM) is employed to analyze the problem. The effects of the physical applicable parameters such as thermo‐geometric fin, thermal conductivity, and heat transfer mode are analyzed. The OHAM solutions are obtained and validity of obtained solutions is verified by the Runge–Kutta fourth‐order method and numerical simulation. A very good agreement is found between analytical and numerical results. Also for investigation of lateral effects on the accuracy of results, numerical simulation (by Ansis software) is compared with the homotopy analysis method (HAM) and numerical solution (by Runge–Kutta) of the energy balance equation. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21104     

Determination of temperature distribution for annular fins with temperature‐dependent thermal conductivity

In this paper, homotopy analysis method (HAM) has been used to evaluate the temperature distribution of annular fin with temperature‐dependent thermal conductivity and to determine the temperature distribution within the fin. This method is useful and practical for solving the nonlinear heat transfer equation, which is associated with variable thermal conductivity condition. HAM provides an approximate analytical solution in the form of an infinite power series. The annular fin heat transfer rate with temperature‐dependent thermal conductivity has been obtained as a function of thermo‐geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20353     

Exact,analytical heat transfer from longitudinal radiating fins of rectangular profile in a tube/fin ensemble

In this technical note, the problem concerning the quantification of heat transfer rates from an array of longitudinal radiating fins of rectangular profile in a tube/fin ensemble to a nonzero temperature sink is investigated. Radiating fins constitute essential elements in the thermal control of spacecrafts and satellites. We consider quasi one-dimensional heat conduction in the longitudinal radiating fins and neglect radiative exchange between the fins and the tubes carrying a hot fluid. It is demonstrated that the governing nonlinear differential equation of second order with constant coefficients and nonhomogeneous can be solved in exact, analytical implicit form. The pertinent temperature distributions eventually provide the magnitudes of heat transfer rates and fin efficiencies influenced by the radiation–conduction parameter and the sink temperature.     

Thermal performance of continuously moving radiative–convective fin of complex cross-section with multiple nonlinearities

Spectral collocation method (SCM) is adopted to predict the temperature distribution in the fin with temperature dependent thermal conductivity, heat transfer coefficient and surface emissivity. These temperature dependent properties or parameters cause multiple nonlinearities of energy equation. In order to reduce these multiple nonlinearities, a local linearization approach is adopted. The spatial distribution of dimensionless temperature is discretized by Lagrange interpolation polynomials. Accordingly, the differential form of energy equation is transformed to the matrix form of algebraic equation. The accuracy of the SCM model is verified by comparing SCM results with available data in references. Meanwhile, compared with analytical solutions, it can be found that the convergence rate of SCM approximately follows exponential law. In addition, effects of various physical parameters, such as Peclet number, thermal conductivity parameter, emissivity parameter, parameter of heat transfer coefficient, convective–conductive parameter and radiative–conductive parameter on the dimensionless temperature, the dimensionless fin-tip temperature and the volume adjusted fin efficiency are comprehensively analyzed.     

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.     

Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Numerical analysis has been done to investigate magnetohydrodynamics nonlinear convective flow of couple stress micropolar nanofluid with Catteneo‐Christov heat flux model past stretching surface with the effects of heat generation/absorption term, chemical reaction rate, first‐order slip, and convective boundary conditions. The coupled highly nonlinear differential equation governing the steady incompressible laminar flow has been solved by a powerful numerical technique called finite element method. The impacts of diverse parameters on linear velocity, angular velocity (microrotation), temperature, concentration profile, local skin friction coefficient, local wall couple stress, local Nusselt number, and Sherwood number are presented in graphical and tabular form. The result pointed out that the enhancement in material parameter β increases the velocity of the fluid while the couple stress parameter K has quite opposite effect. Heat and mass transfer rate of the fluid are enhanced by increasing material parameter while couple stress parameter shows the opposite influence. Moreover, heat and mass transfer rate are higher with the Catteneo‐Christov heat flux model than Fourier's law of heat conduction. The accuracy of the present method has been confirmed by comparing with previously published works.     

Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity

In this paper, heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) and variational iteration method (VIM) that can be applied to various types of differential equations. The results obtained employing the DTM and VIM are compared with a finite difference technique with Richardson extrapolation which is an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM. After these verifications the effects of parameters such as thickness parameter α, dimensionless fin semi‐thickness δ, length ratio λ, thermal conductivity parameter β, and radiation–conduction parameter N_r, on the temperature distribution and fin efficiency are illustrated and explained. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj) . DOI 10.1002/htj.21000     

Analytical solutions of the 1-D heat conduction problem for a single fin with temperature dependent heat transfer coefficient - II. Recurrent direct solution

The recurrent direct solution of the 1-D heat conduction problem for a single straight fin and spine with power-law-type temperature dependent heat transfer coefficient has been derived using inversion of the closed-form solution obtained in the first part of the study. The expression with improving convergence to calculate accurately the dimensionless temperature excess T_e at the fin tip for a given values of the fin parameter N and exponent n in heat transfer equation has been obtained by a linearization method. Equation for the temperature excess distribution throughout the fin has also been derived. The obtained formula for T_e allows to calculate the fin base thermal conductance and augmentation factor. Obtained expressions are seen to be simple and convenient for the engineering design of the fins and finned surfaces.     

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.     

An experimental and theoretical investigation into the heat transfer of a finned water wall tube in a circulating fluidized bed boiler

Heat transfer improvement in a water wall tube with fins was investigated in a circulating fluidized bed (CFB) boiler. Experiments were first conducted in a 6 MWth CFB boiler then a model was developed to analyse and interpolate the results. Temperatures at some discrete points within the wall cross‐section of the tube were measured by burying 0.8 mm thermocouples within a tube. Experimental data showed an increase in heat absorption up to 45 per cent. A good agreement between measured and predicted values was noted. The distribution of temperature in the metal wall and of heat flux around the outer wall of a tube with longitudinal and lateral fins was analysed by numerical solution of a two‐dimensional heat conduction equation. Effects of bed‐to‐wall heat transfer coefficient, water‐to‐tube inside heat transfer coefficient, bed temperature, water temperature and thermal conductivity of the tube material on the heat flux around the water tube are discussed. The present work also examines the influence of the length of the longitudinal fin and the water tube thickness. Heat flux was highest at the tip of the longitudinal fin. It dropped, but increased again near the root of the lateral fin. Copyright © 2000 John Wiley & Sons, Ltd.     

Application of Simplex Search Method for Predicting Unknown Parameters in an Annular Fin Subjected to Thermal Stresses

This article presents an inverse approach aimed at estimating the unknown parameters such as the coefficient of thermal expansion and the Biot number for satisfying a prescribed thermal stresses field in radial fin geometry. The variation of temperature with the radius of fin is obtained by solving the heat conduction-convection equation using regular perturbation method and applying proper boundary conditions. A closed form solution for the temperature dependent stress field has been derived by employing the classical elasticity theory coupled with semi-analytical solution for the temperature field. Using the data obtained from a forward method based on the analytical solution, two unknown parameters such as the coefficient of thermal expansion and the Biot number of the fin are simultaneously estimated by an inverse technique using the Nelder-Mead simplex search method. Effects of measurement errors and number of measurement points have been analyzed in detail. It is found that even with 10 measurement points a fairly good reconstruction of the stress field can be achieved.     

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.