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     

Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective–radiative surface cooling

This article investigates entropy generation in an asymmetrically cooled hollow cylinder with temperature dependent thermal conductivity and internal heat generation. The inside surface of the cylinder is cooled by convection on its inside surface while the outside surface experiences simultaneous convective–radiative cooling. The thermal conductivity of the cylinder as well as the internal heat generation within the cylinder are linear functions of temperature, introducing two nonlinearities in the one-dimensional steady state heat conduction equation. A third nonlinearity arises due to radiative heat loss from the outside surface of the cylinder. The nonlinear system is solved analytically using the differential transformation method (DTM) to obtain the temperature distribution which is then used to compute local and total entropy generation rates in the cylinder. The accuracy of DTM is verified by comparing its predictions with the analytical solution for the case of constant thermal conductivity and constant internal heat generation. The local and total entropy generations depend on six dimensionless parameters: heat generation parameter Q, thermal conductivity parameter β, conduction–convection parameters Nc₁ and Nc₂, conduction–radiation parameter Nr, convection sink temperature δ and radiation sink temperature η.     

Entropy generation analysis in a uniformly heated microchannel heat sink

Present investigation analyzes the issue of entropy generation in a uniformly heated microchannel heat sink (MCHS). Analytical approach used to solve forced convection problem across MCHS, is a porous medium model based on extended Darcy equation for fluid flow and two-equation model for heat transfer. Simultaneously, closed form velocity solution in a rectangular channel is employed to capture z-directional viscous effect diffusion and its pronounced effect on entropy generation through fluid flow. Subsequently, governing equations are cast into dimensionless form and solved analytically. Second law analysis of problem is then conducted on the basis of obtained velocity and temperature fields and expressions for local and average entropy generation rate are derived in dimensionless form. Average entropy generation rate is then utilized as a criterion for assessing the system performance. Finally, the effect of influential parameters such as, channel aspect ratio (α_S), group parameter (Br/Ω), thermal conductivity ratio (C) and porosity (ε) on thermal and total entropy generation is investigated. In order to examine the accuracy of the analysis, the results of thermal evaluation are compared to one of the previous investigations conducted for thermal optimization of MCHS.     

Irreversibility Analysis of MHD Flow over an Exponentially Stretching Sheet

This laminar fluid study investigates the effects of a magnetic field on the entropy generation during fluid flow and heat transfer due to an exponentially stretching sheet. Using the suitable transformations we have obtained the analytical solutions for momentum and energy equation in terms of Kummer's function. The velocity and temperature profiles are obtained for various physical parameters which are utilized to find the entropy generation number N_s and the Bejan number Be. The effects of various parameters on entropy production number and the Bejan number are studied through graphs using velocity and temperature profiles. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21112     

MHD flow over an inclined radiating plate with the temperature‐dependent thermal conductivity,variable reactive index,and heat generation

We study the effects of higher‐order chemical reaction and heat generation on coupled heat and mass transfer by MHD mixed convection from a permeable radiating inclined plate with the thermal convective boundary condition. The governing boundary layer equations are formulated and transformed into a set of similarity equations using dimensionless similarity variables developed by Lie group analysis. The resulting equations are then solved numerically using Maple 13 which uses a fourth–fifth order Runge–Kutta–Fehlberg algorithm for solving nonlinear boundary value problems. A representative set of numerical results are displayed graphically and discussed to show some interesting aspects of the parameters: convective heat transfer (γ), the angle of inclination (α), generation order of chemical reaction (n), reaction rate (λ), the Prandtl number (Pr), and the Schmidt number (Sc) on the dimensionless axial velocity, the temperature, and the concentration profiles. Also effects of pertinent parameters on the skin friction factor, the rate of heat, and the rate of mass transfer are obtained and displayed in tabular form. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20409     

Computation of entropy generation in dissipative transient natural convective viscoelastic flow

Entropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non‐Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this study, a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner‐Rivlin physical model of grade 2 (second‐grade fluid) is used, which can envisage normal stress variations in polymeric flow‐fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank‐Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second‐grade viscoelastic fluid parameter (), viscosity variation parameter (), and viscous dissipation parameter (). Also, group parameter (), Grashof number (Gr), and Prandtl number (Pr) are examined. Numerical solutions are presented for steady‐state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy, and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of , , and Gr. The converse trend is noticed with increasing Pr and . Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall.     

Effect of Viscous Dissipation and Internal Heat Generation/Absorption on Heat Transfer Flow Over a Moving Wedge With Convective Boundary Condition

In this study, the effects of viscous dissipation and internal heat generation/absorption on heat transfer viscous flow over a moving wedge in the presence of suction or injection with a convective boundary condition have been carried out numerically for various values of dimensionless parameters. With the help of similarity transformation, the momentum and energy equations are reduced to a set of coupled non‐linear ordinary differential equations. These equations are solved using the Runge–Kutta fourth‐order method with a shooting technique. The variation in the dimensionless temperature, velocity, heat transfer coefficient, and shear stress have been presented in tabular as well as in graphical form for a range of controlling parameters. It is shown that the dimensionless heat transfer rate is a strong function of viscous dissipation and convective parameters and heat transfer shows an enhanced behavior with the stretching parameter for both the favorable and unfavorable regimes. It is also shown that in the presence of a heat source, the dimensionless temperature and its gradients in thermal boundary layers are found to be high for a high value of the convection parameter. The comparison of present results with the available data shows a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 589–602, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21055     

Heat transfer from hollow cylinder using optimal homotopy asymptotic method

Optimal homotopy asymptotic method (OHAM) is employed to investigate steady‐state heat conduction with temperature dependent thermal conductivity and uniform heat generation in a hollow cylinder. Analytical models are developed for dimensionless temperature distribution and heat transfer for two cases using mixed boundary conditions (Dirichlet, Neumann, and Robin). The inner cylinder is assumed to be insulated in both cases. In the first case, the outer cylinder is assumed to be isothermal whereas in the second case, the outer cylinder is convectively cooled by a fluid of temperature T₂ through a uniform heat transfer coefficient h. The effects of Biot number, dimensionless heat generation, and thermal conductivity parameters on the temperature distribution and heat transfer are determined analytically and validated numerically using MAPLE 14. In both cases, the results obtained by OHAM are found to be in good agreement with the numerical results. It is found that as the Biot number increases, the results approach that of the isothermal case. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20407     

Forced convection and entropy generation inside a channel with a heat‐generating porous block

The flow pattern and heat transfer in a composite system containing a porous region has received considerable attention due to its importance in many engineering applications. In this study a thermal lattice Boltzmann model with nine velocities, D2Q9, is employed to investigate the fluid flow, heat transfer, and entropy generation inside a channel with a heat‐generating porous block. The effects of the porous block's length, porosity, and the Reynolds number, overflow pattern, heat transfer, and entropy generation were studied. The mentioned parameters have different effects on heat transfer and conjugate phenomena. By increasing the block length, Reynolds number, and porosity the dimensionless entropy generation will reduce. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21017     

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     

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     

Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

Entropy generation minimization in turbulent mixed convection flows

This paper reports the results of a numerical investigation of turbulent mixed convection from a symmetrically heated vertical channel, bathed by a steady upward flow of cold air. The computations have been performed using FLUENT 6.2 by employing the k–ε model for turbulence with enhanced wall treatment. The entropy generation rates due to (i) heat transfer across a finite temperature difference and (ii) irreversibility due to fluid friction have been calculated as post-processed quantities with the computed velocity and temperature profiles. Optimal inlet velocities at which the total entropy generation rate reaches a minimum value are found to exist, for every set of heat flux and aspect ratio. Further, this optimum velocity turns out to be independent of the aspect ratio and increases linearly with the heat flux. Simple and easy to use correlations for the optimum Reynolds number and the dimensionless average wall temperatures corresponding to the optima are developed. Plots of total entropy generation rate against the velocity clearly demonstrate that near the optimum conditions, buoyancy does not have a significant role to play in deciding the optimum. For the range of parameters considered in this study, it is seen that for optimum conditions, the ratio of the entropy generation due to fluid friction to total entropy generation rate, known in literature as the Bejan number, varies within a narrow band (0.14–0.22).     

Free Convective Flow of Pseudo‐Plastic and Newtonian Fluid Past a Convectively Heated Vertical Plate in a Darcian Porous Medium with Heat Generation/Absorption

We study the effect of thermal convective boundary condition and yield stress on free convection heat transfer for a pseudo‐plastic and Newtonian fluid past a permeable vertical flat plate which is embedded in a Darcian porous medium in the presence of heat generation/absorption numerically. Instead of using similarity transformations available in the literature, we have developed them by one point transformation and hence transform the governing boundary layer equations into corresponding similarity equations. The resulting similarity equations were solved using Runge–Kutta–Fehlberg fourth fifth (RKF45) order numerical method. The effect of the governing parameters, namely the power index of pseudo‐plastic fluids n, the rheological parameter Ω, heat generation/absorption parameter Q, suction/injection parameter , and the convective heat parameter B on the dimensionless velocity, the temperature and the heat transfer rates were investigated. A close agreement is found between our results and published results. Our present study finds application in printing and polymer industries and fluid phenomena associated with concentrated suspensions.     

Minimization of entropy generation by asymmetric convective cooling

The uniform internal heating of a solid slab and the viscous flow between two parallel walls, are used to illustrate the possibility of minimizing the global entropy generation rate by cooling the external surfaces convectively in an asymmetric way. The known analytic expressions for the temperature field, in the first case, and the velocity and temperature fields, in the second case, are used to calculate the global entropy generation rate explicitly. In dimensionless terms, this function depends on the dimensionless ambient temperature and convective heat transfer coefficients (Biot numbers) of each surface which, in general, are not assumed to be the same. When the Biot numbers for each surface are equal, the entropy generation rate shows a monotonic increase. However, when the Biot numbers are different this function displays a minimum for specific cooling conditions.     

Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi ₁, Biot number for convection on the outside surface Bi ₂, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Entropy Generation of Natural Convection Heat Transfer in a Square Cavity Using Al2O3–Water Nanofluid

Entropy generation of an Al₂O₃–water nanofluid due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subject to different side‐wall temperatures using a nanofluid for natural convection flow. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number between 10⁴ and 10⁷ and volume fraction between 0 and 0.05. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation, average entropy generation, and average Bejan number are determined. The results are compared for a pure fluid and a nanofluid. It is totally found that the heat transfer, and entropy generation of the nanofluid is more than the pure fluid and minimum entropy generation and Nusselt number occur in the pure fluid at any Rayleigh number. Results depict that the addition of nanoparticles to the pure fluid has more effect on the entropy generation as the Rayleigh number goes up.     

On the effect of heat generation/absorption on magnetohydrodynamic free convective flow in a vertical annulus: An Adomian decomposition method

This article deliberates fully developed natural convective flow of heat-generating/absorbing fluid in open-ended vertical concentric annulus under a magnetic field. The momentum and energy equations which arise from the definition of velocity and temperature are written in the dimensional form and then recast into the nondimensional form. Approximate solutions are obtained by using the semi-analytical Adomian decomposition method. The solutions for the velocity, temperature, skin friction, mass flux and rate of heat transfer are obtained. The influence of physical parameters such as heat generation/absorption parameter $\left(\delta \right)$ and Hartmann number (M) are illustrated with the aid of graphs and tables. In the course of this investigation, it is found that an increase in the heat generation/absorption parameter increases the temperature. In addition, the magnitude of the temperature is higher for heat-generating fluid in comparison to heat-absorbing fluid. Furthermore, the temperature and velocity can be controlled by carefully selecting suitable values of the heat generation/absorption parameter and Hartmann number respectively.