A mathematical model of the heat transfer process in a shell and tube condenser for use in refrigeration applications

This paper describes a mathematical model that may be used in predicting the heat transfer performance of a shell and tube condenser. The model uses the Effectiveness-Number of Transfer Units (E-NTU) method of heat exchanger analysis. Given the geometric characteristics, the flow conditions and inlet fluid temperatures the model determines, (a), the necessary heat transfer coefficients; (b), the fractions of the condenser devoted to desuperheating, condensing and subcooling the condensing medium; (c), the total heat rejection; and (d), the exit fluid temperatures.The model has been validated by testing a typical condenser at various operating conditions. The measured performance has been compared with that predicted theoretically and a close correlation has been found to exist between the two.     

An MINLP retrofit approach for improving the flexibility of heat exchanger networks

A mixed integer nonlinear programming (MINLP) model for the retrofit of heat exchanger networks (HENs) in order to improve their flexibility is presented in this paper. As stream flowrates and inlet temperatures and/or heat transfer coefficients are allowed to vary within either specified ranges or discrete sets, a multiperiod hyperstructure network representation is developed based on critical operating conditions (i.e. periods of operation) that limit the network's flexibility. This multiperiod hyperstructure includes all possible network configurations. Structural modifications, such as new stream matches, exchanger reassignments, splitting and mixing of streams are explicitly modeled either considering one-to-one or one-to-many assignment of heat exchangers to stream matches. Energy recovery and utility consumption are not predetermined but are optimized as part of a total annualized cost along with the structural modification cost in the objective function. Thus, trade-offs between operating and retrofit investment costs to improve the flexibility of a HEN are accounted for. The resulting large scale MINLP is solved with the application of the Generalized Benders Decomposition. The proposed multiperiod retrofit model can be included in a general framework to improve the operability of heat exchanger networks.     

Observability and reachability for parallel-flow heat exchanger equations

^** Email: sano{at}cc.kagoshima-u.ac.jp This paper is concerned with the dynamical analysis of parallel-flowheat exchanger equations with observation at the outlet of tube/controlat the inlet of tube. The parallel-flow heat exchanger equationis super-stable under zero boundary condition. The system canbe described by an unbounded operator of lower triangular formthrough a variable transformation. By calculating a C₀-semigroupgenerated by the operator, it is shown that the system is observableif both fluid temperatures are measured at the outlet, and thatthe system is observable with respect to the non-negative coneof the state space if either of them is measured at the outlet.Moreover, it is shown that the system is reachable if both fluidtemperatures are controlled at the inlet, and that the systemis reachable with respect to the non-negative cone of the statespace if either of them is controlled at the inlet.     

Numerical determination of heat exchanger response

In this paper there is presented approximative calculation of the temperature of fluid in fixed point of heat exchanger and in fixed time. In presented method are used Newton-Cotes formulas. Moreover there is evaluated the error which is made during determination of heat exchanger response. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.     

MHD three-dimensional flow of viscoelastic fluid over an exponentially stretching surface with variable thermal conductivity

This study models the magnetohydrodynamic (MHD) three-dimensional boundary layer flow of viscoelastic fluid. The flow is due to the exponentially stretching surface. The heat transfer analysis is performed through prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The thermal conductivity is taken temperature dependent. Series solutions of velocities and temperatures are constructed. Graphical results for PST and PHF cases are plotted and analyzed. Numerical values of skin-friction coefficients and Nusselt numbers are presented and discussed.     

Heat transfer in channel flow of a micropolar fluid

The study of heat transfer in channel flow has been done by previous authors for Newtonian and elastico-viscous fluids. It is the aim of the present paper to study the temperature profile for flow of a micropolar fluid in a channel induced by a constant axial pressure gradient, when the walls are maintained at constant temperatures. We have examined the effects of microrotation on the temperature profile and on the kinetic energy of the fluid. Three cases have been chosen by us for detailed study: (i) both the walls are maintained at different constant temperatures, (ii) both the walls are maintained at the same constant temperature, (iii) one wall is kept at a constant temperature and there is no heat flux at the other wall.     

Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet

This paper deals with the unsteady axisymmetric flow and heat transfer of a viscous fluid over a radially stretching sheet. The heat is prescribed at the surface. The modelled non-linear partial differential equations are solved using an analytic approach namely the homotopy analysis method. Unlike perturbation technique, this approach gives accurate analytic approximation uniformly valid for all dimensionless time. The explicit expressions for velocity, temperature and skin friction coefficient are developed. The influence of time on the velocity, temperature and skin friction coefficient is discussed.     

Numerical Analysis of Heat Transfer for Cooling of Photovoltaic Cells

Photovoltaic cells are devices which convert solar radiation directly into electricity. However, solar radiation increases the photovoltaic cells temperature [1] [2]. The temperature has an influence on the degradation of the cell efficiency and the lifetime of a PV cell. This work reports on a cooling water technique for cells, whereby the cooling system was placed at the front surface of the cells to dissipate away excess heat and to block unwanted radiation. Using water as a cooling medium for the cells, the overheating of closed panel is greatly reduced without prejudicing luminosity and water acts as a filter to remove a portion of solar spectrum in the infrared band but allows transmission of the visible spectrum most useful for the PV operation. The aims of this study are to develop a 3D thermal model to simulate the cooling and heat transfer in Photovoltaic panel and recommend a cooling technique for the PV panel. In order to have a good estimation for the temperature distribution, the three-dimensional flow and heat transfer across the cooling block is investigated numerically by solving the continuity, momentum and energy equations using FLUENT. The second objective of this work is to study the influence of the geometrical dimensions of the panel, water mass flow rate and water inlet temperature on the flow distribution and the solar panel temperature. The results obtained by the model are compared with experimental results from testing the prototype of the cooling device. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Object-oriented modelling and simulation of heat exchangers with finite element methods

The paper describes the derivation of finite-element models of one-dimensional fluid flows with heat transfer in pipes, using the Galerkin/least-squares approach. The models are first derived for one-phase flows, and then extended to homogeneous two-phase flows. The resulting equations have then been embedded in the context of object-oriented system modelling; this allows one to combine the fluid flow model with a model for other phenomena such as heat transfer, as well as with models of other discrete components such as pumps or valves, to obtain complex models of heat exchangers. The models are then validated by simulating a typical heat exchanger plant.     

Unsteady Marangoni convection heat transfer of fractional Maxwell fluid with Cattaneo heat flux

Fractional shear stress and Cattaneo heat flux models are introduced in characterizing unsteady Marangoni convection heat transfer of viscoelastic Maxwell fluid over a flat surface. Governing equations and boundary condition are formulated firstly via the balance between the surface tension and shear stress. Numerical solutions are obtained by new developed numerical technique and some novel phenomena are found. Results shown that the fractional derivative parameters, Marangoni number and power law exponent have significant influence on characteristics velocity and temperature fields. As fractional derivative parameters increase, the temperature profiles rise remarkably and the viscoelastic effects of the fluid enhance with delayed response to surface tension, however the temperature profiles decline significantly with a thinner thickness of thermal boundary layer with the increase of Marangoni number. The average skin friction coefficient increases with the augment of Marangoni number, while the average Nusselt number decreases for larger values of power law exponent.     

Green's function solution of the time-dependent solar collector problem

The Green's function for the time-dependent solar collector problem is derived and examined. It is found that the influence of a point source of irradiance propagates with the speed of the heat transfer fluid. This result contradicts some earlier work.An analytical expression is derived for the output fluid temperature in terms of the irradiance as a function of position and time. Fluctuations in ambient and input fluid temperatures are also considered.     

Numerical simulation of free-surface thermally influenced flows for nonhomogeneous fluids

A finite-difference technique is presented to simulate the behavior of natural water bodies under the influence of pollutants and temperature differences. The mathematical model, which has been discretized, is the closed system obtained by combining the Navier-Stokes equations, the heat transfer equation, the diffusion equations, and an equation relating the fluid density to both the chemical concentration and the temperature. The numerical method is based on the marker-and-cell method, which has been extended to consider the volume expansion due to heat transfer and the density variations.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

Analysis of fluid flow and heat transfer in coolant ducts of friction clutches

This paper deals with the numerical simulation of the fluid flow in coolant ducts as wall as the calculation of temperature field in fluid and solid of a friction clutch. The simulations are carried out by means of commercial software based on a finite volume method in a relative framework, where the fluid flow is not time dependent. The results in dependence of rotation speed and slip velocity show interesting secondary flow in the ducts. Different flow pattern have distinct influence on the temperature field and the heat transfer. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A fast running numerical model based on the implementation of volume forces for prediction of pressure drop in a fin tube heat exchanger

Numerical based design of geometrical structures is common when studying systems involving heat exchangers, a central component in several fields, such as industrial, vehicle and household systems. The geometrical structure of heat exchangers is generally comprised by closely placed fins and tube bundles. The creation of a mesh grid for a geometrically compact heat exchanger will result in a dense structure, which is not feasible for personal computer usage. Hence, volume forces were created based on Direct Numerical Simulations (DNS) on a Flow Representative Volume (FRV) of a tube fin heat exchanger in an internal duct system of a heat pump tumble dryer. A relation of the volume averaged velocity and the volume averaged force was established in two different FRV models with a finite element simulation in COMSOL. This relation was subsequently used to create flow resistance coefficients based on volume averaged expressions of fluid velocity and volume forces. These flow resistance coefficients were implemented in two respective porous models, which represent the entire heat exchanger except the interior arrangements of fins and tube bundles. Hence, the computation time was reduced thanks to the absence of a dense mesh grid. Experimental results of the entire heat exchanger showed good agreement with the second porous model in terms of pressure drop and volume flow rate.     

Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption

The problem of steady, laminar, hydromagnetic, simultaneous heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generating/absorbing fluid over a continuously stretching surface in the presence of the combined effect of Hall currents and mass diffusion of chemical species with first and higher order reactions is investigated. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. Certain transformations are employed to transform the governing differential equations to a local similarity form which are solved numerically. Comparisons with previously published work have been conducted and the results are found to be in good agreement. A parametric study is performed to illustrate the influence of the magnetic field parameter, Hall parameter, the coefficients of space-dependent and temperature-dependent internal heat generation/absorption, the chemical reaction parameter and order of reaction on the fluid velocity, temperature and concentration distributions. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions.     

Heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to a suddenly moved plate

This paper concentrates on the heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to a suddenly moved plate. The heat transfer analysis has been carried out for the prescribed surface temperature. Employing homotopy analysis method, the developed system of equations are solved analytically. The convergence of the obtained series solution is established. The influence of pertinent parameters on temperature profiles and Nusselt number is shown and discussed through several graphs. Further, a comparison between temperature profiles of Newtonian and Oldroyd fluids is also made.     

Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [q ∝ Δ(Tⁿ)] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law (n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law (n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law (n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.