A Thermal Conductivity Prediction Method for Refrigerant Mixtures in the Liquid Phase

Thermal conductivity is an important transport propeny in understanding heat transfer characteristics. It can be evaluated either from experimental measurements or theoretical predictions. In the present srudy, a theoretical model is proposed for predicting the thermal conductivity of a refrigerant mixture. This method requires speed of sound information obtained theoretically for a liquid mixrure and the Carnahan-Starling-DeSantis (CSD) equation of state. This approach is based on applying to mixtures an equation suggested by Bridgman for pure substances. The application to mixtures is accomplished by inserting a coefficient into the equation. In this paper, modifying coefficients for 3 refrigerant mixrures: R22/Rl2, R22/Rll4, R22/R152a, were presented for the temperature range of -40"C to 60"C. Predicted thermal conductivity results were also compared with values obtained by other methods. The approach presented here shows that the thermal conductivity of mixtures can be directly calculated from knowing their thermodynamic properties. a: ,..,.a 1,a2: b: b0 ,b1 ,b2 : C: f;;: K: k: M: N: P: R: T: v,: V: v· W: X: y: NOMENCLATURE equation of state attraction parameter(between species i,j) coefficients for equation (A2) equation of state parameter coefficients for equation (A3) modified coefficients for equation (2) interaction parameter between species i and j thermal conductivity specific heat ratio, C,JC. molecular weight Avogadro's number pressure gas constant temperature speed of sound molar volume specific volume mass fraction molar fraction b/4V Subscripts c: em: i,j: critical properties critical properties for mixtures component i,j Su[:lerScripts 1: m: liquid phase n: polynomial power <r: p; Boltzmann's constant density 365 n· T· r: m: mixture polynomial coefficients at constant temperature condition reduced properties reduced properties for mixtures INTRODUCTION Thermal conductivity property data is necessary for understan ding the heat transfer characteristics of a fluid. It can be determined from either experimental measu rements or theoretical predictions. To date, only a few theoretical equations have been dev eloped to predict the thermal conductivity of mixtures[l-3]. A complication that exists when deal ing with mixture problems is that a mixing rule is needed for estimating accurate mixture properties . Unfortunately, one mixing rule cannot always be broadly suitable for every pair with reasonable accura cy. In addition, the mixing rule usually needs to be based on experimental data. From a theoretical standpoint, thennal conductivity is a property w hich is related to energy transfer through the molecular lattice. Therefore, speed of sound h as some relevance to thermal conductivity. The use of speed of sound has been well establishe d for predicting the thermal conductivity of pure fluids. However, there are no reports in the liter ature of applying this method to fluid mixtures. The purpose of this paper is to use a speed of sound method to predic t the thermal conductivity of refrigerant mixtures. One such method in the literature, which has been used for pure substance, • is an approach known as the Bridgman equations[4]. In this paper, it is proposed that the Bridgman equation be applied to thermal conductivity predictions of mixtures by i ntroducing modified coefficients in the equation. Modified coefficients, which are function s of reduced temperature and the type of pure substance used in the mixture, were found for thre e refrigerant mixtures. This method also requires knowledge of thermodynamic properties, such as pressure-volume-temperature. Since the CSD equation of state has been reported to produce good accuracy for m ixtures, the CSD equation of state was used to calculate both the thermodynamic proper ties and the speed of sound in liquid mixtures[5,6]. Unlike other methods, such as the Filippov method, the method pr esented herein calculates thermal conductivity of mixtures directly from their thermodynamic p roperties without knowing the thermal conductivity of the pure substances. METHODS FOR THERMAL CONDUCTIVITY PREDICTION Prooosed Ao.proach for Mixture Thermal Conductivity A theoretical equation for the thermal conductivity of liquids was p roposed by Bridgman in 1923 and later, modified by Powel et. a!.[4]. The resulting equation, which has been used for pure substances, is where N v " v. Avogadro's number = molar volume the Boltzmann's constant the speed of sound (I) It is proposed here that this equation can be used for mixtures if the equation is modified by a coefficient, Cm, which is unique for the type of pure substances use d in the mixture. Hence, the thermal conductivity for mixtures can be expressed as: