Heat Transfer Analysis Using Fractional Derivativs

Abstract

The determination of temperature distribution and the estimationof exit temperatures during the thermal energy transfer between the twofluid streams in the heat exchangers are of indispensable task to analysethe performance of the heat transfer systems. Hence, many researchersdeveloped several mathematical models to estimate the exit temperatures in theheat exchangers through the determination of temperature distributions. Thisdissertation presents the steady state behavior of the heat transfer processesthrough fractional differential equations in the two different thermal equipments,which are widely used in many industrial applications.The steady state behaviour of heat transfer process in the single passcross flow plate-fin type of heat exchanger with constant specific heat of thefluids is analysed. The governing linear system of energy transfer equationsare solved using the differential transform method and the closed form seriessolutions are identified. The proposed series solution predicts the temperaturedistributions of the hot and the cold fluids and determines the effectiveness ofthe heat exchanger. The introduction of the temperature dependent transportproperties particularly the specific heat is considered as a linear function oftemperature, which converts the governing energy equations into nonlinear, arecrucial in the study of heat transfer in the advanced materials. Further, thefractional derivatives are introduced in the nonlinear energy balance equationsin order to analyse the irregular temperature distribution in the heat transferprocess.The fractional system of nonlinear energy balance equationsincorporating the temperature dependent specific heat are solved and the closed