Models for flows with melting heat and convection

Abstract

Due to extensive applications in engineering and industries, the thermal properties of fluids (materials) have gained a great interest in recent days. Conventional fluids such as water, engine oil, kerosine oil, ethylene oil, gasoline oil etc., possesses very small heat transport capabilities due to its lower thermal conductance. Thermal conductance of mentioned conventional fluids can be improved via suspension of nano-sized (1-100nm) particles, known as nanoparticles. Nanoparticles exist in various varieties such as metal, carbides, nanometals or nitrides (CNTs, graphite). In these nanoparticles, CNTs have promising capability of heat conduction. At room temperature, thermal conductance of carbon substances is five times of ordinary substances. Not only thermal conductance is the unique quality of CNTs but it also possesses exceptional electrical, mechanical properties and applications in atomic transportation and nano-sensors. CNTs are cylindrical shaped substances of carbon fenced by graphene sheet. On the basis of graphene sheet, CNTs are classified into MWCNTs (cylindrical carbon substance fenced by more than one graphene sheet) and SWCNTs (cylindrical carbon substance fenced by one graphene sheet). CNTs are utilized in medicine, batteries, electronic instruments, tissue engineering, solar storages, biosensors, purification process etc. Having such in mind, the presented thesis consists of ten chapters. In chapter one, we have reviewed literature regarding nanomaterials, stretching surface, squeezed flow, melting heat and stagnation flow. Mathematical modeling for concerned equations (continuity, momentum, energy and concentration) in case of viscous and Jeffrey fluids is presented. Xue expressions for CNTs while Hamilton-Crosser expressions for hybrid nanofluid and ordinary nanofluids are established. Moreover fundamental concepts of OHAM and Bvp4c methods for series and numerical solutions are incorporated. Chapter two concentrates on melting effect in three dimensional flow of CNTs (SWCNTs, MWCNTs) over a stretching sheet. Chemical reactions and porous medium are also considered. Nanomaterial is constructed through dispersion of CNTs in water-basefluid. Shooting method (bvp4c) is implemented for solutions development. Moreover comparison between MWCNTs and SWCNTs is also given. Contents of this chapter are published in Results in Physics 8 (2018) 415-421. Chapter three addresses; melting heat and thermal radiation effects in stagnation flow of CNTs (carbon nanotubes). Flow is generated via stretching sheet. Chemical reactions are accounted. Gasoline oil and water are taken as baseliquids. Further conversion of involved PDEs (mass, momentum, energy and concentration) into ODEs is performed through suitable transformations. The obtained ODEs are solved through OHAM. Velocity, temperature, skin friction coefficient, concentration and Nusselt number under involved variables are analyzed graphically. Material of this chapter is published in Communications in Theoretical Physics 69 (2018) 441-448. Chapter four addresses entropy production in squeezing flow of CNTs (carbon nanotubes). Nanomaterial is constructed by adding CNTs in water basefluid. Heat transport in presence of melting heat is explored. Adequate transformations are implemented for conversion of PDEs into ODEs. Shooting technique (bvp4c) is used for the numerical solutions. Contents of this chapter are published in Journal of Thermal Analysis and Calorimetery 140 (2020) 321–329. Unsteady squeezed flow of Jeffrey nanomaterial is discussed in chapter five. Brownian motion and thermophoresis describes nanofluid characteristics. Convection conditions for heat and mass transfer are taken into account. The differential systems are computed for the convergent solutions. The acceptable values for convergence analysis are recognized. Detail analysis is performed for velocity, concentration, temperature, skin friction and Nusselt and Sherwood numbers. Material of of this chapter is published in Physica Scripta 94 (2019) 105703. Chapter six explores melting phenomenon in MHD flow of Jeffrey nanomaterial by a stretched sheet. Heat transfer characteristics are elaborated through Joule heating and viscous dissipation. Thermophoresis and Brownian motion characteristics are analyzed via Boungiorno model for nanofluid. Chemical reaction with activation energy is studied. Flow is addressed in stagnation point region. Field equations (PDEs) are transmitted into ODEs by employing adequate transformations. These non-linear systems (ODEs) are solved by OHAM. Research of this chapter is also published in Physica Scripta 94 (2019) 115702. Jeffrey nanofluid in existence of stagnation point by a permeable stretched cylinder is addressed in chapter seven. Viscous dissipation, Brownian motion, thermal radiation and thermophoresis impacts are considered. Surface is subject to convective heat and mass conditions. Activation energy is taken into account. By adequate transformations, the PDEs are converted into ODEs and then solved employing OHAM. This research is submitted for publication in International Communications in Heat and Mass Transfer. In chapter eight we have arranged comparative study of hybrid nanofluid (MWCNTs+Cu+Water), nanofuid (MWCNTs+Water) and basefuid (water). Flow is due to curved stretching sheet. Flow is explored through slip boundary condition. Heat transport analysis is performed in existence of viscous dissipation, mixed convection and convective boundary condition. Transformation technique is applied in obtaining ODEs. These coupled ODEs are solved via RK-4 algorithms (bvp4c). Material of this chapter is published in Journal of Thermal Analysis and Calorimetery (2020) doi.org/10.1007/s10973-020-09577-z. Chapter nine examines stagnation point flow of hybrid nanofluid (SWCNTs+Ag+Gasoline oil) by a variable thicked stretched sheet. Viscous dissipation and melting effects are taken into consideration for heat transport characteristics. PDEs (expressions) are transmitted into ODEs via transformation technique. Governing ODEs are then converted into system of first order differential system in order to solve by bvp4c. Observations of this chapter are published in International Communications in Heat and Mass Transfer.121 (2021) 104805. Chapter ten deals with hybrid nanomaterial (SWCNTs+CuO+Ethylene glycol) flow by a curved non-linear stretching sheet. Heat transfer features are emphasized via Newtonian heating. Viscous dissipation is also reported. Coupled non-linear ODEs are constructed from the field equations (PDEs) through adequate transformations. These non-linear ODEs are then reduced into system of first order. Impacts of flow parameters on temperature, skin friction, velocity and Nusselt number are presented graphically. Comparison amongst hybrid nanofluid (SWCNTs+CuO+Ethylene glycol), nanofluid (SWCNTs+Ethylene glycol) and basefluid (Ethyleneglycol) is arranged. Observations of this chapter are published in Journal of Thermal Analysis and Calorimetery (2020) doi.org/10.1007/s10973-020-10196-x