Glossary

1.3 Fluid Mechanics and Heat Transfer Basics

3 min read•july 22, 2024

Fluids and heat are key players in chemical engineering. Understanding how they behave and interact is crucial for designing efficient processes and equipment.

Newtonian and non-Newtonian fluids have different flow behaviors. Heat transfer occurs through , , and . These concepts are essential for analyzing flow systems and designing heat exchangers.

Fluid Mechanics

Newtonian vs non-Newtonian fluids

Top images from around the web for Newtonian vs non-Newtonian fluids

  • Newtonian fluid - Wikipedia View original

    Is this image relevant?

  • Non-Newtonian fluid - Wikipedia View original

    Is this image relevant?

  • Newtonian fluid - Wikipedia View original

    Is this image relevant?

1 of 3

Top images from around the web for Newtonian vs non-Newtonian fluids

  • Newtonian fluid - Wikipedia View original

    Is this image relevant?

  • Non-Newtonian fluid - Wikipedia View original

    Is this image relevant?

  • Newtonian fluid - Wikipedia View original

    Is this image relevant?

1 of 3
  • Newtonian fluids exhibit a linear relationship between shear stress and shear rate, with a constant viscosity independent of shear rate (water, air, most gases)
  • Non-Newtonian fluids have a non-linear relationship between shear stress and shear rate, with viscosity varying with shear rate
    • Shear-thinning (pseudoplastic) fluids experience a decrease in viscosity as shear rate increases (polymers, blood, paint)
    • Shear-thickening (dilatant) fluids experience an increase in viscosity as shear rate increases (suspensions, cornstarch in water)
    • Bingham plastic fluids require a yield stress to initiate flow and then behave as Newtonian fluids (toothpaste, mayonnaise)

Principles of fluid mechanics

  • Fluid statics deals with fluids at rest, considering (p=ρghp = \rho g h) and buoyancy forces ()
  • Fluid dynamics analyzes fluids in motion using the (Q=AvQ = A v), (pρ+v22+gz=constant\frac{p}{\rho} + \frac{v^2}{2} + gz = \text{constant}), and (Re=ρvDμRe = \frac{\rho v D}{\mu})
    • occurs at low Reynolds numbers (Re<2300Re < 2300), while occurs at high Reynolds numbers (Re>4000Re > 4000)

Analysis of flow systems

  • drop in pipes can be calculated using the (Δp=fLDρv22\Delta p = f \frac{L}{D} \frac{\rho v^2}{2}), which accounts for friction losses
  • required to overcome pressure drop is given by P=QΔpP = Q \Delta p
  • Pipe sizing involves optimizing diameter based on pressure drop, pumping power, fluid properties, flow rate, and acceptable pressure drop

Heat Transfer

Heat transfer mechanisms

  • Conduction is the transfer of heat through a solid or stationary fluid, governed by (q=−kdTdxq = -k \frac{dT}{dx}) and applied in heat exchangers, insulation, and reactor walls
  • Convection is the transfer of heat between a surface and a moving fluid, described by Newton's law of cooling (q=h(Ts−T∞)q = h (T_s - T_\infty))
    • Forced convection occurs when fluid motion is driven by external means (pumps, fans), while natural convection is driven by buoyancy forces due to temperature gradients
    • Convection is utilized in heat exchangers, cooling towers, and reactor jackets
  • Radiation is the transfer of heat through electromagnetic waves, following the Stefan-Boltzmann law (q=εσ(T14−T24)q = \varepsilon \sigma (T_1^4 - T_2^4)) and applied in furnaces, solar collectors, and high-temperature processes

Heat exchanger calculations

  • Heat exchangers come in various configurations, including double pipe, shell and tube, and plate
  • The method calculates heat transfer rate using Q=UAΔTlmQ = UA \Delta T_{lm}, with ΔTlm\Delta T_{lm} depending on the flow arrangement (counterflow or parallel flow)
  • The relates heat transfer rate to the maximum possible heat transfer rate (ε=QQmax\varepsilon = \frac{Q}{Q_{max}}) and the number of transfer units (NTU=UACminNTU = \frac{UA}{C_{min}})
  • Temperature profiles along the length of a heat exchanger can be determined by calculating inlet and outlet temperatures for both hot and cold fluids

Key Terms to Review (24)

Archimedes' Principle: Archimedes' Principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid that it displaces. This principle is fundamental in understanding fluid mechanics, as it relates to how forces interact with objects in fluids, and it also has implications for heat transfer, particularly when considering thermal convection in fluids.
Bernoulli's Equation: Bernoulli's Equation is a fundamental principle in fluid dynamics that describes the conservation of energy in a flowing fluid. It relates the pressure, velocity, and elevation of a fluid, showing how these factors change along a streamline. The equation highlights the interplay between kinetic energy, potential energy due to elevation, and pressure energy, illustrating how they are interconnected in various fluid flow situations.
Boundary Layer Theory: Boundary layer theory is a concept in fluid mechanics that describes the behavior of fluid flow near a solid surface, where the effects of viscosity are significant. This theory helps to explain how the flow velocity transitions from zero at the surface due to the no-slip condition to the free stream velocity away from the surface, and it plays a critical role in heat transfer, drag forces, and mass transfer in various engineering applications.
Conduction: Conduction is the process of heat transfer through direct contact between materials, where thermal energy moves from a region of higher temperature to a region of lower temperature without the movement of the material itself. This method of heat transfer is crucial for understanding how energy moves in solids and plays a vital role in fluid mechanics and heat transfer applications. Efficient conduction depends on the material properties such as thermal conductivity, which indicates how well a substance can conduct heat.
Continuity equation: The continuity equation is a mathematical statement that represents the conservation of mass in a fluid system, asserting that the mass flow rate of a fluid must remain constant from one cross-section of a pipe to another. This principle is crucial for understanding how fluids behave when they flow through different areas, linking it to fundamental concepts of fluid mechanics, momentum transfer, and heat transfer.
Convection: Convection is the transfer of heat through a fluid (liquid or gas) caused by the movement of the fluid itself. This process occurs when warmer, less dense regions of the fluid rise while cooler, denser regions sink, creating a circulation pattern that facilitates the movement of thermal energy. Convection plays a crucial role in various applications such as heating systems, natural phenomena like ocean currents, and even atmospheric dynamics.
Darcy-Weisbach Equation: The Darcy-Weisbach equation is a fundamental formula used in fluid mechanics to calculate the pressure loss due to friction in a pipe or duct. This equation is crucial for understanding how fluid flow behaves in various systems, linking fluid dynamics with the design of piping systems and heat exchangers, thereby influencing heat transfer processes. It incorporates factors such as pipe length, diameter, fluid velocity, and friction factor to provide a comprehensive analysis of pressure drops across flowing fluids.
Drag Coefficient: The drag coefficient is a dimensionless number that quantifies the drag or resistance of an object in a fluid environment, influenced by factors such as shape, surface roughness, and flow conditions. It plays a crucial role in fluid mechanics by allowing engineers to predict how an object will perform when moving through fluids, aiding in designs that minimize drag for efficiency.
Effectiveness-NTU Method: The effectiveness-NTU (Number of Transfer Units) method is a technique used to analyze the performance of heat exchangers, focusing on their effectiveness in transferring heat between two fluids. This method quantifies the heat exchanger's performance by determining its effectiveness, which is defined as the ratio of the actual heat transfer to the maximum possible heat transfer. Understanding this concept helps in evaluating and designing heat exchangers efficiently by correlating flow arrangement and thermal performance.
Fourier's Law: Fourier's Law states that the rate of heat transfer through a material is proportional to the negative gradient of temperature and the area through which heat is flowing. This principle is fundamental in understanding how heat energy moves in systems, linking concepts of thermal conductivity and temperature gradients to practical applications in engineering and science.
Hydrostatic Pressure: Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity acting on the fluid's mass. This concept is crucial for understanding how fluids behave under different conditions, especially when analyzing fluid statics and dynamics, as well as the transfer of heat within fluid systems. Hydrostatic pressure can significantly impact various engineering applications, such as the design of tanks, pipelines, and other equipment that must withstand fluid forces.
Laminar Flow: Laminar flow is a type of fluid motion characterized by smooth, orderly layers of fluid that move in parallel without mixing. This flow regime occurs at lower velocities and is typically observed in situations where the fluid viscosity is high or the flow is confined, leading to predictable and stable behavior. Understanding laminar flow is essential for predicting how fluids behave in various systems, including in contexts like fluid mechanics and advanced microfluidics.
Log mean temperature difference (LMTD): The log mean temperature difference (LMTD) is a mathematical expression used to determine the temperature driving force in heat exchangers. It provides a single effective temperature difference for heat transfer calculations when temperatures vary along the length of the heat exchanger. Understanding LMTD is essential for designing efficient heat exchangers and analyzing their performance, as it captures the non-linear temperature profile that occurs in these systems.
Mach Number: Mach number is a dimensionless quantity that represents the ratio of the speed of an object moving through a fluid to the speed of sound in that same fluid. This term is essential in fluid dynamics and heat transfer because it helps determine flow characteristics such as compressibility effects, shock waves, and temperature variations in gases. Understanding Mach number is crucial for analyzing high-speed flows in various engineering applications, particularly those involving gases.
Navier-Stokes Equations: The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of viscous fluid substances. These equations account for forces acting on the fluid, such as pressure, viscous forces, and external forces, allowing for the analysis of various fluid flow scenarios, including turbulence and heat transfer.
Pipe flow: Pipe flow refers to the movement of fluids through a pipe system, characterized by the interaction between fluid dynamics and the geometry of the piping. Understanding pipe flow is crucial because it involves analyzing parameters such as velocity, pressure, and flow rate, which are essential in various engineering applications, including chemical processes and energy systems. The behavior of fluids in pipes can be influenced by factors like viscosity, turbulence, and the temperature of the fluid, all of which play a significant role in heat transfer and overall system efficiency.
Pressure: Pressure is defined as the force exerted per unit area on a surface, typically measured in pascals (Pa) or atmospheres (atm). In various contexts, it plays a crucial role in determining how fluids behave, how reactions occur, and how substances interact under different conditions. Understanding pressure is key for predicting the behavior of materials in response to forces and thermal changes.
Pumping Power: Pumping power refers to the energy required to move fluids through a system using pumps, typically expressed in watts or horsepower. This concept is essential for understanding fluid dynamics and energy transfer in processes where fluids are transported, particularly in relation to the efficiency of pumps and the resistance encountered in piping systems. By grasping pumping power, one can analyze how different factors, like flow rate and pressure, influence overall system performance.
Pumping Systems: Pumping systems are assemblies designed to move fluids from one location to another through the application of mechanical energy. They play a crucial role in various industries by facilitating the transportation of liquids, gases, and slurries, and are closely linked to principles of fluid mechanics and heat transfer, which govern their design, efficiency, and operational performance.
Radiation: Radiation is the process by which energy is emitted as particles or waves. It plays a crucial role in heat transfer, where thermal radiation specifically involves the emission of energy from a surface in the form of electromagnetic waves. Understanding radiation is essential for analyzing energy exchanges in systems involving heat transfer, as it differs from conduction and convection, focusing instead on how energy travels through space without requiring a medium.
Reynolds Number: Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It helps to determine whether the flow will be laminar or turbulent, based on the ratio of inertial forces to viscous forces in a fluid. Understanding this concept is crucial for analyzing flow characteristics, designing systems, and optimizing processes involving fluids in various engineering applications.
Specific Heat Capacity: Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). This property is crucial in understanding how fluids absorb and transfer heat, playing a significant role in both fluid mechanics and heat transfer processes. It directly influences thermal management in various applications, affecting everything from temperature control in chemical processes to the efficiency of heating systems.
Thermal Conductivity: Thermal conductivity is a material property that measures the ability of a substance to conduct heat. It reflects how easily heat flows through a material and is crucial in understanding heat transfer mechanisms. The concept plays an essential role in various fields, including fluid mechanics, advanced heat transfer, coupled transport processes, and the development of functional materials for energy applications.
Turbulent Flow: Turbulent flow is a type of fluid motion characterized by chaotic changes in pressure and velocity. This flow regime typically occurs at high velocities and is marked by the presence of eddies and vortices, which create fluctuations that enhance mixing and energy dissipation. Turbulent flow is essential to understanding how fluids interact with their surroundings, impacting heat transfer, resistance in pipes, and mixing processes.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Back
Practice QuizGlossary
Practice QuizGlossary
Next guide