1.3 Fluid Mechanics and Heat Transfer Basics

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 conduction, convection, and radiation. These concepts are essential for analyzing flow systems and designing heat exchangers.

Fluid Mechanics

Newtonian vs non-Newtonian fluids

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• 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 hydrostatic pressure ($p = \rho g h$) and buoyancy forces (Archimedes' principle)
• Fluid dynamics analyzes fluids in motion using the continuity equation ($Q = A v$), Bernoulli's equation ($\frac{p}{\rho} + \frac{v^2}{2} + gz = \text{constant}$), and Reynolds number ($Re = \frac{\rho v D}{\mu}$)
  • Laminar flow occurs at low Reynolds numbers ($Re < 2300$), while turbulent flow occurs at high Reynolds numbers ($Re > 4000$)

Analysis of flow systems

• Pressure drop in pipes can be calculated using the Darcy-Weisbach equation ($\Delta p = f \frac{L}{D} \frac{\rho v^2}{2}$), which accounts for friction losses
• Pumping power required to overcome pressure drop is given by $P = Q \Delta p$
• 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 Fourier's law ($q = -k \frac{dT}{dx}$) 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 ($q = h (T_s - T_\infty)$)
  • 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 ($q = \varepsilon \sigma (T_1^4 - T_2^4)$) 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 log mean temperature difference (LMTD) method calculates heat transfer rate using $Q = UA \Delta T_{lm}$, with $\Delta T_{lm}$ depending on the flow arrangement (counterflow or parallel flow)
• The effectiveness-NTU method relates heat transfer rate to the maximum possible heat transfer rate ($\varepsilon = \frac{Q}{Q_{max}}$) and the number of transfer units ($NTU = \frac{UA}{C_{min}}$)
• Temperature profiles along the length of a heat exchanger can be determined by calculating inlet and outlet temperatures for both hot and cold fluids