Momentum, heat and mass transport, boundary layers, heat exchanger design, diffusion, humidification and unit operations like distillation.
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- Reynolds number (Re) for flow characterization
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Re = rho * v * D / mu = v * D / nu, where rho is density, v is velocity, D is characteristic length, mu is dynamic viscosity, nu is kinematic viscosity- At what Reynolds number does flow typically transition from laminar to turbulent in a pipe?
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Re approximately 2300, though transition can occur between 2000 and 4000- Boundary layer definition
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Region of fluid near a surface where viscous effects are important and velocity changes from zero at the surface to the free stream value- Drag force equation
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F_d = (1/2) * C_d * rho * A * v^2, where C_d is drag coefficient, A is projected area, v is velocity- Friction factor f in the Darcy equation for pipe flow
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Dimensionless number; for laminar flow f = 64/Re; for turbulent flow, use Moody diagram or correlations like Colebrook equation- Pressure drop in a pipe using Darcy equation
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Delta P = f * (L/D) * (rho * v^2 / 2), where L is pipe length, D is diameter- Fourier's law of heat conduction
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Q = -k * A * (dT/dx), where k is thermal conductivity, A is area, dT/dx is temperature gradient- Newton's law of cooling for convective heat transfer
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Q = h * A * (T_surface - T_fluid), where h is convection coefficient, A is area- Stefan-Boltzmann law for radiation heat transfer
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Q = epsilon * sigma * A * (T^4 - T_surroundings^4), where epsilon is emissivity, sigma is Stefan-Boltzmann constant- Thermal resistance analogy in heat transfer
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Thermal resistance R_th = Delta T / Q, analogous to electrical resistance; series resistances add, parallel resistances combine reciprocally- Log mean temperature difference (LMTD) in heat exchangers
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LMTD = (Delta T_1 - Delta T_2) / ln(Delta T_1 / Delta T_2), where Delta T_1 and Delta T_2 are temperature differences at inlet and outlet- Heat exchanger effectiveness definition
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Epsilon = Q_actual / Q_max = (T_hot_in - T_hot_out) / (T_hot_in - T_cold_in), ranges from 0 to 1- Number of Transfer Units (NTU) method for heat exchangers
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NTU = UA / (C_min), where U is overall heat transfer coefficient, A is area, C_min is minimum heat capacity rate- Counterflow versus parallel flow heat exchangers
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Counterflow is more efficient and can achieve larger temperature changes; parallel flow is simpler but less efficient for the same area- Fouling factor in heat transfer calculations
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Accounts for deposits on heat transfer surfaces that increase resistance; acts as a thermal resistance R_f in series with convection resistances
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