Heat Transfer and Fluid Mechanics
This domain tests the transport equations behind boiler performance, heat exchangers, draft and pump/pipe behaviour. Expect calculations involving conduction, convection, radiation, log-mean temperature difference, pressure drop and net positive suction head, with an emphasis on which mechanism controls the result.
Heat-transfer rules
- Conduction: q = kA dT/L. Resistance = L/(kA); resistances in series add.
- Convection: q = hA dT. The film coefficient depends on velocity, properties and geometry; fouling adds a resistance and reduces the overall coefficient U.
- Radiation: q = emissivity x Stefan-Boltzmann constant x area x (Th^4 - Tc^4). Radiation dominates at high furnace temperature.
- Heat-exchanger duty: q = U A LMTD, where LMTD = (dT1 - dT2) / ln(dT1/dT2) for counterflow. Use the correction factor for multipass or crossflow.
Fluid-mechanics rules
- Bernoulli applies along a streamline for steady, incompressible, frictionless flow; real flow adds friction and minor losses.
- Reynolds number = density x velocity x diameter / viscosity. It determines laminar, transitional or turbulent flow.
- Darcy-Weisbach: head loss = f (L/D) (V^2/2g). Loss rises with the square of flow.
- NPSH available must exceed NPSH required by a margin. NPSHa falls as suction lift, suction temperature or suction-line loss increases.
- Affinity laws for a centrifugal pump: flow varies with speed, head with speed squared, power with speed cubed.
Worked example
A counterflow heat exchanger has hot inlet 300 C, hot outlet 200 C, cold inlet 100 C and cold outlet 180 C. dT1 = 300 - 180 = 120 C; dT2 = 200 - 100 = 100 C. LMTD = (120 - 100) / ln(120/100) = 20 / 0.1823 = 109.7 C. Using the arithmetic mean of 110 C would be close here but is not generally correct; with a larger temperature difference the error grows.
Traps that cost marks
Using arithmetic mean temperature difference instead of LMTD; ignoring fouling or tube-wall resistance; using nominal pipe size instead of inside diameter; confusing NPSHa with NPSHr; and applying affinity laws across a system with a large static head. In radiation, temperatures must be absolute, not Celsius or Fahrenheit.
Key points: overall U includes fouling and wall resistance; LMTD is required for heat-exchanger duty; loss varies with flow squared; NPSHa must exceed NPSHr; radiation requires absolute temperature.