Fluid Mechanics and Thermal Sciences
This is the largest GATE ME domain: fluid statics and dynamics, pipe and boundary-layer flow, conduction, convection, radiation, heat exchangers, and the thermodynamics of power and refrigeration cycles. Numerical questions reward clean property and unit handling.
Fluid mechanics
- Continuity A₁V₁ = A₂V₂; Bernoulli p/γ + V²/2g + z = constant along a streamline, with h_L added when losses exist.
- Reynolds number Re = ρVD/μ decides regime; laminar pipe flow has f = 64/Re, turbulent f comes from Moody or Colebrook.
- Darcy–Weisbach: h_f = fLV²/(2gD). Momentum balance on a bend gives the anchoring force.
Heat transfer
- Conduction: q = kA ΔT/L, with thermal-resistance networks for composite walls. Fins use efficiency and effectiveness.
- Convection: Nu = hL/k, correlated through Re and Pr (Dittus–Boelter for turbulent tube flow).
- Radiation: q = εσA(T⁴ − T_sur⁴) with σ = 5.67×10⁻⁸ W/m²K⁴; view factors from reciprocity and summation rules.
Thermodynamics and cycles
- Steady-flow first law: q − w = Δh + ΔKE + ΔPE. Entropy generation is zero for reversible, positive for real processes.
- Rankine efficiency improves with reheat and regeneration; Brayton with intercooling, reheat and regeneration; refrigerator COP = Q_L/W_in.
Worked example
Counterflow heat exchanger: hot 150 → 90 °C, cold 30 → 70 °C. Then ΔT₁ = 150 − 70 = 80 K and ΔT₂ = 90 − 30 = 60 K, so LMTD = (80 − 60)/ln(80/60) = 20/0.2877 ≈ 69.5 K. Note the ends are matched hot-in to cold-out for counterflow; in parallel flow ΔT₁ = 120 and ΔT₂ = 20.
Traps
Applying LMTD to crossflow without the correction factor F; using gauge pressure in one term and absolute in another; forgetting that laminar f depends only on Re; mixing up effectiveness and LMTD methods.