MECH3610 · Advanced Thermofluids
Convection & Boundary Layers
Convection is conduction into a moving fluid at the wall, then sweeping away by bulk motion, and this chapter builds the boundary-layer picture and the dimensionless groups Nu, Re and Pr that all the correlations use. The film temperature for property evaluation and the principle of similarity (equal Re and Pr give equal Nu) are examined as concept questions, and this material underpins every convection calculation in the mid-term and the labs.
What this chapter covers
- 01Wall convection as conduction into the fluid: h = -k_f(dT/dy at wall)/(T_s - T-inf)
- 02Velocity boundary layer delta(x), no-slip condition, and surface shear stress tau_s = mu*(du/dy at wall)
- 03Thermal boundary layer delta_t(x) and how it sets the local convection coefficient
- 04Nusselt number Nu = hL/k as the ratio of convective to pure-conduction flux across the fluid layer
- 05Reynolds number Re = U*x/nu (inertial/viscous) and the flat-plate transition Re_x,c ~ 5e5
- 06Prandtl number Pr = nu/alpha (momentum vs thermal diffusivity) and its effect on delta vs delta_t
- 07Non-dimensionalising the boundary-layer equations collapses everything to Nu = f(Re, Pr)
- 08Film temperature T_f = (T_s + T-inf)/2 for evaluating properties; the principle of similarity for scaling
Principle of similarity: scaling wall flux without recomputing a correlation
- +1The whole method rests on Nu = f(Re, Pr). If Re and Pr are unchanged, Nu and hence h = Nu*k/L are unchanged, so the flux scales only with the driving temperature difference or with the geometry.
- +1(a) Same geometry, same flow, so h is unchanged; q'' = h*(T-inf - T_s) scales linearly with the difference. q''_new = 25 * (1200 - 500)/(1200 - 300) = 25 * 700/900 = 19.4 kW/m2.
- +1(b) Re = U*L/nu: doubling L and halving U leaves U*L unchanged, so Re is the same and Nu is the same. But h = Nu*k/L, so with L doubled, h halves.
- +1With the same driving difference (T_s back at 300 C), the flux tracks h: q''_new = 25 * (L/L_2) = 25 * (1/2) = 12.5 kW/m2. Similarity lets you rescale the answer without touching a correlation.
Key terms
- Velocity boundary layer
- The thin near-wall region delta(x) where the fluid speed rises from zero (no-slip) to 99% of the free-stream value. Its growth sets the surface shear stress tau_s = mu*(du/dy) at the wall.
- Thermal boundary layer
- The near-wall region delta_t(x) over which the temperature changes from the surface value to the free-stream value. Its steepness at the wall fixes the local convection coefficient h.
- Nusselt number (Nu)
- Nu = hL/k, the ratio of convective to pure-conduction heat flux across a fluid layer of thickness L. Nu = 1 is pure conduction; correlations give Nu = C*Re^m*Pr^n.
- Reynolds number (Re)
- Re = rho*U*x/mu = U*x/nu, the ratio of inertial to viscous forces. It sets the flow regime; for a flat plate the laminar-to-turbulent transition is near Re_x,c = 5e5.
- Prandtl number (Pr)
- Pr = c_p*mu/k = nu/alpha, the ratio of momentum to thermal diffusivity. Pr ~ 1 for gases, Pr < 1 for liquid metals, Pr > 1 for oils and water; it fixes the relative thicknesses of delta and delta_t.
- Film temperature (T_f)
- T_f = (T_s + T-inf)/2, the arithmetic mean of the surface and free-stream temperatures, at which temperature-dependent fluid properties are evaluated for external-flow correlations.
Convection & Boundary Layers FAQ
Why is there a boundary layer at all?
Because of the no-slip condition: the fluid touching the wall has zero velocity, so a thin layer of steep velocity gradient (the velocity boundary layer) grows along the surface. A matching thermal boundary layer carries the temperature change from wall to free stream. Heat crosses the wall by pure conduction into this layer and is then swept away by the flow.
What temperature do I evaluate fluid properties at?
For external flow, at the film temperature T_f = (T_s + T-inf)/2, because properties like viscosity and conductivity vary with temperature and the film value is the representative average across the boundary layer. (Internal flow uses the mean/bulk temperature instead.) Using the wrong reference temperature is a common source of error.
What does the principle of similarity let me do?
If two geometrically similar flows have the same Reynolds and Prandtl numbers, they have the same Nusselt number, so a lab-scale measurement transfers to full scale. It lets you rescale h or q'' by geometry and temperature difference without recomputing a correlation — a favourite MECH3610 concept question.
How is this chapter examined?
As concept questions (Nu interpretation, similarity scaling, transition estimates) and as the setup for every external- and internal-flow calculation that follows. Because the exam is open-book, marks favour correct property evaluation at T_f and the right regime decision. Confirm the coverage on Moodle.
Exam move
Fix the physical picture first: convection is wall conduction into a fluid layer, and Nu = hL/k measures how much the motion enhances it. Learn the three groups by their meaning — Re (inertia/viscous, sets regime), Pr (momentum/thermal diffusivity, sets delta vs delta_t), Nu (the dimensionless h) — and always evaluate external-flow properties at the film temperature. Rehearse the similarity argument until you can scale h and q'' by Re, geometry and temperature difference in two lines. This chapter is the grammar for Chapters 6-8, so make Nu = f(Re, Pr) automatic. Confirm the exam format on Moodle.
Working through Convection & Boundary Layers in MECH3610? Sia is AskSia’s AI Engineering tutor — ask any MECH3610 Convection & Boundary Layers question and get a clear, step-by-step explanation grounded in how MECH3610 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
