Energy Transport

Molecular Transport / Diffusion / Conduction

Steady state

Practice problems

Unsteady state

Non Lumped analysis

Lumped Analysis

Convection

Internal Forced

Practice Problems

External Forced

Practice Problems

Natural

Practice Problems

In unsteady conduction problems, start calculation with Bi, unless heat transfer coefficient is an unknown

In the unsteady state conduction lumped analysis, b = hA / rho V Cp
It is to be noted that "rho and Cp" are of the solid NOT of the fluid

In non-Lumped finite medium analysis, Lc = L for plane, Lc = r for cylinders and spheres. But Lc = Volume / Surface area for lumped analysis

Terms to identify "Natural convection" Problems, “Ambient air, still air, quiescent air”

Easy method to find “Resistance term” for half cylinder – divide the denominator in the full cylinder resistance term by 2 and by 4 for a quarter cylinder etc.
For example R for full cylinder = ln (r2/r1) / 2 * Pi*KL (This is what will be given in the formulae sheet)
For half cylinder R = ln (r2/r1) / Pi*KL
For Quarter cylinder R = 2 ln (r2/r1) / Pi*KL
This method is applicable to sphere as well

In external forced convection over a sphere, fluid properties need to be estimated at the free stream velocity and in the Whitaker correlation

Reynolds analogy is for Pr = 1
Colburn analogy is for Pr not equal to 1

In the Stanton number (St = h / rho V Cp), V is Velocity NOT Volume.
Please refer to external flow analogy, slide 14, lecture 6.1

Internal Forced Convection: Terms to identify constant heat flux problems - constant heating, uniform heating, uniform flux.

Internal Forced Convection: Terms to identify constant  Temperature problems - constant Temperature, uniform Temperature

laminar flow analogies (Reynolds for Pr = 1 and Colburn for Pr not equal to 1), applicable only for constant Temperature condition. Please note that Colburn analogy can be used for both laminar and turbulent flows (see Lec 6.2 slide 18)

In internal forced convection, wall condition matters only for laminar flow. For turbulent flow the correlation is same for both constant wall flux and constant wall temperature conditions

Heat Transfer Coefficient

From Fundamental equations

From dimensional analysis

From experiments

friction factor