Temperature varies both in time and space
Energy balance is the basis of all heat transfer calculations
No variation of Temperature with time
HTC needed for rate calculation
Temperature gradient small to be neglected. So Temperature variation with time only studied
Reynolds and Colburn Analogy relates
Energy Transport
Learning Outcomes
Macroscopic variables
friction factor
Heat Transfer Coefficient
From experiments
From dimensional analysis
From Fundamental equations
Important Concepts
Rate = Delta T / R
Bi = hLc/K
Fundamental Definition of HTC
Fourier's law
Newton's law of cooling
Tips for Exam
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
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)
Internal Forced Convection: Terms to identify constant Temperature problems - constant Temperature, uniform Temperature
Internal Forced Convection: Terms to identify constant heat flux problems - constant heating, uniform heating, uniform flux.
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
Reynolds analogy is for Pr = 1
Colburn analogy is for Pr not equal to 1
In external forced convection over a sphere, fluid properties need to be estimated at the free stream velocity and in the Whitaker correlation
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
Terms to identify "Natural convection" Problems, “Ambient air, still air, quiescent air”
In non-Lumped finite medium analysis, Lc = L for plane, Lc = r for cylinders and spheres. But Lc = Volume / Surface area for lumped analysis
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 unsteady conduction problems, start calculation with Bi, unless heat transfer coefficient is an unknown
Mechanisms
Convection
Problem Solving Methodology for Convection problems
Natural
External Forced
Internal Forced
Practice Problems
Constant heat flux
Constant wall temperature
Molecular Transport / Diffusion / Conduction
Unsteady state
Lumped Analysis
Non Lumped analysis
Multidimensional
Product rule for multidimensional heat transfer
Semi Infinite
Finite Media
Steady state
Practice problems
