Energy Transport

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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