Lecture 2 - Lectures 3-4 9 • Case 3 – Heat generation...

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05/11/09 Lectures 3-4 1 Heat Transfer Notes Lecture 3-4 Srinath Ekkad
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05/11/09 Lectures 3-4 2 Conduction Conduction Rate Equation – Fourier’s law Introduce k – thermal conductivity In the limit Dx tends to 0 ;
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05/11/09 Lectures 3-4 3 Conduction For multi-dimensional conduction: k is considered isotropic above – meaning it is uniform spatially and independent of temperature Fourier’s law applies to all matter – solids, liquids, and gases
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05/11/09 Lectures 3-4 4 Apply conservation of energy to a differential CV inside a solid
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05/11/09 Lectures 3-4 5 Rate energy generated =
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05/11/09 Lectures 3-4 6 Special cases Case 1: 1-D, steady state, plane wall Steady state ( ) 1-D in x-direction ( ) No heat generation ( ) Constant k Equation:
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05/11/09 Lectures 3-4 7 Radial Coordinates
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05/11/09 Lectures 3-4 8 Case 2: 1-D, steady state, radial system Steady state 1-D in r direction Constant k No heat generation
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05/11/09
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Unformatted text preview: Lectures 3-4 9 • Case 3 – Heat generation – 1-D steady state constant k • Case 4 – 2-D steady state, constant k, no heat generation 05/11/09 Lectures 3-4 10 • Case 5 – Transient, constant k and no heat generation 05/11/09 Lectures 3-4 11 • Boundary and Initial Conditions – Temperature distributions depend on • Conditions at boundary • Initial conditions in time – Heat conduction equation requires • 2 boundary conditions in each direction (2 nd order in space) • 1 initial condition in time (1 st order in time) 05/11/09 Lectures 3-4 12 • Types of Boundary Conditions – Specified temperature; boundary condition of first kind – Dirichlet condition – Specified heat flux; second kind -Neumann • Finite heat flux • Adiabatic or insulated surface 05/11/09 Lectures 3-4 13 – Convective boundary condition – third kind...
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