This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: University of Ottawa, CHG 2314, B. Kruczek 1 CHG 2314 Heat Transfer Part 2b Steadystate 1D Heat Conduction Conduction and thermal resistance Conduction with heat generation Conduction in extended surfaces University of Ottawa, CHG 2314, B. Kruczek 2 Conduction across the plane wall Note: The case of 1D steady conduction across the plane wall was partly discussed in Part 1  The temperature distribution requires solving the heat diffusion equation z For steadystate 1D conduction with no heat generation the heat diffusion equation simplifies to: z If k is constant, the temperature distribution can be obtained by double integration of the above equation: where C 1 and C 2 are the integration constants, which depend on how we specify the required two boundary conditions = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ dx dT k dx d (3.1) ( ) 2 1 C x C x T + = (3.2) University of Ottawa, CHG 2314, B. Kruczek 3 Conduction across the plane wall  For conditions 1 and 2 the temperature distribution becomes:  Application of Fourier’s law to Eq. (3.3) leads to: ( ) ( ) 2 , 2 , 2 1 , 1 , 1 2 , 1 , ∞ = ∞ = = = − = − − = − = = T T h dx dT k T T h dx dT k T T T T s L x s x s L x s x 4. 3. 2. 1. : conditions boundary Common ( ) ( ) 1 , 1 , 2 , s s s T L x T T x T + − = (3.3) ( ) 2 , 1 , s s x T T L kA dx dT kA q − = − = (3.4) University of Ottawa, CHG 2314, B. Kruczek 4 Thermal resistance  Eq. (3.4) can be alternatively written in the following form: where R t,cond is the thermal resistance for conduction given by:  If heat transfer involves convection and radiation, there is also thermal resistance for convection ( R t,conv ) and thermal resistance for radiation ( R t,rad ) given by: ( ) cond t s s x R T T q , 2 , 1 , − = kA L R cond t = , (3.6) A h R hA R rad rad t conv t 1 1 , , = = (3.13) (3.9) University of Ottawa, CHG 2314, B. Kruczek 5 Thermal resistance  In general, the rate of heat transfer in any 1D steadystate process without heat generation may be expressed by: where ∆ T is the temperature driving force and Σ R t = R tot is the total thermal resistance  Total resistance z Resistances in series: z Resistances in parallel: R A R B R B R A B A tot R R R + = B A tot R R R 1 1 1 + = tot t x R T R T q Δ = Σ Δ = University of Ottawa, CHG 2314, B. Kruczek 6 Thermal resistance  At steady state, the rate of heat transfer in the system can be expressed in several ways, for example:  It is easier to measure the temperature of fluids than of solids, consequently: where U is the overall heat transfer coefficient ( ) ( ) ( ) ( ) CF conv t cond t HF conv t cond t HF conv t s HF conv t s cond t s s x R R R T T R R T T R T T R T T q , , , , , 2 , 1 , , , , 2 , 1 , , , 1 , 1 , , 2 , 1 , + + − = + − = − = − = ∞ ∞ ∞ ∞ ( ) ( ) 2 , 1 , 2 , 1 , ∞ ∞ ∞ ∞ − = − = T T UA q R T T q x tot x or ∑ = Δ = = UA q T R R t tot 1 (3.19) University of Ottawa, CHG 2314, B. Kruczek 7 Composite wall  Consider a composite wall as shown: z The concept of total thermal resistance...
View
Full
Document
This note was uploaded on 05/30/2011 for the course CHG 2314 taught by Professor Kruz. during the Spring '10 term at University of Ottawa.
 Spring '10
 kruz.

Click to edit the document details