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CHME 333 Workbook Handout - Chapter 2

CHME 333 Workbook Handout - Chapter 2 - CHME 333 Workbook...

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1 CHME 333 Workbook Chapter 2 – Introduction to Conduction Objectives o Develop a better understanding of Fourier’s Law Origins Different geometries Definition of thermal conductivity Calculation of heat fluxes o Develop Heat Equation and apply common Boundary Conditions How temperature depends on position and time, e.g. T(x,y,z,t) or T(r, θ ,z,t) Introduction o In Chapter 1 you were introduced to the concept of heat transfer by conduction. You were given the equation for Fourier’s Law and you learned how to apply it to very simple cases. In Chapter 2, we will take a more detailed look at Fourier’s Law, and combined with a thermal energy balance, derive what is called the Heat Diffusion Equation. This Heat Diffusion Equation will enable you to calculate the temperature distribution in an object – T = T(x, y, z, t). In some cases, you will want to calculate the temperature as a function of position and time. In other cases, you will be asked to calculate heat transfer rates. You will do this by simply plugging in the temperature distribution equation (T = T(x, y, z, t)) into Fourier’s Law. We will do this for rectangular, cylindrical, and spherical geometries.

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2 Fourier’s Law – look at it more in depth o A phenomenological rate equation that allows determination of the conduction heat flux from knowledge of the temperature distribution in a medium o General form o Implications Heat transfer is in the direction of _________________________ (reason for minus sign). Fourier’s Law serves to define the thermal conductivity of the medium Thermal diffusivity α = ____________ What are the units of α? Direction of heat transfer is ___________ to lines of __________________________________ . Heat flux is a vector quantity (direction and magnitude) and may be resolved into orthogonal components. Fourier’s Law in coordinate systems