1CHME 333 Workbook Chapter 2 – Introduction to Conduction •Objectives oDevelop a better understanding of Fourier’s Law Origins Different geometries Definition of thermal conductivity Calculation of heat fluxes oDevelop 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 oIn 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 oA phenomenological rate equation that allows determination of the conduction heat flux from knowledge of the temperature distribution in a medium oGeneral form oImplications 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