Heat Transfer

Taught by: Dr. Matt Maschmann
Taken: FS 2014
Text: Introduction to Heat Transfer (Sixth Edition) by: Bergman, Lavine, Incropera, Dewitt

Exam 1 Formula Sheet

Energy Balance

\dot{E}_{in} - \dot{E}_{out} + \dot{E}_{g} = \dot{E}_{st}

\dot{E}_{in} - Time rate of energy entering the system
\dot{E}_{out} - Time rate of energy leaving the system
\dot{E}_{g} - Time rate of energy generated in the system
\dot{E}_{st} - Time rate of change of energy stored in the system

Fourier's Law (Conduction)

q_{x} = -kA\frac{dT}{dx}

q_{x} - Heat rate in the x direction
k - Thermal conductivity
A - Cross sectional area perpendicular to the heat flow
\frac{dT}{dx} - Temperature gradient in the x direction

Newton's Law of Cooling (Convection)

q_{x} = hA(T - T_{\infty})

q_{x} - Heat rate in the x direction
h - Heat transfer coefficient
A - Cross sectional area perpendicular to the heat flow
T - Temperature of the solid surface
T_{\infty} - Temperature of the bulk air

Stephan-Boltzman Law (Radiation)

q_{x} = \epsilon \sigma A(T^{4} - T_{surr}^{4})

q_{x} - Heat rate in the x direction
\epsilon - Emissivity
\sigma = 5.67 * 10^{-8} \left(\frac{W}{m^{2}K^{4}}\right) - Stephan-Boltzman constant
A - Cross sectional area perpendicular to the heat flow
T - Temperature of the solid surface
T_{surr} - Temperature of the surroundings

Heat Diffusion Equation (Conduction)

\frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(k\frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(k\frac{\partial T}{\partial z}\right) + \dot{q} = pc_{p}\frac{\partial T}{\partial t}

Thermal Resistances