Heat Transfer Introduction CBE 150 A Transport Spring
Heat Transfer Introduction CBE 150 A – Transport Spring Semester 2014
Heat Transfer Introduction Goals: By the end of today’s lecture, you should be able to: · define the mechanisms for heat transfer · define Fourier's Law of heat conduction · describe the differences between series resistance and parallel resistance · calculate the total resistance for composite systems in series and parallel · distinguish between natural and forced convection CBE 150 A – Transport Spring Semester 2014
Outline: I. III. IV. V. Mechanisms of heat transfer Heat transfer by conduction Resistances in series and parallel Example problem -- series resistances Convective heat transfer CBE 150 A – Transport Spring Semester 2014
I. Mechanisms of heat transfer Heat is transferred from an area of Low area of temperature. High temperature to an What are three mechanisms for heat transfer? Conduction, Convection, Radiation CBE 150 A – Transport Spring Semester 2014
Name the key mode(s) of heat transfer for the following examples: The ceiling heating coil in a bathroom Heating a pan of water on the stove top Baking a pie The heating system in your car Steam radiator Heat exchanger CBE 150 A – Transport Spring Semester 2014
Heat Transfer is a ‘rate’ process The rate at which heat is transferred is critical in many processes. How can the rate of heat transfer be controlled? CBE 150 A – Transport Spring Semester 2014
II. Heat transfer by conduction For ease of argument, let's consider conduction through a solid. Before proceeding, we need a few definitions and some nomenclature. Heat flux q = q has units of (Btu/ft 2 -hr) or (kcal/m 2 -hr) or (W/m 2). Is q a scalar or vector quantity? Vector CBE 150 A – Transport Spring Semester 2014
Heat transfer rate q has units of (Btu/ hr) or (kcal/hr) or (W). The heat transfer rate, q, measures the total amount of thermal energy flowing across a surface per unit time. On the other hand, Q is the net heat transfer into a control volume. CBE 150 A – Transport Spring Semester 2014
Fourier's Law (one-dimensional): What is the corresponding expression for heat flux (q)? CBE 150 A – Transport Spring Semester 2014
Thermal conductivity. The proportionality constant k is a physical property of the substance called thermal conductivity. k has units of (Btu/hr-ft-°F) or (kcal/hr-m-°C) or (W/m-°K) What is the analogous physical property for momentum transfer? Viscosity (m) The thermal conductivity is a mild function of temperature, but is often assumed constant for most applications. CBE 150 A – Transport Spring Semester 2014
Typical values of thermal conductivity (Btu/hr-ft-°F) : air water glass steel stainless steel copper CBE 150 A – Transport 0. 015 0. 35 0. 45 25 10 225 Spring Semester 2014
CBE 150 A – Transport Spring Semester 2014
This implies what about the heat transfer rate, q? Substitute for q from Fourier's Law: Integration with respect to x, then using the boundary conditions that T = T 1 at x = 0 and T = T 2 at x = Dx yields: CBE 150 A – Transport Spring Semester 2014
Thermal Resistance When doing heat transfer calculations, it proves convenient to define thermal resistance, R: Comparing this definition with our previous result, yields the following relationship for R: [MSH Example 10. 2] CBE 150 A – Transport Spring Semester 2014
For a cylindrical shell, the equivalent expression for thermal resistance is: where ALM is the log mean area, CBE 150 A – Transport Spring Semester 2014
CBE 150 A – Transport Spring Semester 2014
How does q 1 relate to q 2? We can express the rate of heat transfer as a function of (T 3 -T 1): q= We see that the total resistance (RT) for the composite slab is simply the sum of the individual resistances. RT = S Ri CBE 150 A – Transport Spring Semester 2014
CBE 150 A – Transport Spring Semester 2014
CBE 150 A – Transport Spring Semester 2014
Space Shuttle Thermal Protective System The shuttle's thermal protection system (TPS) is designed to keep the temperature of the shuttle's aluminum structure below 350 degrees Fahrenheit (177 C) while temperatures on some external surfaces exceed 2, 300 Fahrenheit (1, 260 C) degrees. This tile was removed from Columbia after the first shuttle mission, in April 1981. Example Problem For a 4 inch thickness, determine the required tile thermal conductivity for an energy flux of 300 BTU/hr ft 2. Compare this value to typical thermal conductivities given on Slide 11. CBE 150 A – Transport Spring Semester 2014
Example Problem -- Series resistances The wall of a downtown Berkeley bank is composed of a 5 -inch layer of Texas granite (k = 1. 5 Btu/hr-ft-°F) on the exterior, a 3/8 -inch layer of wall board (gypsum, k = 0. 25 Btu/hr-ft-°F), a 3 -inch thick layer of air (k = 0. 023 Btu/hr-ft-°F), another 3/8 - inch layer of wall board (gypsum, k = 0. 25 Btu/hr-ft-°F), and finally, a 1/4 - inch thick layer of oak paneling on the interior (k = 0. 12 Btu/hr-ft-°F). A fire has been burning unnoticed on the inside of the bank for 20 min such that the interior oak paneling temperature has reached a steady state value of 700°F. Will anyone touching the exterior of the building experience pain or discomfort (note: scalding water ≈ 140°F)? Assume that the rate of heat loss is 50 Btu/hr-ft 2. CBE 150 A – Transport Spring Semester 2014
10 Minute Problem -- Series resistances A thick-walled tube of stainless steel having a k = 21. 63 W/m K with dimensions of 0. 0254 m ID and 0. 0508 m OD is covered with 0. 0254 m thick layer of an insulation (k = 0. 2423 W/m K). The inside-wall temperature of the pipe is 811 K and the outside surface of the insulation is 310. 8 K. For a 0. 305 m length of pipe, calculate the heat loss and the temperature at the interface between the metal and the insulation. CBE 150 A – Transport Spring Semester 2014
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