It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. Of course, the longer lived substance will remain radioactive for a much longer time. As can be seen, the amount of material necessary for 1 curie of radioactivity can vary from an amount too small to be seen 0. A sample of material contains 1 mikrogram of iodine Note that, iodine plays a major role as a radioactive isotope present in nuclear fission products , and it a major contributor to the health hazards when released into the atmosphere during an accident.
Iodine has a half-life of 8. As can be seen, after 50 days the number of iodine atoms and thus the activity will be about 75 times lower. Multiplying Whole Numbers.
DOE Fundamentals Handbook - Material Science (Volume 1 of 2)
Dividing Whole Numbers. Hierarchy of Mathematical Operations Summary. Equivalent Fractions. Addition and Subtraction of Fractions. Decimal to Fraction Conversion. Addition and Subtraction of Decimals Multiplying Decimals. Dividing Decimals. Rounding Off. Changing Decimals to Percent.
Percent Differential. MA Page ii. Basic Rules for Exponents.
Zero Exponents. Negative Exponents. Fractional Exponents. Writing Numbers in Scientific Notation. Converting Scientific Notation to Integers Addition. The Radical. Simplifying Radicals. Addition and Subtraction. Dissimilar Radicals. A-1 Rev. A-1 Page iv Rev. Olivio, C. Thomas and Olivio, Thomas P.
DOE Fundamentals Handbook - Material Science (Volume 1 of 2)
MA Page vi Rev. The number n, in a , is called the index of the root. The nth root of a number a is a number b which has the property that the product of n values of b is a. For example, the third or cube root of 8 is 2, because 2x2x2 equals 8. Absolute Value of a This expression represents the magnitude of a variable without regard to its sign.
It signifies the distance from zero on a number line. That is, the absolute value of -6 is 6 because -6 is 6 units from zero. It is given the symbol A where A is any number or variable. What is the heat flux and the heat transfer rate through the floor? The heat transfer rate may be considered as a current flow and the combination of thermal conductivity, thickness of material, and area as a resistance to this flow.
If the thermal resistance term? The electrical analogy may be used to solve complex problems involving both series and parallel thermal resistances. The student is referred to Figure 2, showing the equivalent resistance circuit. A typical conduction problem in its analogous electrical form is given in the following example, where the "electrical" Fourier equation may be written as follows. T Rth Rev.
Calculate the thermal resistance of each layer of the wall and the heat transfer rate per unit area heat flux through the composite structure. Solution: RCu? Btu 0. Heat transfer across a pipe or heat exchanger tube wall is more complicated to evaluate. Across a cylindrical wall, the heat transfer surface area is continually increasing or decreasing. Figure 3 is a cross-sectional view of a pipe constructed of a homogeneous material. From the discussion above, it is seen that no simple expression for area is accurate.
Neither the area of the inner surface nor the area of the outer surface alone can be used in the equation. For a problem involving cylindrical geometry, it is necessary to define a log mean cross-sectional area Alm.
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Alm Aouter Ainner ? This expression for log mean area can be inserted into Equation , allowing us to calculate the heat transfer rate for cylindrical geometries. HT Page 12 Rev. The temperature of the inner surface of the pipe is oF and the temperature of the outer surface is oF.
Calculate the heat transfer rate through the pipe.
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Calculate the heat flux at the outer surface of the pipe. Find the interior surface temperature. HT Page 14 Rev. Conduction Heat Transfer Summary? Conduction heat transfer is the transfer of thermal energy by interactions between adjacent molecules of a material. Heat flux Q Heat conductance problems can be solved using equivalent resistance formulas analogous to electrical circuit problems. Convection Convection involves the transfer of heat by the motion and mixing of "macroscopic" portions of a fluid that is, the flow of a fluid past a solid boundary.
The term natural convection is used if this motion and mixing is caused by density variations resulting from temperature differences within the fluid.
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The term forced convection is used if this motion and mixing is caused by an outside force, such as a pump. The transfer of heat from a hot water radiator to a room is an example of heat transfer by natural convection. The transfer of heat from the surface of a heat exchanger to the bulk of a fluid being pumped through the heat exchanger is an example of forced convection. Heat transfer by convection is more difficult to analyze than heat transfer by conduction because no single property of the heat transfer medium, such as thermal conductivity, can be defined to describe the mechanism.
Heat transfer by convection varies from situation to situation upon the fluid flow conditions , and it is frequently coupled with the mode of fluid flow. In practice, analysis of heat transfer by convection is treated empirically by direct observation. The exact definition of the bulk temperature Tb varies depending on the details of the situation.
For flow adjacent to a hot or cold surface, Tb is the temperature of the fluid "far" from the surface.
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For boiling or condensation, Tb is the saturation temperature of the fluid. For flow in a pipe, Tb is the average temperature measured at a particular crosssection of the pipe. HT Page 18 Rev. Typically, the convective heat transfer coefficient for laminar flow is relatively low compared to the convective heat transfer coefficient for turbulent flow.