2. Foundations for Heat Exchanger Development P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Understand the Concept to Know Better Use!!!

3. Newton’s Law of Cooling

4. Realization of Newton’s Law of Cooling A general heat transfer surface may not be isothermal !?! Fluid temperature will vary from inlet to exit !?!?! The local velocity of flow will also vary from inlet to exit ?!?! How to use Newton’s Law in a Real life? Why Sir Newton discovered such an implicit parameter?

5. Newton’s law of cooling : As a principle of Temperature Measurement Historical Background: This law of cooling is named after English physicist Isaac Newton who, in the late 17th century, conducted the first experiments on the nature of cooling. Newton applied this principle to develop an industrial thermometer with high range. The conventional method used in 17 th century is thermal expansion of alcohol as a principle of thermometry.

6. These conventional thermometers were used almost exclusively for meteorological or medical purposes. NEWTON was the first, to try to overcome the limitations of thermometry which restricted it to meteorology or medicine and to develop thermometers capable of investigating a wide range of thermal phenomena in the laboratory.

7. Development of Calibration The Newton's method of establishing the different degrees of heat is of this kind: A thermometer with linseed- or olive-oil in it, of rather thick glass, and in fact open except that it is stopped with cotton to prevent the oil from flowing out, He plunges into melting tin, and he likewise plunges it into boiling water, and into dry earth heated by the Sun and into melted snow…..

8. Measurements Noted the degree of rarefaction of oil at all these conditions and time taken for the oil to change from one degree to other degree of rarefaction. "first it was found by the thermometer with linseed oil, that if, when it was placed in melted snow, the oil possessed the space of 10000 parts; then the same oil rarefied with the heat of a human body possessed the space of 10256 parts.

9. Newton’s Measured Scale Melting Snow : 0 N Heat of Summer : 4, 5 & 6 N… Incubated egg & body heat: 12 N Greatest heat hand can stand in stirred water & Heat of blood : 14-3/11 N. Greatest heat hand can stand in still water & Heat of blood : 17 N Water begins to boil : 33 N Water boils vehemently : 34 N Water scarcely acquires any greater heat by boiling: 34.5 N

10. Newton's Law of Cooling Based on the measured values of time and temperatures, Newton Proposed following hypotheses: 1) The rate at which heat passed from the iron to the moving air was proportional to the temperature difference between iron and air. This law about rate of heat transfer is sometimes mistakenly referred to as Newton’s law of cooling. 2) At equal intervals of time these temperature differences or excesses were in constant ratio. This law is about the time course of the fall in temperature and is therefore Newton’s ‘law’ of cooling.

12. Newton’s Experiments to Develop High Range Thermometry In order to investigate the high range Thermometry: Newton resorted to a stratagem which has always been considered to be ingenious. He heated an ingot of iron until it was glowing and with a pair of tong. Another pretty thick heated piece of iron red-hot, which was taken out of the fire with a pair of pincers, which was also red-hot. Both were laid in a cold place, where the wind blew continually upon it.

13. A plausible 'wind tunnel' for Newton's cooling experiments.

14. Measurements made by Sir Newton Started putting on thick piece particles of several metals, and other fusible bodies. The time of its cooling was marked, till all the particles were hardened. The time of cooling of the second iron was market, till equal to the heat of the human body.

16. Newton’s Law for High Temperature Thermometry Then supposing that the excess of the degrees of the heat of the iron when the particles were hardened above the heat of the atmosphere, found by the thermometer, were in geometrical progression when the times are in an arithmetical progression. If the excess of the temperature of the body above its surroundings is observed at equal intervals of time, the observed values will form a geometrical progression with a common ratio. The several degrees of heat were discovered...~

17. Experimental Results of Newton’s Law of Cooling

19. Local Convection Heat Transfer Consider convection heat transfer as a fluid passes over a surface of arbitrary shape: Apply Newton’s law cooling to a local differential element with length dx. h is called as Local Convection Heat Transfer Coefficient, W/m 2 K

20. The total heat transfer rate Q is Where, h avg is the average convection heat transfer coefficient for the entire surface. where Therefore

21. Concept of Solid Fluid Interaction Diffuse reflection U 2 U U Φ U2 U2 Φ U1 U1 U1U1 Φ U2U2 Specular reflection Perfectly smooth surface (ideal surface) Real surface The convective heat transfer is defined for a combined solid and fluid system. The fluid packets close to a solid wall attain a zero relative velocity close to the solid wall : Momentum Boundary Layer.

22. The fluid packets close to a solid wall come to thermal equilibrium with the wall. The fluid particles will exchange maximum possible energy flux with the solid wall. A Zero temperature difference exists between wall and fluid packets at the wall. A small layer of fluid particles close the the wall come to Mechanical, Thermal and Chemical Equilibrium With solid wall. Fundamentally this fluid layer is in Thermodynamic Equilibrium with the solid wall.

23. Heat Transfer in Equilibrium Layer The thickness of stagnant layer decides the magnitude of normal temperature gradient at the wall. And hence, the thickness of wall fluid layer decides the magnitude of convective heat transfer coefficient. Typically, the convective heat transfer coefficient for laminar flow is relatively low compared to the convective heat transfer coefficient for turbulent flow. This is due to turbulent flow having a thinner stagnant fluid film layer on the heat transfer surface. At the wall for fluid layer : At Thermodynamic equilibrium

24. Estimation of Heat Transfer Coefficient Estimation of heat transfer coefficient is basically computation of temperature profile. A general theoretical and experimental study to understand how the stagnant layer is developed. The global geometry of the solid wall and flow conditions will decide the structure of stagnant layer. Basic Geometry : Internal Flow or External Flow.