Basics of heat transfer 17
- 1. HEAT • Heat: It is denoted by symbol Q and is defined as follows “heat is something which appears at the boundary when a system changes its state due to a difference in temperature between the system and surroundings.” • Heat appears only at the boundary while the change takes place inside the system. • Sign Convention: If heat flows from system to surroundings, the quantity is said to be positive and if heat flows from surroundings to system it is said to be negative. In other words, Heat received by system=+Q Heat rejected by system=-Q
- 2. Difference between Heat Transfer and Thermodynamics: • Let us take an example of a hot steel bar kept in a water bath. • Thermodynamics predicts only the equilibrium temperature and state of the system but it doesn’t predicts the time taken by the system to reach that equilibrium and the temperature of the hot steel bar. • Heat Transfer on the other hand helps in predicting the temperature of both the bar and the water as a function of time. • MODES OF HEAT TRANSFER: There are three modes of heat transfer: • Conduction • Convection • Radiation • Heat transfer occurs as a result of combinations of these modes of heat transfer. Heat always flows in the direction of lower temperature.
- 3. CONDUCTION • The transfer of heat from one part of a substance to another part of the same substance, or from one substance to another in physical contact with it, without any displacement of molecules forming the substance. • In solids, the heat is conducted by the following two mechanisms: i. Lattice Vibrations (the faster moving molecules or atoms in the hottest part of a body transfer heat impact some of their energy to adjacent molecules). ii. By transport of free electrons (Free electrons provide an energy flux in the direction of decreasing temperature). • In liquids, the process is similar but as they are more closely placed than gases, the intermolecular forces comes into play.
- 4. • In gases, the kinetic energy of a molecules is a function of temperature. The molecules are in constant random motion with energy and momentum. When a molecule from high T region coincides with a molecule of low T region, it loses energy by collisions.
- 5. • FOURIER’S LAW OF HEAT CONDUCTION: •It states that,” for a homogeneous solid, the rate of heat flow is directly proportional to area of section at right angles to the direction of heat flow and to change of temperature with respect to length of the path of heat flow.”
- 6. • Mathematically, Q ∝ A.(dt/dx) Where, Q= Heat flow through the body per unit time (Watts) A= Surface area of heat flow (m2) dt= Temperature difference of the faces of block (K or ᵒC ) dx= Thickness of body in direction of flow (m) Thus, Q= −𝒌.A(dt/dx) Where k= constant of proportionality also known as thermal conductivity of body.
- 7. • -ve sign is to take care of the decreasing temperature along the direction of increasing thickness. The temperature gradient (dt/dx) is always negative along positive x direction. • Assumptions of Fourier Law: Conduction of heat takes place under steady state conditions. The heat flow is unidirectional. The temperature gradient is constant and the temperature flow is linear. There is no heat generation. The material is homogeneous and isotropic.
- 8. • Essential Features of Fourier Law: It is applicable to all matter. ( Solid, Liquid, Gas) It is based on experimental evidence. It is a vector expression indicating the heat flow rate is in the direction of decreasing temperature. It helps to define the thermal conductivity of medium through which heat is conducted.
- 9. • The thermal conductivity of materials is defined as,” amount of energy conducted through a unit area and unit thickness in unit time when the difference in temperature between the faces causing heat flow is unit temperature.” • Conduction of heat occurs mostly in pure metals, less in alloys and much less in non-metals. • Thermal conductivity depends on the following factors: Material Structure. Moisture Content. Density of material. Pressure and temperature of operating conditions. Units of k are W/mK or W/mᵒC
- 10. • Thermal conductivity of a metal varies when it is heated or treated with mechanical process. • Thermal conductivity of most metals decreases with the increasing temperature. • The dependence of thermal conductivity (k) on temperature for most materials is mostly linear.
- 11. CONVECTION • It is the mode of energy transfer between a solid surface and the adjacent liquid or gas in motion and it involves the combined effect of conduction and fluid motion. The faster the fluid motion, the greater is the convection. • The rate equation for the convective heat transfer between a surface and an adjacent fluid is described by Newton’s Law of Cooling.
- 12. Statement of Newton’s Law of Cooling: •The coefficient of convective heat transfer (h) is defined as “the amount of heat transmitted for a unit temperature difference between the fluid and unit area of surface in unit time.”
- 13. •Q=h.A(ts-tf) Where Q= rate of conductive heat transfer A= area exposed to heat transfer ts=Surface Temperature tf=Fluid Temperature h=coefficient of convective heat transfer Units of h are W/m2K or W/m2ᵒC
- 14. The value of ‘h’ depends on: 1. Thermodynamic and transport properties 2. Nature of fluid flow 3. Geometry of Surface 4. Prevailing thermal conditions.
- 15. RADIATION •It is the transfer of heat through space or matter by means other than conduction or convection. •Radiant energy(being electromagnetic radiation) requires no medium for propagation and will pass through vaccum.
- 16. • LAWS OF RADIATION: Wien’s Law: It states that the wavelength λ corresponding to the maximum energy is inversely proportional to absolute temperature T of hot body. λmT=constant (or) λm∝ 𝟏/𝑻 Stefan-Boltzmann Law: The emissive power of black body is directly proportional to fourth power of absolute temperature. Q∝ 𝑻4
- 17. Mathematically, Q = F. 𝜎.A (T1 4 – T2 4) Where, F= a factor depending on geometry and surface properties. 𝜎 = 𝑆𝑡𝑒𝑓𝑎𝑛 − 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡= 5.67×10 ̄ ̄⁸ W/ m2K4 A = Area of surface, m 2