Passive Solar Heating and Cooling PDF

Passive Solar Heating and Cooling REE 614 (RD 648) Law of Thermodynamics and Element of Heat Transfer Mohamed Eltarkawe The Libyan Academy - Some course materials were adopted from lectures by Harlan...

Passive Solar Heating and Cooling REE 614 (RD 648) Law of Thermodynamics and Element of Heat Transfer Mohamed Eltarkawe The Libyan Academy - Some course materials were adopted from lectures by Harlan H. Bengtson & Jamal Yassin Law of Thermodynamics In a thermodynamic process, macroscopic properties of the system, such as volume, heat (thermal energy), and flow of atoms or molecules of the system, change with time. In the absence of any thermodynamic process, the macroscopic properties of the systems do not change with time, and the system is said to be in thermal equilibrium. There are basically four laws of thermodynamics as follows: The Zeroth Law of Thermodynamics If two systems, B and C, are in thermal equilibrium with another system, A, then systems B and C are also in thermal equilibrium with each other. The First Law of Thermodynamics Energy can be converted from one form to another with the interaction of heat, work and internal energy, but it cannot be created nor destroyed. It is also termed as the “energy conservation law for thermodynamic systems.” The Second Law of Thermodynamics It is impossible to transfer heat spontaneously from a colder to a hotter body without causing any other changes in the system. The state of entropy of the entire universe, as an isolated system, will always increase over time. The Third Law of Thermodynamics The entropy of any system approaches a minimum constant value as the temperature approaches absolute zero. Element of Heat Transfer Conduction Conduction is the transfer of heat/thermal energy from the more energetic particles (means higher temperature) of a substance to the adjacent lower energetic (lower temperature) ones (microscopic H.T). Fourier’s law of heat conduction The thermal conductivity of gases, liquids, and solids depends on temperature. 𝐾0 is the thermal conductivity at temperature 𝑇0 ; and β is a constant for the material. Thermal diffusivity (α): Thermal diffusivity is property of the material that governs the diffusion of heat through the material. The higher the value of thermal diffusivity, the greater the diffusion of heat through the material. Biot number (Bi): The Biot number is important in cases where a solid body is immersed in hot fluid for heating. In terms of thermal resistance, it is the ratio of thermal resistance faced by conductive heat transfer to the thermal resistance faced by convective heat transfer. A smaller Biot number implies lower thermal caused to the conduction through the solid body. Dimensionless parameters Test = 30 min = 0.5 hour Every day = 8 hours Every day = 8/0.5 = 16 test 10 X 10 ( points X curves) = 100 test in one graph 100 graph X 100 test = 10000 test 10000/16 = 625 days of work 625 days/ 260 = 2.5 years to finish the job There are 250 business days in every year ( 52X5) Convection The transfer of heat from one place to another due to the movement of fluid (bulk motion H.T). Dimensionless heat-convection parameters Nusselt number (Nu): The Nusselt number gives insight about the dominance of convective heat transfer or conductive heat transfer for fluids. It is defined as the ratio of the convective heat-transfer coefficient to the conductive heat-transfer coefficient for fluids. (1 means it is only conduction) Reynold’s number (Re): Reynold’s number is defined for the heat-transfer problem in force mode of operation. It is the 𝑢 ratio of fluid dynamic force ρ𝑢02 to viscous drag force μ 𝑋0 and is given by Prandtl number (Pr): The Prandtl number relates fluid motion and heat transfer to the fluid. It is defined as the ratio of momentum diffusivity (μ/ρ) to thermal diffusivity (K/ρ𝐶𝑝 ) and is given by Grashof number (Gr): This is the ratio of buoyancy force to viscous force. It is given by Rayleigh number (Ra): This is the ratio of the thermal buoyancy to viscous inertia. It is expressed as All of the numbers defined in this section can be obtained using the properties of air and water listed in Appendix V. The properties are calculated at average temperature Tf given as follows: where T1 is hot surface temperature; and T2 is fluid temperature. The Nusselt number, as given in Eq. (3.22a), depends on the type of flow (free or forced). For free convection The above relation is obtained using dimensional analysis at the boundary layer. The values of C’ and n are estimated using experimental data for systems with same geometrical shapes and size. For some geometrical shapes used in solar thermal technology, given in Table 3.3, K’ governs the entire physical behavior of the problem. Some empirical relations used for free convention are also given in Table 3.4. 0.333 Example 3.4 Estimate the convective heat transfer coefficient for a horizontal rectangular surface (1.0 m × 0.8 m) maintained at 134 °C. The hot surface is exposed to (a) water and (b) air at 20 °C.ρ Page 713 ρ ρ=1 Page 714 3.77e9 350 7.2 w/m2 Forced convection For forced convection, the rate of heat transfer is enhanced by circulating the fluid over the hot surface using an external source of energy such as pump (liquid) or fan (air/gas). The empirical relation for forced convective heat transfer through cylindrical tubes may be represented as For fully developed laminar flow in tubes at constant wall temperature, we have the relation The heat-transfer coefficient calculated from this relation is the average value over the entire length of the tube. When the tube is sufficiently long, the Nusselt number approaches a constant value of 3.66. For the plate heated over its entire length, the average Nusselt number is given by Example 3.7 (Page 105) Convective heat transfer due to wind Wind blowing parallel to the exposed surface (convection & radiation). Note, if V =0 , this equation will give the heat-transfer coefficient for natural convection. Wind blowing parallel to the exposed surface (convection only). Another expression for the convective heat-transfer coefficient Radiation Radiation is transmitted/propagated through space/vacuum in the form of electromagnetic waves. the net radiation exchange between a horizontal surface (T1) with emittance (ɛ) and area (A) and the sky temperature, Tsky, is given by The sky temperature in terms of local air temperature can be given by the relation, Tsky and Ta are both in degrees Kelvin. Another commonly used relations are given as Heat-transfer coefficient due to radiation To check this equation, see class notes Note: Assume emittance is 0.994, Boltzman = 5.67 × 10−8 W/(m2·K4) Overall Heat-Transfer Coefficient (A) Parallel slabs: the heat transfer rate, Q , through structure convection or radiation or both where R = Ra + R1 + R2 + R3 + Rb; and U is the overall heat-transfer coefficient, W/m2 K. (B) Parallel slabs with air cavity  ‫مطلوب حساب استهالك الكهرباء من وحدات التدفئة – مثال انظر الي االطار االحمر‬ ‫‪Room‬‬ ‫‪number‬‬ ‫‪P‬‬ ‫‪T‬‬ ‫‪11‬‬ ‫ال تستخدم نفس االرقام بل استخدم المعلومات التي جمعتها من منزلك – رقم الغرفة و نوع المدفئة (او وحدة التدفئة المركزية) و القدرة و عدد‬ ‫ساعات العمل و بالتالي احسب االستهالك اليومي و الشهري‬