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1. Title of Project work Presented by Name of the Student1 ( Roll No. ) As per A B C Order in batch Name2 ( Roll No. ) Name1 ( Roll No. ) B.Tech (Mechanical Engineering) Under the guidance of Name of the Supervisor Designation Department of Mechanical Engineering Gayatri Vidya Parishad College of Engineering (Autonomous) Visakhapatnam-530048

2. ABSTRACT Studies on pressure drop and heat transfer in microchannel heat sinks are of paramount importance in cooling of electronic devices, in which large amount of heat is to be dissipated from small areas. A CFD analysis is carried out to predict the pressure drop and heat transfer rates in laminar flow in rectangular microchannels . 2 3/1/2025

3. A computer source code in Python is developed for SIMPLE algorithm to solve 3-D u, v and w momentum balance equations to obtain the pressure and velocity fields in a rectangular microchannel . The energy balance equation is also solved to yield the temperature fields. Friction and heat transfer coefficients are calculated from the velocity and temperature fields for water and nanofluids (alumina-water) of three different concentrations (0.6, 1.2 and 1.8%v) for Reynolds numbers ranging from 10 to 600. 3 3/1/2025

4. Chapter-I INTRODUCTION Microchannel heat sinks constitute an innovative cooling technology for the removal of a large amount of heat from a small area. Convective heat transfer in microchannels has been proved to be a very effective method for the thermal control of microelectronic devices. Nanofluids are used to increase heat transfer rates. Phase change heat transfer is used when the heat to be removed is very large. 4 3/1/2025

5. Chapter-II REVIEW OF LITERATURE Peng et al. [1] investigated the single-phase forced convective heat transfer and flow characteristics of water in microchannel structures having hydraulic diameters and distinct geometric features experimentally. The empirical correlations were suggested for calculating both the heat transfer and pressure drop based on the Reynolds number. 5 3/1/2025

6. Adams et al. [2] conducted experimental investigation on turbulent, single-phase forced convection in circular micro channels with diameters of 0.76-1.09 mm . The y developed a generalized correlation for Nusselt numbers based on their own experimental data and those of earlier investigators [1]. 6 3/1/2025

7. 2.1 Scope of the present work The survey of literature indicates experimental studies on forced convection heat transfer in laminar flow of nanofluids through microchannels. However theoretical investigations on this topic are found to be scarce in literature. A theoretical analysis is carried out presently on laminar flow and heat transfer in a rectangular microchannel with the flow nanoliquids in the channel. 7 3/1/2025

8. A significant aspect of the present study is that a computer-based method is developed to solve the pressure-linked 3-D momentum balance equations using SIMPLER algorithm , along with the energy equation with an objective of predicting the pressure drop and heat transfer coefficients for water and nanofluids (Alumina-water) of different concentrations (0.6, 1.2 and 1.8)%v Validation of present work is done with the experimental study of Peng et al. [1] and Jung et al. [13] 8 3/1/2025

9. Chapter-III Theoretical Analysis 3.1 Physical model The fluid (water or a nano liquid) enters a rectangular microchannel at a mean velocity u m and bulk temperature T in The height, width and length of the microchannel are H, W and L. The channel wall is maintained at a constant temperature T w 9 3/1/2025

10. Fig.3.1 Flow and heat transfer in a rectangular channel 10 3/1/2025

11. 3.2 Governing equations The problem is governed by the following set of equations: Continuity equation u-momentum equation   11 3/1/2025

12. 3.4 Method of solution 3.4.1 Grid generation The volume of the channel is divided into a number of control volumes such as NX, NY and NZ in x, y and z directions respectively. Staggered grid According this concept of Patankar [21] used for transport equations, separate grids are chosen for p, u, v and w. The grids for u, v and w are staggered backward from that of p in x, y and z directions respectively. The control volumes for u i,J,K and v I,j,K are shown as examples with the nodes for p I,J,K in the both the control volumes. 12 3/1/2025

13. 13 3/1/2025 Fig.3.5 Edges and corners in a rectangular channel

14. 14 3/1/2025 Fig. 3.7 The concept of boundary node

15. Walls (6 Nos.) i=3; 3  J  (NY-2); 3  K  (NZ-2) i=(NX-1); 3  J  (NY-2); 3  K  (NZ-2) 4  i  (NX-2); J=2; 3  K  (NZ-2) 4  i  (NX-2); J=(NY-1); 3  K  (NZ-2) 4  i  (NX-2); 3  J  (NY-2); K=2 4  i  (NX-2); 3  J  (NY-2); K=(NZ-1) 15 3/1/2025 The boundary conditions are implemented at all the nodes given below.

16. SIMPLER Algorithm 16 3/1/2025

17. Chapter-IV RESULTS AND DISCUSSION Numerical results are obtained for velocity and temperature profiles in the rectangular microchannel . Friction and heat transfer coefficients are calculated from the velocity and temperature fields. Results are obtained for water and nanofluids for different Reynolds numbers ranging from 10 to 600. 17 3/1/2025

18. Table 4.1 Comparison of pressure drops computed from the present theory with those from Fanning’s equation Reynolds numbers Re Pressure drop from present theory (Pressure drop from Fanning’s equation) Dp , kPa Hydraulic diameters (mm) 0.343 0.3 0.24 0.2 0.133 100 1.28 (1.4) 1.92 (2.1) 3.79 (4.1) 6.556 (7.1) 22.49 (23.9) 200 2.58 (2.82) 3.85 (4.2) 7.61 (8.2) 13.148 (14.2) 45.007 (47.9) 400 5.19 (5.63) 7.757 (8.4) 15.283 (16.4) 26.413 (28.4) 90.082 (95.8) 600 7.817 (8.45) 11.687 (12.6) 22.976 (24.6) 39.728 (42.57) 135.171 (143.7) 18 3/1/2025

19. Peng et al. [1] presented experimental data for friction factors and Nusselt numbers for water flowing in rectangular microchannels Table 4.2 19 3/1/2025 Fluid Water Reynolds numbers 100 to 600 Duct sizes (mm) 1)0.3X0.1 2)0.2X0.2 3)0.3X0.2 4)0.3X0.3 5)0.4X0.3 Hydraulic diameters (mm) 1)0.133 2)0.2 3)0.24 4)0.3 5)0.343

20. Fig.4.1 variation of friction coefficient with Reynolds number for D h = 0.133mm 20 3/1/2025

21. CHAPTER-5 CONCLUSIONS The following salient conclusions can be drawn from the envisaged theoretical model. A computer code is developed for SIMPLER algorithm, which can be used for various applications involving laminar flow in rectangular channels. Heat transfer studies have also been conducted by adding the energy equation to the SIMPLER algorithm. 21 3/1/2025

22. The heat transfer results of the present theoretical analysis are validated by a comparison with the experimental data of two different investigators in literature. The good agreement indicates that the present theoretical analysis can be used to predict heat transfer rates in microchannels for water and nanofluids . 22 3/1/2025

23. 5.1 Scope for future work The SIMPLER algorithm has been developed presently for laminar flow in a rectangular channel. This work can be extended to turbulent flow by modifying the wall boundary conditions, by considering the laminar sub layers and by considering a suitable turbulent model for the turbulent core. 23 3/1/2025

24. REFERENCES X.F. Peng, G.P. Peterson, “Convective heat transfer and flow friction for water flow in micro channel structures”, International Journal of Heat And Mass Transfer, 1996, Vol. 39, pp. 2599–2608. T.M. Adams, S.I. Abdel- Khalik , S.M. Jeter, Z.H. Qureshi, “An experimental investigation of single-phase forced convection in micro channels”, International Journal of Heat And Mass Transfer, 1998, Vol. 41, pp. 851–857. T.M. Adams, M.F. Dowling, S.I. Abdel- Khalik , S.M. Jeter, “Applicability of traditional turbulent single-phase forced convection correlations to non-circular micro channels”, International Journal of Heat And Mass Transfer , 1999, Vol. 42, pp. 4411–4415. 4. W. Qu , G.M. Mala, D.Q. Li, “Heat transfer for water flow in trapezoidal silicon micro channels”, International Journal of Heat And Mass Transfer, 2000, Vol. 43, pp. 3925–3936. W. Qu , I. Mudawar , “Experimental and numerical study of pressure drop and heat transfer in a single-phase micro channel heat sink”, International Journal of Heat And Mass Transfer , 2002, Vol.45, pp. 2549–2565.   24 3/1/2025

25. Omer Bugra Kanargi , Poh Seng Lee, Christopher Yap, “A numerical and experimental investigation of heat transfer and fluid flow characteristics of a cross-connected alternating converging–diverging channel heat sink”, International Journal of Heat And Mass Transfer , 2016, Vol. xxx, pp. xxx–xxx. H.Vesteeg , W.Malalasekra , “An introduction to computational fluid dynamis – Finite volume method,second edition, Pearson education limited, New Delhi, 2007. 25 3/1/2025

26. Appendix-I Regression equations for properties The properties of water and nanofluids vary with temperature. Hence equations are obtained for density, viscosity, specific heat and thermal conductivity as functions of temperature. The general form of equation is T in K.   26 3/1/2025

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