CN2125E FAQ 1. WWWR P.212 Example 3: How to know that the saturated steam (0.276MPa) has a temperature 404K? Answer: Please refer to the Steam Table from your thermodynamics textbook. 2. How to read the values of thermal conductivity, heat transfer coefficients and other relevant transport properties from the textbook? Answer: Please choose the closest value with appropriate interpolation. In homework assignments, quizzes and final examination, please also give the page number of your reference for this. It is anticipated that some variation could be found because most of these values come from experiments. 3. The derivation for differential heat transfer equations are rather complicated (Chapter 16 WWWR) and (Chapter 2 ID), do we need to know the detailed derivation? Answer: No, you should understand just once the derivation for rectangular coordinate, the derivations for cylindrical and spherical coordinates can be realized in a similar way and there is no need to worry about the detailed derivations. Instead, the focus should be on understanding the physical meanings about the respective terms in these equations, for instance, which terms contribute to conduction in the radial direction, etc. From: Wang Chi-Hwa Sent: Wednesday, January 28, 2015 5:11 PM To: Guo Erjia Subject: RE: Question about CN2125 Dear Erjia: (1) surface resistance refers to surface convective heat transfer resistance. (2) Yes, for the case Bi > 100, surface convective heat transfer resistance is very low. Best Regards, Chi-Hwa Wang CN2125 From: Wang Chi-Hwa Sent: Wednesday, January 28, 2015 4:13 PM To: 'annabelle -' Subject: RE: CN2125 Question Dear Annabelle: Yo=constant = Yo(t=0) = (T0-Ts)/(T0-Ts)=1. That is why it disappears from the formula in equation 18-13. Best Regards, Chi-Hwa Wang CN2125 From: annabelle - [mailto:arrowstarheart@hotmail.com] Sent: Tuesday, January 27, 2015 2:59 PM To: Wang Chi-Hwa Subject: CN2125 Question Dear Prof Wang, For the derivation of equation 18-13 in the week 3 ppt, how come Y0 disappears from the last line of working? Thank you. Yours sincerely, Annabelle From: Guo Erjia [mailto:guoerjia@nus.edu.sg] Sent: Wednesday, January 28, 2015 12:31 AM To: Wang Chi-Hwa Subject: Question about CN2125 Hi Prof Wang, I am a student taking CN2125 this semester. I have a question about today's lecture on Unsteady-State Conduction. What is meant by the term "surface resistance" in the context of the Biot modulus? For example, for Bi >100 (negligible surface resistance) where Bi is proportional to conductive resistance/convective resistance, does surface resistance here refer to convective resistance being very low? It would be greatly appreciated if you could enlighten me on this question! Thank you, Guo Erjia -----Original Message----From: Wang Chi-Hwa Sent: Thursday, February 13, 2014 9:24 AM To: Goh Yu Kian Subject: RE: Question regarding CN2125 Unsteady Heat Transfer Dear Yu Kian: In CN2125, if L/D > 10, you can approximate the 2-D problem as 1-D problem. Best Regards, Chi-Hwa Wang CN2125 -----Original Message----From: Goh Yu Kian Sent: Wednesday, February 12, 2014 3:41 PM To: Wang Chi-Hwa Subject: Question regarding CN2125 Unsteady Heat Transfer Dear Lecturer, You mentioned in the class that sometimes,we only need to consider onedimension in cylinder case.For example:A 2 (feet) long cylinder with 0.25 (feet) diameter,is this a one-dimension or two-dimension when calculating surface area?Is 10 times difference big enough to neglect axial direction heat transfer? Regards, Yu Kian ________________________________________________________________________ From: Wang Chi-Hwa Sent: Friday, January 21, 2011 8:18 AM To: Mohamed Ziaudeen Shahul Hameed Subject: RE: Thermal conductivity values- HW assignment 1. Dear Mohamed ziaudeen shahul hamee: Please use the following fixed values for your solution. Fiberglass blanket, kb = 0.038 W/m.K; plywood siding, ks = 0.12 W/m.K, Plasterboard, kp = 0.17 W/m.K. Sincerely yours, Chi-Hwa Wang From: Mohamed Ziaudeen Shahul Hameed Sent: Thursday, January 20, 2011 10:47 PM To: Wang Chi-Hwa Subject: Thermal conductivity values- HW assignment 1. Hi Prof, In question 3.13 from ID text book, which is given as CN2125E assignment 1( Question no -2 ) need some clarifications about the thermal conductivity (K) values for wood, fiberglass and plaster board. In WWWR text book , there are no specific thermal conductivity values for the above materials and even In ID text book ,for plaster there are three different values. Can you please provide us some reference to find the thermal conductivity values for the above materials. Thanks and regards, Mohamed ziaudeen shahul hameed. Year -2. From: Wang Chi-Hwa Sent: Friday, January 21, 2011 8:08 AM To: Li Xuan Subject: RE: Question Regarding An Example in ID Book Dear Xuan: Thank you for your e-mail. The governing equation does not contain any convection because for this problem, the governing equation is applied to the solid phase where there is no convection. Please take note that general differential energy reduces to Heat / Diffusion Equation when there is no convective terms. Conversely, the boundary condition is the matching of conduction and convection flux at the interface. Sincerely yours, Chi-Hwa Wang CN2125 From: Li Xuan Sent: Thursday, January 20, 2011 10:13 AM To: Wang Chi-Hwa Subject: Question Regarding An Example in ID Book Dear Prof Wang, I have some doubt regarding Example 2.3 on P79 of ID Book (6th edition, section 2.4 Boundary and Initial Conditions). I am wondering why Heat Differential Equation is used instead of the General Form of The Differential Energy Equation when there’s convection involved in this question? Would the result be more accurate using the general form? Best Regards, Li Xuan -----Original Message----From: Wang Chi-Hwa Sent: Thursday, January 20, 2011 8:41 AM To: Du Wei Subject: RE: Questions about CN2125 Dear Wei: Thanks for your e-mail. (1) "Incompressible Flow" and "Isobaric flow" represent two typical systems usually encountered in flow process. These two are named and compared here for governing equation. Although same in the formula, they represent different physical meanings. (2) Thank you very much for your correction on this typographical mistake. I have amended it on the CN2125 Website. It should be dT/dx instead. Sincerely yours, Chi-Hwa Wang CN2125 -----Original Message----From: Du Wei Sent: Tuesday, January 18, 2011 8:21 PM To: Wang Chi-Hwa Subject: Questions about CN2125 Dear Prof.Wang, I'd like to ask you some questions regarding heat conduction. 1. For the special forms of differential energy equation, the two special cases you showed us are A. an incompressible fluid without energy sources and with constant k, B. isobaric flow without energy sources and with constant k. Both A and B will lead to the formula: density*Cv*DT/Dt=k*laplacian T. I'm wondering that how does the condition of an incompressible flow or isobaric flow contribute to simply the original energy equation? In other words, I think the conditions of no energy sources and constand k alone will reduce to that form of equation. Hope you could explain to me. 2. On the slide 4 of lecture notes 2, for 1D, steady state transfer by conduction, the simplified expression is d(x^i*partial T partial x)/dx=0, why is it still partial derivative inside the bracket? should it be an ODE? Thank you very much! Best regards, Du Wei _______________________________________________________________________ From: Wang Chi-Hwa Sent: Monday, February 02, 2009 9:32 AM To: Pan Yue Subject: RE: CN2125 question (insulated boundary condition) Dear Yue: For insulated surface -k dT/dx =0, no heat transfer. Because k can not be zero, dT/dx has to be zero. This has nothing to do with symmetry. Symmetry is used applied to the geometry center "e.g. centerline). Sincerely yours, Chi-Hwa Wang CN2125 From: Pan Yue Sent: Sunday, February 01, 2009 10:45 PM To: Wang Chi-Hwa Cc: Pan Yue Subject: CN2125 question (insulated boundary condition) Dear Prof, I have a question about the boundary condition at insulated surface. Why is dT/dx=0 at insulated surface? if it is because of symmetry, how to apply symmetry here? Thank you very much. Yours sincerely, Pan Yue From: Wang Chi-Hwa Sent: Monday, February 02, 2009 9:30 AM To: Ewe Ai Ting Subject: RE: enquires on CN2125 Dear Ai Ting: (1) Please refer the thermal circuit I drew during all the seven tutorial sessions last week for explanation on this part. Q is the total heat transfer. Any question, please visit me in the tutorial this week for verbal explanation on this point further. (2) For conduction, the delta is the temperature between two solid interfaces. For this case, one interface one temperature. For convection, delta T refers to T(surface of solid) - Tsurrounding. Sincerely yours, Chi-Hwa Wang CN2125 From: Ewe Ai Ting Sent: Sunday, February 01, 2009 5:20 PM To: Wang Chi-Hwa Subject: enquires on CN2125 Dear Sir I have encountered some enquires on CN2125. May I ask for tutorial 2 qn17.13. what is the meaning of the step total heat transfer is equal to q1+q2? and also, heat flux q through the wall is constant, what is the physical meaning of q? is the q equal to the total heat transfer? In addition, to find overall q from q=deltaT/R.For the delta q, the temperature difference is between the inner surface and outer surface or inner surface and the surrounding? Thank you for your time! =) Regards From: Wang Chi-Hwa Sent: Monday, February 02, 2009 9:11 AM To: Tan Geok Meng Subject: RE: regarding unsteady state conduction Dear Geok Meng: (1) If the question has mentioned any "time", it is most likely to be an unsteady problem. Otherwise, steady heat transfer problem. (2) You use semi-infinite wall problem when no "length" of the object is given. 1(Tsurroundings-T)/(Tsurroundings - Tinitial) = (T-Tinitial)/(Tsurface - Tinitial). (3) Yes, when a cylinder's end effects can be neglected, we can treat it as an infinite cylinder as no axial heat transfer is considered. Sincerely yours, Chi-Hwa Wang CN2125 From: Tan Geok Meng Sent: Saturday, January 31, 2009 5:25 PM To: Wang Chi-Hwa Subject: regarding unsteady state conduction Hi sir, i have a few questions regarding the lecture this week. 1) how do we differentiate between unsteady and steady state heat transfer? from what i know, unsteady state heat transfer has an accumulation term, but how do we differentiate them just by reading the question itself? 2) when do we use the semi infinite wall equation, and how do we manipulate it to change it to from (T-Tinitial)/(Tsurface - Tinitial) to (Tsurroundings-T)/(Tsurroundings - Tinitial)? 3) if they mentioned that a cylinder's end effects can be neglected, do we treat it as an infinite cylinder and use the corresponding graph in appendix f or do we still use the figures for a finite cylinder? thanks From: Wang Chi-Hwa Subject: RE: enquiry on steady state conduction Dear Shi Han: Thanks for your e-mail. (1) There is still heat transfer through the fin by conduction but eventually they escape from the side surface to surrounding air by convection. (2) Under an ideal situation, the entire fin would have the same temperature with the base. (3) In reality there would be temperature drop along the fin axis. As a result, the fin efficiency is less than 100%. Sincerely yours, Chi-Hwa Wang Cn2125 Co-instructor From: Oh Si Han Subject: enquiry on steady state conduction Dear sir, I would like to clarify following concept covered in Chapter 17(steady heat conduction): You mentioned that in order to calculate the total heat transfer from an extended surface, at the base of the fin, whatever heat transferred from the fin to the surrounding must come frm the original source( conduction from base to fin at x=0), resulting in eqn 17-42 q=-kA(dT/dx) atx=0 does this assume that there is no heat conduction through the fin(because fin is of constant and uniform temp), such that heat transfer to the fin at the base=heat transferred by fin to surrounding? Is this also what is meant by the case of ideal heat transfer rate from the fin, if the entire fin were at base temperature? Whereas in reality temperature of fin decreases with increasing distance away from the base, hence the actual heat transfer rate is less than the ideal heat transfer rate from the fin, resulting in the term fin efficiency? Thank you for your advice Regards, Oh Si Han From: Wang Chi-Hwa To: Wong Tzu Qun Subject: RE: fin surfaces Dear Tzu Qun: Thanks for your e-mail. (1) A( fin)h(T-Tinfinite) for fins include the convective heat transfer from the "exposed surface area of fin", including the tip. Only convection from the surface of fin is considered. (2) WWWR Equation 17-43 (5th Edition) considers shows the boundary condition case(a). The equation estimates the convective heat transfer from the "exposed surface area of fin", including the tip. (3) As conveyed in my lecture, the use of "q=-kA dT/dx" considers the total convective heat transfer from the surface as all the heat comes eventually from the base of fin by conduction. Sincerely yours, Chi-Hwa Wang CN2125 Co-instructor From: Wong Tzu Qun Subject: fin surfaces Dear Prof Wang, thank you for your prompt reply previously. Regarding chapter 2, fin surfaces, does the heat transfer formula A( fin)h(T-Tinfinite) for fins include the heat transferred from the base of the fin via conduction to the tip of fin and convection to surroundings by its surface area or does it account for convection by its surfaces to surroundings only?( assuming the primary surface was heated up, or has temperature differnence from the surroundings). what about equation 17-43? If it only accounts for convection soley, do we use q=-kA dT/dx to solve for the conduction part? thank you. regards. wong tzu qun From: Wang Chi-Hwa Subject: RE: Queries on General Solution for Straight Fin with 3 Different Boundary Conditions Dear Kah Pin: Thanks for your e-mail. (1) The 3 sets of boundary conditions are three standard sets for discussion. We derived the theoretical solutions corresponding to all of them for illustration. In general, solution for case (c) is used in all subsequent graphical display as shown in Figure 17.11. (2) Referring to my answer for part (1), the three cases are for different physical situations. (3) Ao refers to the exposed area of the primary surface. This is the area of primary surface excluding the base of the fin. Sincerely yours, Chi-Hwa Wang CN2125 Co-instructor From: Yeo Kah Pin Subject: Queries on General Solution for Straight Fin with 3 Different Boundary Conditions Greetings, Prof Wang I have the following questions regarding the above. 1) When do we use each of the 3 different sets of boundary conditions? 2) Why is there a need for 3 sets of BCs? 3) Does A0 refer to the exposed primary surface area OR the surface of the base of the fin? Thank you for your time and advice. Regards Stanley -----Original Message----From: Wang Chi-Hwa Subject: RE: Questions regarding the last example on the Fri lecture Dear Yung Chuan: Please refer to my summary at the beginning of the lecture today: For circular fins, "t" refers to the "half thickness" in the formula (rL-r0) sqrt(h/kt). For straight rectangular fins, "t" refers to the "full thickness" in the formula L sqrt(h/kt). Sincerely yours, Chi-Hwa Wang CN2125 Co-instructor -----Original Message----From: Chua Yung Chuan Subject: Questions regarding the last example on the Fri lecture Dear Prof, I have a question here. In the last example on your Fri lecture, or on pg 242 of WWWR 4th edition, you use the t as the thickness. However, I always think that thickness = 2t and for the formula of L sqrt(h/kt), the t is referring to half of the thickness. Am I right? Thank you. Yung Chuan From: Wang Chi-Hwa Subject: RE: questions regarding cn2125 Dear Xinling: Thanks for your e-mail. Primary surface refers to the original surface of the hot object. Any (circular or straight rectangular) fins are added on top of the primary surface and termed as "extended surfaces". Sincerely yours, Chi-Hwa Wang CN2125 Co-instructor From: Chen Xinling Subject: questions regarding cn2125 Dear Sir, I have some questions with regard to the cn2125 module. During the last lecture, you mentioned about the primary surface of fin. What do you mean by the primary surface? Thank you so much! =) Best Regards, Chen Xinling From: Wang Chi-Hwa Subject: RE: Regarding amendment of Fig 17.11 in WWWR Dear John: Thanks very much for your e-mail. Attached please find my response to your question. (1) If one is dimensional and the other is dimensionless, the system is dimensionally inconsistent. Please recall one example in CN2112 Fluid Mechanics. The Moody diagram shows you a relationship between Fanning Friction Factor (dimensionless) against Reynolds Number (dimensionless) under different sets of roughness factor (dimensionless). (2) I think you have made some minor mistake in the attached calculation. Please refer to my transparency for today on this subject. The term "(Ro/Ri)(h/kt)^(1/2)" has a unit "1/m". the term "(Ro - Ri)(h/kt)^(1/2)" is dimensionless. Sincerely yours, Chi-Hwa Wang CN2125 Co-instructor From: Soh Hui Qing John Subject: Regarding amendment of Fig 17.11 in WWWR Dear Sir during the lecture on Friday you said that we should change the abscissa of Fig 17.11 in the WWWR textbook from (Ro/Ri)(h/kt)^(1/2) to (Ro - Ri)(h/kt)^(1/2). According to your argument, the parameter (Ro/Ri)(h/kt)^(1/2) is not dimensionless while the ordinate of the graph, the efficiency, is a dimensionless quantity. And so if we have (Ro/Ri)(h/kt)^(1/2) as the xaxis, we will not get a dimensionless number and therefore the parameter for the x-axis is incorrect. I would like to raise 2 doubts pertaining to this argument: 1. Why is it necessary for both the y and x axes to be dimensionless at the same time? Can't we have one axis with units and the other without? 2. Even if we need both axis to be dimensionless, the original parameter in the text (Ro/Ri)(h/kt)^(1/2) is already dimensionless Ro/Ri is already dimensionless, h/kt is also dimensionless (h has units of W/m².K, k has units of W/m.K, t has units of m so kt will have the same units as h). Rather, the amended quantity (Ro - Ri)(h/kt)^(1/2) has a dimension of length, since h/kt is dimensionless. Hence, changing the parameter from (Ro/Ri)(h/kt)^(1/2) to (Ro - Ri)(h/kt)^(1/2) seems to contradict your argument of dimensions. Please enlighten me sir, thanks. Best regards John Soh from CN2125 class From: Wang Chi-Hwa Subject: RE: Today Lect Dear Devid: In this case, we are solving the temperature profile within the solid object. There is no convection within the solid. The contribution of convective heat transfer is inherently in the boundary condition: T=Ts. The large Biot number corresponds to high convective heat transfer. Under this condition, at any time, the surface temperature on solid is the same as the surrounding fluid Ts. Sincerely yours, Chi-Hwa Wang, CN2125 Co-instructor From: Devid Desfreed Kennedy Subject: Today Lect Hi Sir, I will like to ask regarding today lecture, For the part when the Bioret Number is very big and the temp of the object is both time and position dependent, How come in the equation derivation, there is no heat transfer by convection term, which was used for the previous case? Kindly advise on this. Thanks Cheers, Devid From: Wang Chi-Hwa Subject: RE: heat transfer coefficient affecting fin effectivness, fin heat transfer rate. Dear Leslie: Example 3 (WWWR Page 238-240) has both air and water sides in all cases considered. Our question is to determine the addition of the fin on which side will enhance the overall heat transfer rate more. It is not true on the higher "h" side as shown in the calculation result. Sincerely yours, Chi-Hwa Wang From: Yeo Qi Fu Leslie Subject: heat transfer coefficient affecting fin effectivness, fin heat transfer rate. Dear Prof Wang, Thank you for seeing me today. I have another question which I hope u can enlighten me on. I read that a small heat transfer coefficient, h is preferred to increase fin effectiveness. Also, like in the example we did on the fin between air and water, it is better to put the fin on the air (lower h value) to increase the rate of heat transfer. However, to my understanding, a greater value of h gives better transfer of heat via convection. So why is it that fins transfer heat better in presence of a medium with lower values of h? Thank you. Cheers, Leslie From: Wang Chi-Hwa Subject: RE: tutorial 2 question 1 Dear Jingning: Thanks for your e-mail. (1) The LHS "q" is also positive based on your drawing. (2) The difference could be due to the difference in the 4th Edition and 5th Edition books. 4th Edition. k =0.073(1+0.0054T). -> Tw = 307.1K. 5th Edition. Problem 17.4: k =0.0073(1+0.0054T). -> Tw ~ 300 K Sincerely yours, Chi-Hwa Wang CN2125 Co-instructor From: Bi Jinning Subject: tutorial 2 question 1 Dear Prof, I have a question about the provided solution for question 1 of tutorial2. In the solution line 2, LHS is negative but RHS definitely is positive as T<925 but T>300. I've circled the question part in the attachment. Also, I've tried to calculate the answer but it seems a bit different from the given one. My answer for Tr.w is 300.43 which is very close to the air temperature. Based on this temperature, the L value is quite different, which is 1.074m. I tried many times with the calculation but still cannot get the provided answer. I'm wondering if the answer given is wrong? Thanks for your time and advise!!! Jinning From: Wang Chi-Hwa Subject: RE: A small Q Dear Kennedy: Yes, you are right. heat diffusion Eq is a special case of energy Eq when there is no convection term. Referring to my week one slides: Slide 35. The Heat (Diffusion) Equation considers all physical terms for energy balance in a control volume except convective terms. Slide 45. The Differential Energy Equation considers all physical terms for energy balance in a control volume including convective terms. Sincerely yours, Chi-Hwa Wang CN2125 Co-instructor From: Devid Desfreed Kennedy Subject: A small Q Hi Prof, I am reading through my note, and wondering what is the difference between the heat diffusion Eq and the Energy Eq? Can I say that the heat diffusion Eq is a special case of energy Eq? Best Regards, Devid Kennedy

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