Saturday, September 09, 2006

Adventures in Houston

Last week, four of us (Archana, Satish, Suman and Self) decided to drive down to Houston (in my Eagle Talon) and see the Munnabhai Movie. We had read lots of happy reviews about the same online, and decided to see what the fuss was all about.

So, we found ourselves speeding towards Houston - when a slightly disconcerting feeling made itself prominent. The engine was "vibrating" (at frequencies lower than the expected piston frequency). We started to smell something burning too. So, we stopped on the shoulder and tried to investigate. Realizing it was too risky, we pulled into a by-road in Navasota and checked the smell. By this time the car has ceased jerking. Dismissing all this as a figment of our imaginations, we set out on our way to Houston all again.

And in that steep fly-over near Hempstead, we realized that our car was not going to make it to the top. The engine was overhearting - the temperature reading showed "H" almost consistently. The A/C was breathing out hot air even if the setting was the coldest. We realized that the car was out of coolant. And emergency stop was effected on the shoulder near the maxima on the flyover. After a call to an uncle, we managed to get some coolant into the radiator (after wrestling with one of those radiator caps with "Do not open" explicity written on top).

After a few agonizing moments on top of the fly-over, (including one in which a surprised Satish woke up and found the car "stranded" on top of the bridge), the car cooled down enough to make it to a yonder gas station. Coolant and water was procured - and was poured into the car. We reckoned we'd solved the mystery of the car. We felt happy about ourselves - just like Sherlock Holmes would have after sovling the Baskerville mystery, say. Back on the way to Houston we were.

And guess what! We were taking an exit onto Houston - and the car stops bang in the middle of the road. After a few agonizing minutes (with the blinkers on), we somehow manage to push the car onto the shoulder. We fed it more coolant - and somehow pushed the car to the theater. An offer to help from a considerate Sardarji is graciously refused (more due to it being unpragmatic than anything else - I mean .. where would he park his car?) in doing so.

The car was parked in the theater. The journey to the theater was quite trying. Seeing the needle to to 'H' is quite agonizing. I got the feeling that the car was going to explode on me any moment.

A stroke of good luck was that Harsha (whom I had called to meet us at the theater) decided to pop up for the movie anyway. I met him in the theater. A reunion was effected; the movie was enjoyed, one's prejudices against Sanjay Dutt notwithstanding. After all, absurdity conquers all. I felt that references of Gandhi were particularly pertinent - and the movie packed an elegant punch.

After the movie, it was time to get the automobile reparied. Archana and Harsha (in his spanking new Honda civic) were despached to scout around for auto-repair shops. Looking at Harsha's brand new car, one could but not help thinking that he and I were in the same batch at IIT - look at his car - and then look at mine. After some such cynical humor, we finally got word that an Autozone armed with mechanics existed in yonder Bellaire. The car chugged its way to Bellaire only to find a stuffed-to-the brim autozone which did not even have distilled water, leave alone mechanics. We bought a "sealant", which was used in the car. It did not work.

We made our way to 'Masala Wok', a chinese flavoured Indian restauraunt. This is where I had another stroke of good luck - Suman and Satish called over Vijay, one of our friends back at A&M. He too popped over, and Harsha and Vijay hat another sentimental reunion. We then realized that the best place to park the car was Vijay's. So, we made our way there (stopping once or twice to cool the engine).

Harsha and I and Archana went to her place. Rather than go to Harsha's place, we decided to sleep at Archana's. We slept there, and I was woken up by Harsha who said "How can you sleep in this light?" at 7:30. After some finger-brushing we had a breakfast (and more importantly, coffee) at IHOP. And then we bid good-bye to Harsha. Archana and I went to Vijay's on her Corolla (which had a fit radiator). We spied a firestone beside Vijay's apartment. I took the car to firestone. I must confess that I was quite disappointed to learn that the shop was a Firestone, since their tendencies to charge the earth are quite well known. But as a beggar, I had no choice. I just had to part with all the money that they would ask me to part with.

They told us they'd take a little while to get the car up and runnning. They told me it'd be $400. My wallet won't need to diet anymore, I suppose. We still had a couple of hours to kill, so we deicided to go to IKEA. While at Archana's place, I had slept on a divinely comfortable futon. So, I contemplated getting myself one if possible. Suman concurred. We walked all around Ikea, got the futon (and lots of other useless stuff). We managed to stuff it into Archana's car (by stuffing self and Satish in the back seat).

Of course, one must make a passing mention of the divine commestibles served up by the Scandinavian chefs down at IKEA. The vegetarian Lasagna was a slice of heaven, as was the cheese cake. The rationale behind having such an excellent food court bang in the middle of IKEA eluded us. Perhaps, we reckoned, Scandinavians cook well in general.

Finally we went home, to Vijay's house and got the car. After a tearful adieu to the $400, a rather comparitively eventless trip home was effected. A thoroughly filling dinner was had at the Aunt's place, and home was gone to after a real long time.

Wednesday, August 23, 2006


Converting from TA to the more "prestigious" position of an RA is, in reality, no reason to celebrate. As a matter of fact, it is a reason for dismay. It shall be elaborated in the following text.

The people who decide the payscale of graduate students are not professors on a noble mission to spread education to the world. They are engineers with a simple mission: to screw graduate students off as much cash as they possibly can without it fitting the definition of slavery. For slavery is illegal in this nation.

I was a Teaching Assistant till now. The department took care of all my tuition and fee. The tuition is a significant amount: and the univeristy mandates its payment by professors/departments for graduate students. So, the tuition has to be paid inevitably. The fee is less significant: rougly equal to one month's salary. It is "optional" for both the professor or the department to pay this. It was paid last year for me: they were trying to "attract" new students.

So, essentially, the university pays the same amount every month to me (preserving my pay scale). But I have to pay the fee too! And so, the upshot is that I am being screwed off $254 every month. That's a good 20% of my pay. (And my guide notionally thinks that he is preserving my pay-scale).

But I think I should shut up and not complain about this. The conditions of graduate students (assistants) were uttlerly wretched a few years ago. I have heard horror stories of students living 9 in an apartment! I have heard PhD students living with $600 a month. Conditions reminding one of those Chawls in Mumbai.

I'm living more respectably, for sure. I have a bedroom and a bathroom (more or less) of my own. I have a nice car. I have a steady job and an exciting guide. A nice sum in the bank too. No moral authority to complain, actually. And I'm here to work, not to complain about these things.

Thursday, July 27, 2006

Reversing the Heat Equation

Today's class on Partial differential equations gave me a whole new perspective on the ubiquitous heat equation (whose forms in various coordinate systems, I "solved" numerically for my Masters thesis). I'm going to share that perspective here.

Let's start with something simple and 1d. A rod (with temperature independent conductivity), perhaps. You're given a rod with a non-steady state temperature profile. One end of the rod has been maintained at a constant high temperature for 20 minutes - and you are handed over the rod after the 20 minutes. The entire rod is convecting (and has always been) with the ambient (with a constant heat transfer coefficient). Eventually, it would have reached a steady state - but that would have taken more than 20 mintues. So, essentially, you're given a rod whose temperatur distribution still being governed by the heat equation rather than the Laplace equation. In other words, the profile is still evolving.

Is it possible to predict the initial temperature profile, given an instantaneous temperature profile as detailed above?

The answer, well, is yes and no.

Yes, because, if a solution does exist, it is unique - fact that can be proven by some math [1]. So, essentially, for a given final temperature profile T_f(x), the ambient temperature (T_inf), the boundary conditions (T_o and T_(x=L)) . Starting with the T_f(x) and going back in time (by solving the reverse heat equation), one can, in principle, recover the initial temperature profile.

No, because, well, it diverges. A primitive variable seperable closed-form expression for the solution makes things quite clear.

where, the a's are the Fourier coefficients of T_f(x). In the case of the forward heat equation, the exponent would have been negative, rendering the higher harmonics more or less neglegible But, in the reverse case, this term would tend to blow up at higher values of n. If T_f(x) were purely sinusoidal (only one a_n), then the equation would be quite friendly. The equation poses no problem for a small number of harmonics.

But suppose there were a "little" noise. Noise usually has many frequencies, some quite high. The corresponding terms would blow up. Evaluating the above series is not going to be easy.

This gives us another elegant insight: the "sharper" a profile (a profile with a discontinuity, for instance would yield infinite terms in the fourier space), the more difficult it is to reconstruct the original temperature profile. This figures: the larger the local temperature gradient, the faster it tends to smooth itself out! Minor spatial fluctuations in temperature are removed faster by the diffusion equation.

Let us now consider a 5 cm x 5cm x 5cm copper block. (Copper because it's always at more or less the same temperature at ambient heat transfer coefficients). Suppose we heat it up to a temperature and cool it in air, and measure its temperature by a thermocouple with an accuracy of 0.1C. Suppose we measure time with a digital watch with an accuracy of 1 sec. Suppose, also, that we know the heat transfer coefficients accurately. Given the time since the start of convective cooling (measured by the stop-watch, actually) and the final temperature , can the initial temperature be determined?

Yes, you would say. Exponenital cooling curve. Easy to fit it.

Suppose we look at a situation where the instruments would say that a steady state has been reached. There's no way to get back the original temperature --- there's many possible solutions!!!!!!! The only way out is it use more accurate devices.

And now, add to this the complexity of temperature profiles. Suppose we were using steel piece (lower conductivity) , and somehow "magically" obtained its temperautre profile at a certain time throughout its volume. Suppose the profile was somewhat jagged (but steadying out gradually) ......... Well, with a lot of computers one can arrivie at an estimate ... with an error bar.

And this wisdom can be applied to the Navier stokes too. The only process in the entire N/S equations that "loses" information is, actually, viscous dissipation. Turbulence generates entropy faster by wrinkling the instantaneous temperature and velocity profiles to bring about high amounts of heat transfer and viscous dissipation respectively.

Maybe I'm getting way too carried away here.....

Monday, July 03, 2006

An Encounter with V.D

They're dealing with foully high Reynolds Numbers in my lab: to the tune of 400,000. You read right. 400,000. And they're not using water; they're using air. Needless to say, a plethora of compressors are being used to produce such high flow rates. Mach Numbers, incidentally are still incompressible.

Just to put things in perspective, I'll tell you that I'm working on Gas Turbine cooling. And also that gas turbine blades are cooled by air bled from the compressor. The blades are essentially porous. "Cool" air passes through them and stops them from melting. This gives designers latitude to allow higher temperatures in the turbine; letting the same do its bit in dealing with the imminent energy crisis. The flow within the blade can be likened to that through a channel ( thanks to similitude, a subject beaten to death in undergraduate fluid mechanics courses). The higher the heat transfer, the better. It is found that a ribbed channel would sustain higher turbulence, thereby increasing the heat transfer.

So, we're studying a ribbed channel for enhancement in heat transfer. The experiment essentially uses copper plates (infinite thermal conductivity for all practical purposes) to provide "regionally averaged" heat transfer data. Lots of copper plates (seperated by insulating gaskets) make the channel. These plates have thermocouples stuck on them everywhere.

It really perplexed me to learn that they were conducting an "adiabatic" test for this experiment. And adiabatic test is the following: air from the ambient is sucked in through the compressor; made to flow through the channel. No heat of any sort is supplied to the channel in this test. Temperatures are read by the thermocouple. The readings from this test are then subtracted from the actual heat transfer case.

I looked online for precedents. I looked at old work. I asked friends. I finally realized that this test was to account for the viscous dissipation. So, I set out to quantify the same using the data that I had. I looked at temperature differences in the channel; I found that the last plate was heated up by roughly 0.9 C in a smooth channel due to viscous dissipation and by 1.5C for a ribbed channel. This figures, as ribs would certainly create more entropy.

And I presented this to my guide. He nodded, and said that aerodynamic heating was not expected to be significant in my case. When you know everything in the subject, nothing probably excites you anymore.

Incidentally, one aspires to reach such a situation. And reaching such a situation entails a lot of excitement on the way.

Friday, June 09, 2006

New Apartment

It's June right now. And I'm apartment hunting. Or I was apartment hunting until today. I saw one today. An "efficiency". And I think I will take it.

It will cost a little more than what I am paying now. And that will be exacerbated by the fact that my pay, in all probablility will actually decrease! My guide will have to support me as a Research Assistant: which means that he will pay me. The money that he shall provide me will probably be lesser than what I am earning now. Some sort of existence will have to be eked out; wireless connections will have to be be stolen; meals will have to be sacrificed. Even more so, if I want to live in my own place!

I've been looking at places all around the city. I still found the one I saw today the best. I guess I will proceed to take that up. The location is very nice - almost where I am right now. Walking distance to the university. Safe too, I suppose. And I think the parking is under a tree or something. Will keep cool in winter.

I really want to get out of the place that I am "living" in right now. The room mate crashes downstairs (and never cleans the kitchen), the bed is crawling with bed-bugs, the air conditioner does not work in my room.

Life is quite good here, despite all that. I am playing tennis regularly. I am gradually getting used to driving the car everywhere. Good for me, I guess.

Oh well. There's no more points to be made right now. Had some rajma for dinner. Lumpy, unlike mom's. Maybe next time I could grind the onions and tomatoes.

Thursday, June 08, 2006

Post Trip, Post Car Update: All the scraping

Yup. I've got a car now. An Eagle Talon (what's that?) thingy made in 1995.

And it's june here. Summer is over in India, and has just started here! Bloody maximum temperatures are refusing to see the happier side of 30C, and today is around, well, 38C.

A trip to Purdoo was effected recently, a jolly good time was had by all entities in question, viz. Self and Radha. The car was taken posession of after the aforementioned trip.

Working in a distant lab right now. A place called turbo-lab. Though, technically, I am a PhD student, my current job is to, well, scrape dried up glue from a copper piece. Is this what they meant by the romance of research? Or is there something else that I shall discover in time? Is it okay if I send by brain on vacation?

I'm hunting around for an apartment to stay alone in next semester. Staying alone is bound to be an improvement in standard of living.

Now that I am mobile, I have the opportunity to go anywhere I want. And now that I am mobile, I have lost the will to go anywhere! I have been to the movies only once with my car until now. There's this movie called "Cars" coming tomorrow. Perhaps that should be seen soon.

Oh well. The coffee has brewed. Let me drink that and get back to the scraping in the lab. After the scraping, life promises to get more interesting. I've heard talk of some "sticking". I am SO excited.

Friday, May 19, 2006


Driving in the US of A is a pleasure, especially if you have driven in India. You don't feel scared your car is going to "die" at traffic signals (thanks to the automatic transmissions), your left leg is free (should you want to dance about). There's two meters of space between two consecutive cars. And you can coast at speeds known only to truckers and airplanes in India.

It is a piece of cake a drive here. Everyone obeys rules here: Indicators are followed like the holy bible is followed here; speed limits are respected. Miles are covered faster than kilometers are covered in India. Roads are wide, to say the least.

So, it is extremely ironic that I managed to fail my driving test here. Apparently, I merged into traffic too hastily, and should have allowed a car some 200 meters away to pass before me. The examiner (for that is what she is) said "That car was coming way too fast for you to turn. Come back next time". She must be paid by the volume of people whom she "examines", not by the hour.

I will have to disturb a friend early morning next week again. Woe is him, not just me.