S Karthik; International Journal of Advance Research, Ideas and Innovations in Technology © 2018, www.IJARIIT.com All Rights Reserved Page | 462 ISSN: 2454-132X Impact factor: 4.295 (Volume 4, Issue 5) Available online at: www.ijariit.com Design improvements in heat exchanger using partial differential equations Karthik S karthik0398@yahoo.com SRM Institute of Science and Technology, Chennai, Tamil Nadu ABSTRACT In today’s world, where the loss of energy due to engineering applications is increasing at an alarming rate, therefore efficiency is much needed in order to save the energy. The aim of the paper is to propose a new design of heat exchanger which would result in a substantial increase in the efficiency of the heat exchanger. The basic principle used to increase the efficiency is to change the shape of the tube holding fluid. In this paper, instead of using conventional cylindrical tubes for heating fluid, a cone-shaped tube with cold fluid entering the pipe through the base end and hot fluid coming out of the vertex end is used. This is achieved by tweaking the surface area to volume (SAV) ratio of the fluid carrying tubes. Since the Gaussian curvature through the axis of the tubes is zero, it’s a Euclidean surface. Thus there wil l be no change in properties if the conical tube is bent in the form of a helix. For a given volume, the object with minimum SAV ratio is a sphere as a consequence of isoperimetric inequality in 3 dimensions. Efficiency can be further increased by bending the shape of the tubes in form of a spherical helix. This would create a central heat source and constant temperature at the contact surface. Therefore there is a gradual decrease in volume as we go from base to the vertex of the conical tube would mean that pressure of hot fluid would increase as temperature and degree of freedom is constant. Keywords— Heat exchanger efficiency, Energy conservation, Mathematical modeling, Surface area to Volume ratio 1. INTRODUCTION This project aims to increase the efficiency of heater tubes of the heat exchanger. This is achieved by altering the shape of the tubes carrying cold fluid without changing the Gaussian curvature of the central axis. This is essential makes the heat exchanger tube a Euclidean surface and thus properties of the tube are maintained. 1.1 Surface area to volume ratio For a heat exchanger, a high surface area to volume ratio would be favorable as more area for a particular volume of fluid would be available for heat exchange ie fluid would convert into the hot fluid at a faster rate if SAV ratio is high. On the contrary, a low SAV ratio would mean less area is available for a particular volume of fluid for heat exchange which would result in a slower rate of heat loss. Considering all these factors, we are proposing a design which has a conical fluid tube shaped in the form of a spherical helix. 1.2 Cone vs. cylinder Let us consider a right circular conical pipe of saying height ‘h’ and a right circular conical pipe of lateral length ‘l’. Here l = h Volume of cylinder = pi*(r^2)*h Volume of cone = [pi*(r^2)*h]/3 Surface area of cylinder = 2*pi*r*h Surface area of cone = 2*pi*r*l For cones where h>>r; h = l (approximately) Surface area of cone = 2*pi*r*h Surface to Volume Ratio = SA/V For cylinder, SAV = 2/r For cone, SAV = 6/r