Introduction

Today, the heat transfer enhancement in volume unites the transformation of heat transfer sections and the changes of boundary conditions are some of the important factors in different fields of heat transfer. In recent years [1,2,3,4,5,6,7,8,9,10,11,12,13], producing compact heating systems has become a basic and challenging purpose for obtaining higher efficiency in different industries. According to some previous studies, to increase the produced power in some power plants, or to some upgrading, there is an emergency need to increase the heat transfer capacity in existing systems [14,15,16,17,18,19,20]. One of the best solutions for this problem is using nanofluids instead of water in this cooling system. Among the effective methods, adding metallic and nonmetallic particles to the base fluid, called nanofluid, has become an innovative and impressive method for heat transfer enhancement. In fact, nanofluids are a new generation of fluids with higher potentiality and efficiency in the industrial applications. Recent studies have revealed that unlike the fluids, nanofluids have significant rate of heat transfer enhancement [21,22,23,24,25,26,27,28,29,30,31,32,33,34]; therefore, in novel equipment, the heat transfer issue has high importance among the researchers using this science. By combining some methods such as using nanofluids and microchannels with other methods, the researchers have improved the efficiency of heat transfer equipment. Behnampour et al. [35] numerically investigated the effect of using rectangular, triangular and trapezoidal ribs on behavior and laminar heat transfer of water/AgO nanofluid flow with nanoparticles volume fractions of 0–4% in a rectangular microchannel. His results demonstrated that the rectangular rib causes the most changes of velocity profile in the central line of flow and the triangular rib has the best rate of performance evaluation criterion. Akbari et al. [36] numerically studied the effect of rib height changes on flow and laminar heat transfer of water/Al2O3 nanofluid in a two-dimensional microchannel. He figures out that, by increasing rib height, Reynolds number and volume fraction of nanoparticles, the rate of heat transfer improves. In another research, the effect of rectangular rib on the behavior and laminar heat transfer of water/Al2O3 nanofluid flow in a three-dimensional rectangular microchannel has been studied by Akbari et al. [37]. His numerical results demonstrated that, by increasing Reynolds number, rib number and volume fraction of nanoparticles, the heat transfer on the heated surfaces improves. Karimipour et al. [38] simulated the effect of using rectangular rib on the forced heat transfer of water/Ag nanofluid in a rectangular microchannel under the constant thermal boundary condition. His numerical results indicated that, in higher Reynolds numbers, by increasing volume fraction of nanoparticles and rib number, Nusselt number enhances significantly. Gravandyan et al. [39], by using rectangular ribs with different pitches, studied the effective factors on flow structure and heat transfer of water/TiO2 in a two-dimensional microchannel. He figured out that sudden changes of fluid flow velocity in the microchannel have different effects on friction factor behavior, and by increasing Reynolds number, these effects become more considerable. Also, in the indented zones, the enhancement of AR ratio has a great effect on the depreciation of fluid momentum. Although numerous studies have been done in heat transfer field, due to the advantages of using nanofluids in different geometrics [40,41,42,43,44,45,46,47,48], investigating heat transfer mechanisms is continuous. In this paper, the effect of using rectangular, triangular, trapezoidal, oval and parabolic ribs has been simulated in a two-dimensional rectangular microchannel with constant heat flux boundary condition. In order to improve the heat transfer in the studied microchannel, oil/MWCNT has been used in different volume fractions. The effect of simultaneous use of nanofluid, minimized dimensions, the existence of rib with different forms, numerical simulation of flow parameters and the forced and laminar heat transfer with the mentioned properties have made the present research more advantageous. The results of present numerical simulation have been compared by different values of volume fraction of nanoparticles, Reynolds numbers and rib shapes.

Problem statement and geometrical dimensions

The present study has been simulated in a two-dimensional rectangular microchannel with the length of L = 7.5 mm and the height of d = 50 µm. The top wall with the length of L and the bottom wall with the length of K = 3.75 mm are insulated from the inlet area. The rest of the bottom wall of microchannel with the length of L–K = 3.75 mm is under the constant heat flux of q″ = 10,000 W m−2. The inlet temperature of cooling fluid is constant and T c = 298 K. Oil and the nanoparticles of MWCNT are in thermal equilibrium. This research has been done in Reynolds numbers of 1, 10, 50 and 100 and volume fractions of 0, 2 and 4% of solid nanoparticles and for the rectangular, oval, parabolic, triangular and trapezoidal rib shapes. In order to have better comparison for each rib shape described in this research, the height (H) and the length of rib (m) have been considered as constant. Figure 1 indicates the considered geometrics of the present research.

Fig. 1
figure 1

The schematic of the studied microchannel. a Elliptical, b rectangular, c trapezoidal, d triangular, e parabolic

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In Fig. 1, p is the pitch of rib, H is rib height, d is the height of microchannel, L is the length of microchannel, K is the inlet length of microchannel, m is the width of rib, and w is the outlet length of microchannel. In this research, the numerical simulation of heat transfer and nanofluid flow inside the mentioned microchannel has been done for the rectangular, trapezoidal and triangular rib shapes. In this study, in order to have better investigation and accurate comparison of the numerical results in different rib shapes, in all of the states, p, H, m and w have been considered constant and, respectively, equal with p = 300 µm, H = 20 µm, m = 100 µm and w = 2250 µm. The molecular diameter of oil fluid is d f = 2 Å, and the nanoparticles of carbon nanotubes are spherical and have uniform shape with the diameter of d p = 5 nm [49]. The properties of oil fluid, MWCNT nanoparticles [49] and nanofluid with different volume fractions are presented in Table 1.

Table 1 The thermophysical properties of the base fluid and solid nanoparticles
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Governing equations of the two-dimensional laminar flow

The governing equations of flow and the forced, two-dimensional, laminar, constant and single-phase heat transfer including consistency, momentum and energy equations are as follows [50]:

$$\frac{\partial u}{\partial x} + \frac{\partial x}{\partial y} + \frac{\partial w}{\partial z} = 0$$
(1)
$$u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} = - \frac{1}{{\rho_{\text{nf}} }}\frac{\partial p}{\partial x} + \nu_{\text{nf}} \left( {\frac{\partial }{\partial x}\left( {\frac{\partial u}{\partial x}} \right) + \frac{\partial }{\partial y}\left( {\frac{\partial u}{\partial y}} \right)} \right)$$
(2)
$$u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} = - \frac{1}{{\rho_{\text{nf}} }}\frac{\partial p}{\partial x} + \nu_{\text{nf}} \left( {\frac{\partial }{\partial x}\left( {\frac{\partial v}{\partial x}} \right) + \frac{\partial }{\partial y}\left( {\frac{\partial v}{\partial y}} \right)} \right)$$
(3)
$$u\frac{\partial T}{\partial x} + v\frac{\partial T}{\partial y} = \alpha_{\text{nf}} \left( {\frac{\partial }{\partial x}\left( {\frac{\partial T}{\partial x}} \right) + \frac{\partial }{\partial y}\left( {\frac{\partial T}{\partial y}} \right)} \right)$$
(4)

The equations related to the non-dimensioning of governing equations of laminar and forced nanofluid flow are described as follows [51]:

$$\begin{aligned} X = \frac{x}{H},\quad Y = \frac{y}{H},\quad U = \frac{u}{{u_{\text{c}} }},\quad V = \frac{v}{{u_{\text{c}} }},\quad P = \frac{{\bar{P}}}{{\rho_{\text{nf}} u_{\text{c}}^{2} }}, \hfill \\ \theta = \frac{{T - T_{\text{c}} }}{\Delta T},\quad Re = \frac{{u_{\text{c}} \times H}}{{\upsilon_{f} }},\quad Pr = \frac{{\upsilon_{\text{f}} }}{{\alpha_{\text{f}} }},\quad \Delta T = \frac{{q\prime \prime D_{\text{h}} }}{{k_{\text{f}} }} \hfill \\ \end{aligned}$$
(5)

By substituting the dimensionless Eq. (5) in Eqs. (1–4), the consistency, momentum and energy equations in the dimensionless state can be written as follows [52]:

$$\frac{\partial U}{\partial X} + \frac{\partial V}{\partial Y} = 0$$
(6)
$$U\frac{\partial U}{\partial X} + V\frac{\partial U}{\partial Y} = - \frac{\partial P}{\partial X} + \frac{{\mu_{\text{nf}} }}{{\rho_{\text{nf}} \nu_{\text{f}} }}\frac{1}{Re}\left( {\frac{{\partial^{2} U}}{{\partial X^{2} }} + \frac{{\partial^{2} U}}{{\partial Y^{2} }}} \right)$$
(7)
$$U\frac{\partial V}{\partial X} + V\frac{\partial V}{\partial X} = - \frac{\partial P}{\partial Y} + \frac{{\mu_{\text{nf}} }}{{\rho_{\text{nf}} \nu_{\text{f}} }}\frac{1}{Re}\left( {\frac{{\partial^{2} V}}{{\partial X^{2} }} + \frac{{\partial^{2} V}}{{\partial Y^{2} }}} \right)$$
(8)
$$U\frac{\partial \theta }{\partial X} + V\frac{\partial \theta }{\partial Y} = \frac{{\alpha_{\text{nf}} }}{{\alpha_{\text{f}} }}\frac{1}{RePr}\left( {\frac{{\partial^{2} \theta }}{{\partial X^{2} }} + \frac{{\partial^{2} \theta }}{{\partial Y^{2} }}} \right)$$
(9)

The dimensionless boundary conditions for the studied geometrics of the present paper are defined as follows:

$$U = 1,\quad V = 0\;\;{\text{and}}\;\;\theta = 0\quad {\text{for}}\;\;X = 0\;\;{\text{and}}\quad 0 \le Y \le 1$$
(10)
$$V = 0\;\;{\text{and}}\;\;\frac{\partial U}{\partial X} = 0\;\;{\text{for}}\;\;X = 150\;\;{\text{and}}\;\;0 \le Y \le 1$$
(11)
$$U = 0,\quad V = 0\;\;{\text{and}}\;\;\frac{\partial \theta }{\partial Y} = 0\;\;{\text{for}}\;\;Y = 1\;\;{\text{and}}\;\;0 \le X \le 150$$
(12)
$$U = 0,\quad V = 0\;\;{\text{and}}\;\;\frac{\partial \theta }{\partial Y} = 0\;\;{\text{or}}\;\;\frac{\partial \theta }{\partial Y} = - \frac{{k_{\text{f}} }}{{k_{\text{nf}} }}\;\;{\text{for}}\;\;Y = 0\;\;{\text{and}}\;\;0 \le X \le 150$$
(13)

The equations related to the computation of nanofluid properties and flow parameters

Following equations are used for calculating the density [53] and the specific heat capacity of nanofluid [54]:

$$\rho_{\text{nf}} = \left( {l - \varphi } \right)\rho_{\text{f}} + \varphi \rho_{\text{s}}$$
(14)
$$\left( {\rho C_{\text{p}} } \right)_{\text{nf}} = \left( {l - \varphi } \right)\left( {\rho C_{\text{p}} } \right)_{\text{f}} + \varphi \left( {\rho C_{\text{p}} } \right)_{\text{s}}$$
(15)

Chon equation [55] has been used for computing the thermal conductivity of nanofluid.

$$\begin{aligned} & \frac{{k_{\text{m}} }}{{k_{\text{f}} }} = 1 + 64.7\,\phi^{0.746} \,\left( {\frac{{d_{\text{f}} }}{{d_{\text{np}} }}} \right)^{0.369} \left( {\frac{{k_{\text{np}} }}{{k_{\text{f}} }}} \right)^{0.7476} \,Pr^{0.9955} \,Re^{1.2321} \\ & Re = \frac{{\rho_{\text{f}} k_{\text{b}} T}}{{3\pi \mu^{2} l_{\text{f}} }},\quad Pr = \frac{{\mu_{\text{f}} }}{{\rho_{\text{f}} \alpha_{\text{f}} }},\quad \mu = A \times 10^{{\frac{B}{T - C}}} ,\quad C = 140({\text{K}}), \\ & B = 247({\text{K}}),\quad A = 2.414 \times 10^{ - 5} \,({\text{Pa}} . {\text{s}}),\quad T = T_{\text{in}} \\ \end{aligned}$$
(16)

In the above equations, the indexes of ρ, k, φ and Cp are, respectively, the density, thermal conductivity coefficient, volume fraction of nanoparticle and the specific heat capacity and the subindexes of s, f and nf are, respectively, the solid nanoparticles, base fluid and nanofluid. For calculating the effective dynamic viscosity, Brinkman equation is used [56,57,58]:

$$\mu_{\text{nf}} = \frac{{\mu_{\text{f}} }}{{\left( {l - \varphi } \right)^{2.5} }}$$
(17)

For calculating the local Nusselt number along the microchannel walls, following equation is used [59]:

$$Nu(x) = \frac{h(x)\;.\;H}{{k_{\text{f}} }}$$
(18)

For calculating Fanning friction factor, following equation is used [60]:

$$C_{\text{f}} = \frac{{\tau_{\text{w}} }}{{\frac{1}{2} \times \rho \times u_{\text{in}}^{2} }}$$
(19)

The performance evaluation criterion [61] and the pressure drop [62, 63] between the inlet and outlet sections are calculated by following equations:

$${\text{PEC}} = \frac{{\left( {\frac{{Nu_{\text{ave}} }}{{Nu_{{{\text{ave}},\varphi = 0}} }}} \right)}}{{\left( {\frac{f}{{f_{\varphi = 0} }}} \right)^{{\left( {1/3} \right)}} }}$$
(20)
$$\Delta P = \bar{P}_{\text{out}} - \bar{P}_{\text{in}}$$
(21)

Numerical procedure and assumptions

In the present paper, the finite volume method [64,65,66,67,68,69,70,71,72,73] and the second-order discretization have been used for simulating the fluid flow and heat transfer [74, 75]. In order to couple the velocity–pressure equations in the numerical solving of this paper, SIMPLEC algorithm has been used [76, 77]. Also, for obtaining acceptable results, the maximum residual has been considered 10−6 [78,79,80]. The flow inside the microchannel is laminar, steady, Newtonian, single-phase and incompressible, and the no-slip boundary condition has been applied to the microchannel walls. In this simulation, the nanofluid is homogeneous and the radiation effects are negligible.

Independency from grid and validation

Table 2 indicates the demanded grid number for results independency from gridding. The selected grid number has been studied from 20,000 to 60,000 for the oil as the base fluid in Reynolds number of 50. In this investigation, the independency of flow and heat transfer parameters is intended. For the chosen grid number, the amounts of average Nusselt number and friction factor on the indented wall with rectangular ribs have been compared in different grid numbers. According to the changes of parameters in chosen grid number, it is observed that the grid number of 60,000, in comparison with less grid numbers, has more accurate results. In this research, this grid number has been used as an acceptable grid number in the simulation of numerical solving domain of heat transfer and flow.

Table 2 The study of grid independency for state of Re = 50 and φ = 0.0% of nanoparticles
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Figure 2 indicates the validation of the present paper with the research of Behnampour et al. [35]. Behnampour et al. [35] numerically investigated the laminar flow of water/Ag nanofluid in a rectangular microchannel with nanoparticles volume fractions of 0–4% by using finite volume method and SIMPLEC algorithm. In Fig. 2, the numerical results of calculated average Nusselt number on the heated wall of microchannel with rectangular ribs in Reynolds number range of 1–100 have been compared with each other. According to the coincidence of results with the numerical study of Behnampour et al. [35], the numerical solving procedure and its simulation are accurate.

Fig. 2
figure 2

The validation of present numerical investigation with the study of Behnampour et al. [35]

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Results and discussion

Figures 3 and 4 demonstrate the changes of local Nusselt number along the indented wall (hot wall) in different rib shapes and for the base fluid and nanofluid with volume fraction of 4%, respectively. Also, these figures indicate the investigation of local Nusselt number in Reynolds numbers of 1–100. Placing different rib shapes along the microchannel and on the direction of fluid motion causes sudden changes of average Nusselt number graphs, and by increasing fluid velocity, the amount of these changes enhances. By colliding the fluid with ribs, due to the deviation of fluid direction, significant changes have been created in velocity parameters, influencing the amounts of heat transfer coefficient and Nusselt number. In all of the local Nusselt number graphs, it can be observed that the maximum rate of sudden jumps in Nusselt number behavior has been seen along the primary ribs and gradually; by decreasing fluid momentum, due to the collusion of fluid with other ribs, these sudden changes are reduced. Also, the shape of ribs causes significant changes in local Nusselt number graphs; therefore, the existence of rib with sharp angles causes the most sudden changes in these figures. The existence of rib with curved surfaces causes better contact of flow with surface. According to Figs. 3 and 4, the enhancement of volume fraction and Reynolds number causes the improvement in Nusselt number. Hence, comparing to Figs. 3 and 4, it has higher level.

Fig. 3
figure 3

The local Nusselt number figures along the indented surface for the base fluid

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Fig. 4
figure 4

The local Nusselt number figures along the indented surface for nanofluid with volume fraction of 4% of nanoparticles

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The changes of pressure drop along the central line of flow in Reynolds numbers of 10 and 100, and different rib shapes and volume fractions of 0, 2 and 4% of nanoparticles are demonstrated in Figs. 5 and 6, respectively. By moving the fluid among the ribs, the amount of fluid mixture improves. On the other hand, due to the encounter and contact of fluid with surface, fluid momentum decreases and this behavior causes the enhancement of pressure drop. When fluid velocity is higher, due to the augmentation of velocity changes and higher depreciation of fluid, the momentum drop increases. Also, the existence of ribs with different forms influences the hydrodynamical behavior of cooling fluid flow. The impressionability of pressure changes caused by rib shape in Reynolds number of 10, comparing to Reynolds number of 100, is less. The main reason of this manner is because of slower motion of fluid and less changes of fluid velocity because of colliding with obstacles. Also, the enhancement of volume fraction of nanoparticle causes the augmentation of density and fluid viscosity which entails more energy drop of fluid.

Fig. 5
figure 5

The changes of pressure drop figures along the central line of flow for Reynolds number of 10

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Fig. 6
figure 6

The changes of pressure drop figures along the central line of flow for Reynolds number of 100

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Figures 7 and 8 explain the behavior of local dimensionless temperature along the central line of flow in different volume fractions of nanoparticles and rib shapes in Reynolds numbers of 1 and 50, respectively. Using ribs on hot surfaces and the collusion of fluid with ribs cause more changes in the dimensionless temperature profile at the central line of flow. In Reynolds number of 10, due to slower motion of fluid and sufficient time for heat transferring from the hot surface with the cooling fluid, the pattern of dimensionless temperature figure is somehow related to the rib shape. The increase in fluid velocity causes significant reduction in dimensionless temperature and this behavior decreases the growth of thermal boundary layer. This behavior indicates the reduction in hot surfaces impression on the central line of flow. The enhancement of volume fraction of nanoparticles and Reynolds number entails the dominancy of inlet fluid temperature (better cooling) on the internal areas of microchannel.

Fig. 7
figure 7

The changes of dimensionless temperature figures along the central line of flow for Reynolds number of 1

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Fig. 8
figure 8

The changes of dimensionless temperature figures along the central line of flow for Reynolds number of 50

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Figure 9 indicates the amounts of average Nusselt number at the range of Reynolds numbers of 1–100 in volume fractions of 0, 2 and 4% of nanoparticles and different rib shapes. In the average Nusselt number figures, it can be observed that the enhancement of volume fraction of nanoparticles in the base fluid causes the improvement in conductive heat transfer coefficient and the increase in Nusselt number. This behavior is completely obvious in Reynolds numbers of 50 and 100, comparing to Reynolds numbers of 1 and 10. The increase in fluid velocity, rib shapes and geometrics causes the enhancement of convection heat transfer coefficient and Nusselt number. In Reynolds numbers of 50 and 100, the rib shape causes significant changes in heat transfer enhancement, and in Reynolds numbers of 1 and 100, there is less changes. According to the studied rib shapes, for the mathematical numbers of 1 and 10, the maximum amount of heat transfer is related to the trapezoidal rib shape. In Reynolds numbers of 50 and 100, the sharp angles of rib cause heat transfer enhancement; therefore, in the investigated states, the rectangular rib shape has the maximum value of heat transfer. In all Reynolds numbers, the minimum amount of heat transfer is related to the parabolic rib shape. This behavior is because of the penetration of velocity gradients on the direction of fluid motion in this rib shape. Each shape of rib which can influence the disordering of thermal boundary layer has the maximum amount of Nusselt number. In Reynolds numbers of 50 and 100, after the rectangular rib, the oval, trapezoidal, triangular and parabolic rib shapes have the maximum and minimum amounts of Nusselt number, respectively.

Fig. 9
figure 9

The average Nusselt number figures in different rib shapes and Reynolds numbers

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Figure 10 demonstrates the amounts of average friction factor in different Reynolds numbers, volume fractions and rib shapes. Because of the fluid motion among the ribs, fluid momentum becomes deprecated. Also, by adding higher amounts of volume fractions of nanoparticles to the base fluid, due to the viscosity and higher density of cooling fluid and the contact of surface and fluid, more friction factor has been created on the internal surfaces of microchannel. On the other hand, the fluid motion on the indented surfaces causes the contact of cooling fluid with microchannel walls, and in lower Reynolds numbers, due to the slow velocity of fluid, the fluid contacts with surfaces completely. This behavior causes the fiction coefficient figures to have higher levels in Reynolds numbers of 1, comparing to other Reynolds numbers. On the other hand, by increasing Reynolds number, due to the enhancement of fluid momentum, the contact of fluid with microchannel walls does not completely happen; therefore, by increasing Reynolds number, the level of friction factor graphs reduces. Among the investigated rib shapes, the rectangular rib shape, due to the creation of the most velocity gradients on the direction of cooling fluid, has the maximum value of friction factor. By generally observing the behavior of friction factor, it can be said that the increase in rib length and the existence of sharp angles of ribs have great influence on velocity domain; therefore, this behavior causes the increase in friction factor. In all of the studied Reynolds numbers, the rectangular, trapezoidal, oval, parabolic and triangular rib shapes have the maximum and minimum amounts of average friction factor, respectively. In the parabolic rib shape, comparing to the oval form, by increasing fluid velocity in Reynolds number of 100, the amount of average friction factor becomes more significant.

Fig. 10
figure 10

The changes of average friction factor figures in different rib shapes, Reynolds numbers and volume fractions

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Figure 11 shows the performance evaluation criterion for different rib shapes and volume fractions of nanoparticles and Reynolds numbers of 1, 10, 50 and 100. The performance evaluation criterion is a quantitative comparison between Nusselt number and friction factor in the indented microchannel in each volume fraction, comparing to the pure oil as the base fluid. In all of the studied Reynolds numbers, the enhancement of fluid velocity causes significant augmentation of performance evaluation criterion. The reason of this behavior is the influence of Nusselt number and heat transfer enhancement, comparing to the friction factor enhancement, because of adding volume fraction of nanoparticles. In all of the figures, the increase in volume fraction of nanoparticles has a great effect on the enhancement of performance evaluation criterion and the figures with higher volume fractions have higher levels. Among different studied rib shapes, in Reynolds number range of 1–100, the best conformity between Nusselt number enhancements and the friction factor happens in the parabolic, triangular, trapezoidal, oval and rectangular rib shapes, respectively. Although the existence of sharp angles of the rectangular rib shape entails Nusselt number enhancement, these angles cause significant augmentation of velocity gradients in the cooling fluid and therefore cause the increase in friction factor.

Fig. 11
figure 11

The performance evaluation criterion in different rib shapes and Reynolds numbers

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Figure 12 explains the amounts of average pressure drop in the central line of flow for each different rib shape in Reynolds number range of 1–100. These figures investigate different Reynolds numbers and volume fractions of nanoparticles, separately. The enhancement of volume fraction of nanoparticles and fluid velocity causes the increase in viscosity–density and the momentum of cooling fluid, respectively. The existence of ribs on the direction of fluid motion causes momentum damping and the reduction in kinetic energy of fluid. On the other hand, each shape of ribs which can create more velocity gradients has higher pressure drop on the direction of fluid motion and in all Reynolds numbers, and the maximum amount of pressure drop is related to the graphs with higher level of volume fraction. The behavior of pressure drop changes is similar to the behavior of average friction factor. In all of the investigated Reynolds numbers, the rectangular, trapezoidal, oval, parabolic and triangular rib shapes have the maximum and minimum amounts of average friction factor, respectively. Also, by increasing Reynolds number, the behavior of oval rib improves and its amount reduces.

Fig. 12
figure 12

The average pressure drop figures in different rib shapes and Reynolds numbers

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Conclusions

In this research, the effect of using rectangular, oval, parabolic, triangular and trapezoidal rib shapes on the manner of laminar heat transfer of oil/MWCNT nanofluid in a two-dimensional rectangular microchannel with the length of L = 7.5 mm and the hydrodynamical diameter of H = 50 µm has been numerically investigated. The results of this research have been compared with each other in Reynolds numbers of 1, 10, 50 and 100 and different volume fractions of solid nanoparticles. The increase in volume fraction of nanoparticles and Reynolds number entails the dominancy of inlet fluid temperature (better cooling) on all of the internal areas of microchannel. The augmentation of solid nanoparticles, due to the collusion of particles with ribs, causes the enhancement of density and fluid viscosity and more energy drop of fluid. By colliding the fluid with ribs, due to the deviation of fluid direction, significant changes have been created in velocity parameters, influencing the amounts of heat transfer coefficient and Nusselt number. In the investigated states, the rectangular and parabolic ribs have the maximum and minimum amounts of average Nusselt number, respectively. Also, the rectangular, trapezoidal, oval, parabolic and triangular ribs have the maximum and minimum amounts of average friction factor, respectively. Among different studied rib shapes, in Reynolds numbers of 10, 50 and 100, the best conformity of Nusselt number enhancements and friction factor has been obtained in the parabolic, rectangular, trapezoidal, oval and rectangular rib shapes, respectively. In general, according to the importance of heat transfer enhancement methods, it is expected that the results of this research, as well as other researches in this field, be applicable and useful in today’s industries such as in electronics, power stations, aerospace and automobile manufacturing.