What do I need to trickle charge rechargable batteries with a solar panel
Under charge currents of &lt;&lt; C/1 a Nimh cell is fully charged at about 1.45V. Using 1.4V/cell gives you slight lee way at the loss of a small amount of capacity. Slightly lower again is even safer. 

If you don't mind wasting solar energy (and that should not be a problem here), feed the batteries through a diode (if there is not one in the panel already, and clamp the battery voltage at 5.6V (1.4V/cell). [ Or 5.4V at 1.35V/cell for good safety].
I assume battery temperatures are in the 20 -30C range usually - best voltage will vary somewhat with temperature but that should work well enough. 

That panel is perhaps 2 Watts  (you may have a spec there or can measure short circuit current in full sun). If so then Imax is about atts/Vmax_power = say 2W / 15V  =~~ 130 mA.   Actual could be 50 200 MA - neither extreme being too likely. 

100 - 200 mA is too much for a cheap TL431 clamp regulator by itself.
A TL431 driving a TO220 P Channel MOSFET (plus a few resistors) or an N Channel MOSFET plus any small PNP transistor will give you a clamp regulator suitable for the task.

TL431 divider string top resistor can be maybe 100k so drain on battery when there is no sun is around 50 uA = not a problem in this application. 



Or you could use a standard series regulator such as an LM317 plus 2 resistors set to 5.6V would work but backfeed via the regulator and resistors adds slight complexity.  

There are other ways but the TL431 + MOSFET clamp should work well enough.



TL431 "turns on" when gate voltage >= 2.5V.
Z1 on pulls Q1 gate low turns Q1 on which dissipates excess energy in Q1 + Rload.
Rload is optional if MOSFET can dissipate all energy OK - but usually using a resistor avoids needing a heatsink.
Rload = V/I &lt;= (Vbattery_max - V_FET_on) / I_panel_max
V_FET_ON is the voltage drop across the fully on MOSFET
= Rdson x I_panel_max.
With a MOSFET with Rdson = say 0.1 Ohm then on voltage at say 150 mA = 
= V = IR = 0.15 x 0.1 = 15 millivolts, so a half decent FET needs minimal allowance for on voltage.  

Say V_FET_on = 0.1V, Imax = 150 mA, Vbat max = 5.5V.
Rload = V/I = (5.5 - 0.1) / 0.150 = &lt;= 36 Ohms.
33 Ohms OK.
Lower OK but FET will then make up some of load and dissipation may be higher. 







simulate this circuit &ndash; Schematic created using CircuitLab

LM336 datasheet - All LM336 datasheets I found were poor (Faichild, TI, LT).NONE gave adj pin current.
If Vclamp is not correct R3 &amp; R2 may need to be lowered while maintaining 1.2:1 ratio.
eg 33k : 27K